Processing device, system, method, and program

Abstract

Provided are a processing device, a system, a method, and a program capable of improving the accuracy of decomposition by correcting at least a portion of a substrate distribution map by performing non-negative matrix factorization on a measurement distribution map of X-ray powder diffraction. A processing device (400) for performing non-negative matrix factorization on a measurement distribution diagram of X-ray powder diffraction is provided with: a measurement distribution diagram acquisition unit (410) for acquiring a plurality of measurement distribution diagrams; a decomposition unit (420) that performs non-negative matrix factorization on the measurement distribution diagram and calculates a base distribution diagram; an index calculation unit (430) that acquires the base distribution map and calculates an index based on the unevenness of the base distribution map; a basis distribution diagram classification unit (440) that classifies the basis distribution diagrams into a plurality of groups on the basis of the indicators; and a basis distribution map correction unit (450) that performs correction on at least one of the plurality of groups on the basis of the index and calculates a corrected basis distribution map.

Description

TECHNICAL FIELD

[0001] The present application relates to a processing device, a system, a method, and a program. BACKGROUND

[0002] X-ray powder diffraction is used in various fields. By analyzing a profile of an X-ray powder diffraction measurement, for example, it is possible to perform identification (qualitative analysis) of a constituent component of a powder sample, and quantification. In the past, a crystal phase was identified by comparing a measurement profile or a peak position-integral intensity list (d-value-intensity list; d-I list) created from the measurement profile with a known substance diffraction pattern.

[0003] Patent Literature 1 discloses a crystal phase identification method that is a crystal phase identification method of identifying a crystal phase contained in a sample from a powder diffraction pattern of the sample using a database, and includes: a whole pattern fitting step of performing whole pattern fitting on a first diffraction pattern that is a powder diffraction pattern of the sample using crystal phase information contained in the sample to calculate a theoretical diffraction pattern of the already identified crystal phase; a residual information generation step of generating residual information of the sample based on a difference between the theoretical diffraction pattern and the first diffraction pattern; and a residual information search matching step of selecting a new crystal phase contained in the sample by comparing the residual information with the database.

[0004] Patent Literature 2 discloses a spectral data analysis device that is a spectral data analysis device that calculates a plurality of basis spectrum data and activation data indicating the magnitude of each basis spectrum by performing non-negative matrix factorization on a set of observed spectral data calculated from a signal of an analysis target, and calculates the plurality of basis spectrum data and the activation data by searching for a minimum value of a target function that includes a degree of divergence between the set of observed spectral data and a set of estimated spectral data calculated from the plurality of basis spectrum data and the activation data, and a regularization term that evaluates linear independence of the plurality of basis spectrum data or the activation data.

[0005] Prior art documents

[0006] Patent documents

[0007] Patent Literature 1: Japanese Patent Application Publication No. 2014-178203

[0008] Patent Literature 2: Japanese Patent Application Publication No. 2019-87042 SUMMARY

[0009] In the case where the kinds of the mixture are various or the measured profile includes a profile of an amorphous substance, the number of peaks of each profile is increased. However, in such a case, if the measured profile is processed and the method of searching for matching using a d-value-intensity list described in Patent Document 1 is applied as in the past, the accuracy of qualitative analysis is deteriorated.

[0010] In addition, the technique described in Patent Document 2 is to improve the accuracy of decomposition by assuming that the profiles are highly independent of each other. However, the profile of an amorphous substance is different from the profile of a crystalline substance, and is often a wide profile having no sharp peak. Therefore, in the case where a part of the profiles is wide, such as the case where the measured profile includes a profile of an amorphous substance, if the regularization with respect to linear independence is applied to search for a combination having high linear independence, the accuracy of decomposition is likely to be deteriorated, and the accuracy of the subsequent qualitative analysis / quantitative analysis is deteriorated.

[0011] The present inventors have made diligent studies, and as a result, have found that in the case where the measured profile of X-ray powder diffraction includes a wide profile, the accuracy of decomposition and the accuracy of the subsequent qualitative analysis / quantitative analysis are improved by correcting at least a part of the base profiles by performing non-negative matrix factorization on the measured profile, and have completed the present application.

[0012] The present application is achieved in view of such a situation, and an object thereof is to provide a processing device, a system, a method, and a program capable of improving the accuracy of decomposition by correcting at least a part of the base profiles by performing non-negative matrix factorization on the measured profile of X-ray powder diffraction.

[0013] Solutions for solving the problem

[0014] (1) In order to achieve the above object, the processing device of the present application is a processing device that performs non-negative matrix factorization on a measured profile of X-ray powder diffraction, characterized by comprising: a measured profile acquisition unit that acquires a plurality of measured profiles; a decomposition unit that performs non-negative matrix factorization on the measured profiles, and calculates base profiles; an index calculation unit that acquires the base profiles, and calculates an index based on the concave-convex of the base profiles; a base profile classification unit that classifies the base profiles into a plurality of groups based on the index; and a base profile correction unit that performs correction based on the index on at least one group of the plurality of groups, and calculates a corrected base profile.

[0015] (2) In addition, in the processing device of the present application, the decomposition unit performs non-negative matrix factorization on the measured profile with the corrected base profile as an initial condition.

[0016] (3) In addition, in the processing device of the present application, characterized in that the index is RTV (relative total variation).

[0017] (4) In addition, in the processing device of the present application, characterized in that the number of groups is two, and the group in which correction based on the index is performed is a group including the substrate profile originating from an amorphous material.

[0018] (5) In addition, the processing device of the present application is characterized by further comprising a profile number setting section that sets the number of substrate profiles included in the group in which correction based on the index is performed.

[0019] (6) In addition, in the processing device of the present application, characterized in that one of the corrections performed by the substrate profile correction section is correction in which the value of the RTV becomes smaller.

[0020] (7) In addition, the processing device of the present application is characterized by further comprising a dendrogram creation section that calculates statistics between a plurality of the measurement profiles, creates a dendrogram, and the decomposition section performs non-negative matrix factorization on a cluster including a group of similar profiles selected from the dendrogram by the processing device or selected by a user.

[0021] (8) In addition, the processing device of the present application is characterized by further comprising: a peak search section that performs peak search on the substrate profile after the non-negative matrix factorization, and creates a d-value-intensity list; and a qualitative section that performs qualitative analysis using the d-value-intensity list.

[0022] (9) In addition, the processing device of the present application is characterized by further comprising a quantitative section that performs quantitative analysis using data on which the qualitative analysis has been performed.

[0023] (10) In addition, the system of the present application is characterized by comprising: an X-ray diffraction device that comprises an X-ray generation section that generates X-rays, a detector that detects X-rays, and a goniometer that controls the rotation of a sample; and the processing device of any one of (1) to (9) above.

[0024] (11) In addition, the method of the present application is a method of performing non-negative matrix factorization on a measurement profile of X-ray powder diffraction, characterized by comprising: a step of obtaining a plurality of measurement profiles; a step of performing non-negative matrix factorization on the measurement profiles, and calculating substrate profiles; a step of obtaining the substrate profiles, and calculating an index of unevenness based on the substrate profiles; a step of classifying the substrate profiles into a plurality of groups based on the index; and a step of performing correction based on the index on at least one group of the plurality of groups, and calculating corrected substrate profiles.

[0025] (12) In addition, the program of the present application is a program for non-negative matrix factorization of measurement profiles of X-ray powder diffraction, characterized by causing a computer to execute: a process of obtaining a plurality of measurement profiles; a process of performing non-negative matrix factorization on the measurement profiles, calculating base profiles; a process of obtaining the base profiles, calculating an index of unevenness based on the base profiles; a process of classifying the base profiles into a plurality of groups based on the index; and a process of performing correction based on the index on at least one group of the plurality of groups, calculating corrected base profiles. BRIEF DESCRIPTION OF DRAWINGS

[0026] Fig. 1 is a conceptual diagram showing a case of non-negative matrix factorization.

[0027] Fig. 2 is a conceptual diagram showing one example of the configuration of a system of X-ray diffraction measurement.

[0028] Fig. 3 is a block diagram showing one example of the configuration of a control device and a processing device.

[0029] Fig. 4 is a block diagram showing a modification example of the configuration of a control device and a processing device.

[0030] Fig. 5 is a block diagram showing a modification example of the configuration of a control device and a processing device.

[0031] Fig. 6 is a block diagram showing a modification example of the configuration of a processing device.

[0032] Fig. 7 is a block diagram showing a modification example of the configuration of a processing device.

[0033] Fig. 8 is a block diagram showing a modification example of the configuration of a processing device.

[0034] Fig. 9A is a schematic diagram showing one example of a UI for setting and the like of a component analysis function.

[0035] Fig. 9B is a schematic diagram showing an explanation of a part of a function of a UI for component analysis.

[0036] Fig. 10 is a schematic diagram showing one example of a UI for setting and the like of a function for tree diagram creation.

[0037] Fig. 11 is a schematic diagram showing one example of a UI for setting and the like of a function for search matching, quantification.

[0038] Fig. 12 is a flowchart showing one example of the action of the processing device.

[0039] Fig. 13 is a flowchart showing a modification of the action of the processing device.

[0040] Fig. 14 is a flowchart showing a modification of the action of the processing device.

[0041] Fig. 15 is a flowchart showing a modification of the action of the processing device.

[0042] Fig. 16A 、 Fig. 16B is a coordinate graph showing the base distribution graph after the decomposition of each of Example 1 and Comparative Example 1.

[0043] Fig. 17A to Fig. 17C is a coordinate graph showing the true content ratio, the analysis result by Example 1, and the analysis result by Comparative Example 1 of Samples 91 to 101, respectively.

[0044] Fig. 18 is a coordinate graph showing the time variation of the temperature and humidity of the environment in which the samples of Example 2 and Comparative Example 2 are placed.

[0045] Fig. 19 is a coordinate graph showing the base distribution graph of the amorphous of each of Example 2 and Comparative Example 2.

[0046] Fig. 20A 、 Fig. 20B is a coordinate graph showing the analysis result by Example 2 and the analysis result by Comparative Example 2, respectively.

[0047] Explanation of reference numerals

[0048] 100 system

[0049] 200 X-ray diffraction device

[0050] 210 X-ray generating section

[0051] 220 incident side optical unit

[0052] 230 goniometer

[0053] 240 sample stage

[0054] 250 emission side optical unit

[0055] 260 detector

[0056] 300 control device

[0057] 310 control section

[0058] 320 device information storage section

[0059] 330 measurement data storage section

[0060] 340 display section

[0061] 400 processing device

[0062] 410 profile acquisition section

[0063] 415 dendrogram creation section

[0064] 420 decomposition section

[0065] 430 index calculation section

[0066] 435 profile number setting section

[0067] 440 base profile classification section

[0068] 450 base profile correction section

[0069] 460 peak search section

[0070] 470 qualitative section

[0071] 480 quantitative section

[0072] 510 input device

[0073] 520 display device DETAILED DESCRIPTION

[0074] Next, an embodiment of the present application will be described with reference to the accompanying drawings. For easy understanding of the description, the same reference numerals are attached to the same constituent elements in each drawing, and repetitive description is omitted.

[0075] [Principle]

[0076] In a measurement profile (profile; curve / profile) of X-ray powder diffraction, profiles of a plurality of substances or a background are superimposed. In a case where the kinds of the mixture are many or in a case where the profile includes an amorphous substance, the number of peak repetitions increases. In such a case, the accuracy of peak search deteriorates, and the conventional search matching using a peak position-integral intensity list (d-value-intensity list; d-I list) is mostly unsuitable.

[0077] Non-negative matrix factorization (NMF) is a method of decomposing a matrix of non-negative values into a product of matrices of non-negative values. In order to easily perform search matching, it is considered to decompose a measured profile of X-ray powder diffraction into a weighted sum of a plurality of profiles (a profile that can include a background). Each profile and its weight are non-negative values, and therefore, in order to express a measured profile of X-ray powder diffraction by a weighted sum of a plurality of profiles, it is suitable to perform non-negative matrix factorization.

[0078] Fig. 1 is a conceptual diagram showing a case of non-negative matrix factorization. Fig. 1 The left side of shows a matrix in which n measured profiles of X-ray powder diffraction having m measurement points are arranged. The result of performing non-negative matrix factorization on this is Fig. 1 The right side of shows a matrix in which n measured profiles of X-ray powder diffraction having m measurement points are arranged. The result of performing non-negative matrix factorization on this is Fig. 1 The wavy equal sign of does not only mean strict identity, but also includes a case in which the degree of departure is below a prescribed value, indicating the closeness between the left side and the right side.

[0079] A measured profile of X-ray powder diffraction sometimes includes a wide profile. The case including a wide profile refers to, for example, a case including an amorphous profile, and the like. In such a case, if non-negative matrix factorization is performed in which regularization with respect to linear independence is applied to search for a combination having high linear independence as in Patent Document 1, the accuracy of search matching thereafter sometimes deteriorates, and therefore, it is not suitable.

[0080] The method of the present application is a method of correcting at least a part of the base profiles obtained by performing non-negative matrix factorization on a measured profile of X-ray powder diffraction in a case in which the measured profile includes a wide profile. The correction is performed with respect to a part of the base profiles that is considered more accurate if it is wider, so as to make the concave-convex of the profile smooth. The method of the present application can perform non-negative matrix factorization with good accuracy in a case in which a measured profile includes a wide profile, and the accuracy of qualitative analysis / quantitative analysis thereafter is high. Furthermore, although various methods of performing non-negative matrix factorization on a matrix given as a matrix of non-negative values have been proposed, the present application can use a general method. The detailed method of the present application is described in detail in the embodiments.

[0081] [Embodiment]

[0082] [Overall system]

[0083] Fig. 2is a conceptual diagram showing one example of the configuration of the system 100 that performs X-ray diffraction measurement. The system 100 has an X-ray diffraction apparatus 200, a control apparatus 300, and a processing apparatus 400. The X-ray diffraction apparatus 200 configures an optical system that causes X-rays to be incident on a sample and detects diffraction X-rays generated from the sample, and has a goniometer in the optical system. Further, Fig. 2 The configuration shown is one example, and various other configurations can be employed.

[0084] The control apparatus 300 is connected to the X-ray diffraction apparatus 200 and performs control of the X-ray diffraction apparatus 200 and processing and storage of data acquired. The processing apparatus 400 performs non-negative matrix factorization on a measurement profile of X-ray powder diffraction and corrects at least part of a base profile. The control apparatus 300 and the processing apparatus 400 are apparatuses that have a CPU and a memory, and can be a PC terminal or a server on the cloud. In addition, not only all of the apparatuses can be provided on the cloud, but also part of the apparatuses or part of the functions within the apparatuses can be provided on the cloud. The input apparatus 510 is, for example, a keyboard or a mouse and performs input to the control apparatus 300 or the processing apparatus 400. The display apparatus 520 is, for example, a display and displays a measurement profile or a result of non-negative matrix factorization, and the like.

[0085] By using such a system 100, it is possible to measure a profile of X-ray powder diffraction, perform non-negative matrix factorization on the measurement profile, and correct at least part of a base profile. In addition, it is possible to perform qualitative analysis or quantitative analysis using the base profile that has been subjected to non-negative matrix factorization and correction of at least part of the base profile.

[0086] Further, in Fig. 2 , the control apparatus 300 and the processing apparatus 400 are described as the same PC. However, the method of the present application can measure a measurement profile independently of the X-ray diffraction apparatus 200 or the control apparatus 300 and correct at least part of a base profile obtained by performing non-negative matrix factorization on the measurement profile. Therefore, as in Fig. 3 , the processing apparatus 400 can also be configured as an apparatus different from the control apparatus 300. Fig. 3 is a block diagram showing one example of the configuration of the control apparatus 300 and the processing apparatus 400. In addition, as in Fig. 4 , the processing apparatus 400 can also be configured as part of the functions included in the control apparatus 300. In addition, as in Fig. 5 , the processing apparatus 400 and the control apparatus 300 can also be configured as an integrated apparatus. Fig. 4 and Fig. 5 are block diagrams showing a modification example of the configuration of the control apparatus 300 and the processing apparatus 400. Hereinafter, a case where the control apparatus 300 and the processing apparatus 400 are configured as different apparatuses will be described.

[0087] [X-ray diffraction apparatus]

[0088] The X-ray diffraction apparatus 200 is configured to include an X-ray generating section 210 that generates X-rays from an X-ray focal point, i.e., an X-ray source, an incident-side optical unit 220, a goniometer 230, a sample stage 240 on which a sample is set, an emission-side optical unit 250, and a detector 260 that detects X-rays. The X-ray generating section 210, the incident-side optical unit 220, the goniometer 230, the sample stage 240, the emission-side optical unit 250, and the detector 260 that constitute the X-ray diffraction apparatus 200 are general apparatuses, and thus the description thereof is omitted.

[0089] [Control device]

[0090] The control device 300 is configured by a computer in which a CPU (Central Processing Unit), a ROM (ReadOnly Memory), a RAM (Random Access Memory), and a storage are connected to a bus. The control device 300 is connected to the X-ray diffraction apparatus 200 and receives information.

[0091] The control device 300 has a control section 310, a device information storage section 320, a measurement data storage section 330, and a display section 340. Each section can transmit and receive information through a control bus L. The input device 510 and the display device 520 are connected to the CPU via appropriate interfaces.

[0092] The control section 310 controls the operation of the X-ray diffraction apparatus 200. The device information storage section 320 stores device information acquired from the X-ray diffraction apparatus 200. The device information includes information about the X-ray diffraction apparatus 200, such as the device name, the type of the X-ray source, the wavelength, the background, and the like. In addition to this, information required for non-negative matrix factorization of a measurement profile of X-ray powder diffraction, such as the type of the constituent element of the sample, the composition, and the like, information required for correction of a base profile, such as a Gaussian filter, a method of polynomial approximation, a method of TV regularization, and the like, can be included.

[0093] The measurement data storage section 330 stores the measurement profile acquired from the X-ray diffractometer 200. It is also possible to include, in correspondence with the measurement profile, information necessary for non-negative matrix factorization of the measurement profile of X-ray powder diffraction, such as the kind of the radiation source, the wavelength, the background, the kind of the constituent element of the sample, the composition, a Gaussian filter, a method of polynomial approximation, a method of TV regularization, and the like, which are necessary for correction of the background profile. The display section 340 causes the measurement profile or the background profile to be displayed on the display device 520. Thereby, the user can confirm the measurement profile or the background profile. In addition, the user can instruct or designate the control device 300, the processing device 400, and the like, based on the measurement profile or the background profile.

[0094] [Processing device]

[0095] The processing device 400 is constituted by a computer in which a CPU, a ROM, a RAM, a memory, and the like are connected to a bus. The processing device 400 can also be connected to the X-ray diffractometer 200 via the control device 300.

[0096] The processing device 400 is provided with a measurement profile acquisition section 410, a decomposition section 420, an index calculation section 430, a background profile classification section 440, and a background profile correction section 450. Each section can transmit and receive information by controlling the bus L. In the case where the processing device 400 and the control device 300 are constituted differently, the input device 510 and the display device 520 are also connected to the CPU of the processing device 400 via an appropriate interface. In this case, the input device 510 and the display device 520 can be different from the input device and the display device connected to the control device 300.

[0097] The measurement profile acquisition section 410 acquires a plurality of measurement profiles. The measurement profile acquisition section 410 can acquire the measurement profile directly from the X-ray diffractometer 200 or via the control device 300. The measurement profile acquisition section 410 can also acquire, in correspondence with the measurement profile, information necessary for non-negative matrix factorization of the measurement profile of X-ray powder diffraction, such as the kind of the radiation source, the wavelength, the background, the kind of the constituent element of the sample, the composition, a Gaussian filter, a method of polynomial approximation, a method of TV regularization, and the like, which are necessary for correction of the background profile. These information can also be stored to a storage section of the processing device 400, which is not illustrated.

[0098] The decomposition section 420 performs non-negative matrix factorization on the measurement profile, and calculates a basis profile. For example, an N-row and M-column matrix in which the measurement profiles of N X-ray powder diffractions with M measurement points are arranged is assumed to be X. At this time, the non-negative matrix factorization of X is expressed as mathematical expression (1) below. W is a coefficient matrix, and B is a basis matrix. W indicates the weight of B. Each row of the basis matrix B is a basis profile (basis vector). In addition, R is a hyperparameter indicating the number of basis profiles. Furthermore, M, N, and R indicate the maximum value of the variable, and m, n, and r indicate the variable.

[0099] [mathematical expression 1]

[0100]

[0101] The non-negative matrix factorization can apply an optimization method such as an alternating least squares method, a multiplicative update method, a coordinate descent method, or the like to which regularization is applied. As the regularization, a weight or sparsity of the profile to be decomposed can be given.

[0102] The decomposition section 420 preferably performs non-negative matrix factorization on the measurement profile with the corrected basis profile as an initial condition. The non-negative matrix factorization on the measurement profile with the corrected basis profile as an initial condition means that the coefficient matrix W is updated for a matrix in which a part of the rows of the basis matrix B is replaced with the corrected basis profile, and furthermore, the basis matrix B is updated for the updated coefficient matrix W, and thus the measurement profile is subjected to non-negative matrix factorization.

[0103] The index calculation section 430 acquires the basis profile, and calculates an index based on the concave-convex of the basis profile. The index can be an index based on any definition, but is assumed to be an index that can represent the characteristics of the concave-convex of the basis profile and can compare the characteristics. Thus, the basis profile can be classified into a plurality of groups according to the characteristics of the concave-convex of the basis profile.

[0104] The index is preferably an RTV (Relative Total Variation). The RTV is an index defined for a function f in general using mathematical expression (2) below. The RTV is a representative index that can well represent the characteristics of the concave-convex of a function. For the above-described basis matrix B(r, m), when the basis profile of the r-th row of the basis matrix B(r, m) is expressed as B(r) as mathematical expression (3) below, it is defined by mathematical expression (4) below. r (m) when the basis profile of the r-th row of the basis matrix B(r, m) is expressed as B(r) as mathematical expression (3) below, it is defined by mathematical expression (4) below.

[0105] [mathematical expression 2]

[0106]

[0107] [mathematical expression 3]

[0108] B r (m) = B(r, m)... (3)

[0109] [Equation 4]

[0110]

[0111] The index is preferably RTV, but other indexes can also be used as long as they are indexes that can represent the characteristics of the unevenness of the base distribution map. For example, the displacement amount before and after smoothing processing of the base distribution map, the number of peaks when peak searching is performed on the base distribution map, the half-value width, the integrated intensity can be evaluated, and evaluation can also be performed by a combination of these indexes.

[0112] The base distribution map classification section 440 classifies the base distribution map into a plurality of groups based on the index calculated by the index calculation section 430. The classification of the base distribution map can be, for example, to set a plurality of numerical ranges that do not overlap with respect to the index, and to classify the base distribution map having a value of the index within the numerical range as a base distribution map belonging to the group of the numerical range. In addition, it is also possible to classify into a plurality of groups based on the index using the K-means method.

[0113] It is preferable that the plurality of groups be two, and the group in which the correction based on the index is performed is a group that contains the base distribution map originating from the amorphous material. Thereby, it is possible to perform the correction based on the index with respect to the base distribution map originating from the amorphous material.

[0114] The base distribution map correction section 450 performs the correction based on the index with respect to at least one group of the plurality of groups classified by the base distribution map classification section 440, and calculates a corrected base distribution map. The base distribution map correction section 450 can also perform the correction with respect to two or more groups of the plurality of groups classified. In addition, it is also possible to perform the correction with respect to all groups. In these cases, each correction contains a different correction.

[0115] In the case where the index is RTV, it is preferable that one of the corrections performed by the base distribution map correction section 450 be a correction in which the value of the RTV becomes smaller. Thereby, for example, it is possible to perform a correction that makes the base distribution map closer to the actual distribution map with respect to the distribution map of the amorphous material or the like, which is closer to the actual distribution map if the value of the RTV is smaller. Furthermore, even in the case where an index other than RTV is used, when an index is used in which the absolute value of the value of the index becomes smaller in the case where the unevenness of the base distribution map is small, as with the above, it is preferable that one of the corrections performed by the base distribution map correction section 450 be a correction in which the absolute value of the value of the index becomes smaller.

[0116] The correction in which the value of the RTV becomes smaller can be any correction. Specifically, for example, it is possible to perform a correction such as smoothing using a filter such as a Gaussian filter, polynomial approximation using a polynomial of a low order such as a polynomial of 5 or less, TV regularization, and the like.

[0117] By such a configuration, in a case where the measurement profile contains a wide profile, at least a part of the base profiles obtained by performing non-negative matrix factorization on the measurement profile can be corrected, and the accuracy of the decomposition can be improved.

[0118] Fig. 6 is a block diagram illustrating a modification example of the configuration of the processing device 400. As shown in Fig. 6 The processing device 400 preferably has a profile number setting section 435. The profile number setting section 435 sets the number of base profiles included in the group that performs the correction based on the index. The number of profiles set by the profile number setting section 435 is a value smaller than the value of the hyperparameter R.

[0119] The profile number setting section 435 preferably sets the number of base profiles included in the group that performs the correction based on the index based on the index calculated by the index calculation section 430 or according to an instruction from the user. In a case where the number of base profiles included in the group that performs the correction based on the index is set by the profile number setting section 435, the base profile classification section 440 classifies the number of base profiles set as the group that performs the correction based on the index. Thereby, in a case where the measurement profile contains two or more wide profiles, the base profiles corresponding to them can also be appropriately corrected, and the accuracy of the decomposition can be further improved.

[0120] Fig. 7 is a block diagram illustrating a modification example of the configuration of the processing device 400. As shown in Fig. 7 The processing device 400 preferably has a dendrogram creation section 415. The dendrogram creation section 415 calculates a statistic between a plurality of measurement profiles, and creates a dendrogram.

[0121] In a case where the dendrogram creation section 415 creates a dendrogram, the decomposition section 420 preferably performs non-negative matrix factorization on a cluster containing a group of similar profiles selected by the processing device 400 from the created dendrogram or selected by the user.

[0122] By calculating a statistic between a plurality of measurement profiles, creating a dendrogram, and performing non-negative matrix factorization on a cluster containing a group of similar profiles selected from the created dendrogram, it is expected that a measurement profile containing a characteristic profile common to each measurement profile is less likely to be removed. As a result, non-negative matrix factorization can be performed on a plurality of measurement profiles with good accuracy.

[0123] Fig. 8 is a block diagram illustrating a modification example of the configuration of the processing device 400. As shown in Fig. 8As shown, the processing device 400 preferably has a dendrogram creation section 415, a distribution map number setting section 435, a peak search section 460, a qualitative section 470, and a quantitative section 480. The dendrogram creation section 415 and the distribution map number setting section 435 are functional sections identical to the dendrogram creation section and the distribution map number setting section described above.

[0124] The peak search section 460 performs peak search on the basis distribution maps after non-negative matrix factorization, and creates a d-value-intensity list. The peak search is performed on a selected one of the basis distribution maps that is a result of non-negative matrix factorization. The selection of the basis distribution map can be performed by a user, or by the peak search section 460 or another functional section of the processing device 400. In addition, the d-value-intensity list is created for each basis distribution map on which peak search is performed. Preferably, peak search is performed on all of the distribution maps except for the distribution maps judged to be background.

[0125] The qualitative section 470 performs qualitative analysis using the d-value-intensity list. The qualitative analysis can be performed by search matching on the created d-value-intensity list. The qualitative analysis can be performed using known methods. Since it is expected that the corrected basis distribution maps are more accurate than the basis distribution maps without correction, the qualitative analysis performed using the d-value-intensity list created from the corrected basis distribution maps makes it easier to identify components or increases the accuracy of identification.

[0126] The quantitative section 480 performs quantitative analysis using the data on which qualitative analysis is performed. The quantitative analysis can be performed using known methods. In addition, in the configuration of the processing device 400, the dendrogram creation section 415, the distribution map number setting section 435, the peak search section 460, the qualitative section 470, and the quantitative section 480 are optional functional sections, and the configuration can be one in which any one or more of them is not included. Fig. 8

[0127] With such a configuration, it is possible to correct a part of the basis distribution maps by performing non-negative matrix factorization on the measured distribution maps of X-ray powder diffraction measured by an X-ray diffractometer, and it is possible to perform qualitative analysis and quantitative analysis using the same.

[0128] [User Interface]

[0129] ​In a case where the user gives an instruction of a parameter or the like of the processing device 400, a user interface (UI) function by which various settings can be made by a mouse operation or a keyboard operation is preferably used, for example. In addition, the function of the processing device 400 is preferably configured to cooperate with the function of another device. Hereinafter, one example of the UI for setting a parameter of the processing device 400, and the UI when the function of the processing device 400 cooperates with the function of another device will be described. It is assumed that the function of the processing device 400 is implemented as software.

[0130] Fig. 9A is a diagram showing one example of the UI for setting a function for component resolution and the like. In addition, Fig. 9B is a diagram showing a part of the function of the UI for component resolution ( Fig. 9A ). On the screen of Fig. 9A , the user can give an instruction of acquisition of a measurement profile, setting of a parameter, setting of a number of profiles, calculation of a dendrogram, execution of non-negative matrix factorization, display of a measurement profile, display of a base profile, data transfer, and the like to the processing device 400. The setting panel of the parameter can set an optimization method of non-negative matrix factorization, a value of a hyperparameter, a number of iterations, regularization, and a number of base profiles belonging to a group in which correction based on an index is performed. The value of the hyperparameter can be automatically estimated and set using Akaike information criterion, Bayesian information criterion, or the like, or can be configured to display an estimated value by an Estimate button. The data transfer button transfers data of a result of non-negative matrix factorization to a search matching, quantitative function.

[0131] Fig. 10 is a diagram showing one example of the UI for setting a function for dendrogram creation and the like. On the screen of Fig. 10 , the user can give an instruction of setting of a statistical quantity, data processing, selection of clustering, and the like for dendrogram creation to the processing device 400.

[0132] Fig. 11 is a diagram showing one example of the UI for setting a function for a search matching, quantitative function and the like. By pressing a data transfer button on the screen of Fig. 9A , Fig. 11 the screen is activated. On the screen of Fig. 11 , the user can give an instruction of execution of a search matching, setting of compound information, and the like to the processing device 400 or another device.

[0133] In addition, Fig. 9A , Fig. 9B to Fig. 11The setting items and the like shown in FIG. 12 are one example, and in a case where a user sets these setting items, it is also possible to set so as to be able to set only a part of these setting items or so as to be able to set all of the setting items. In addition, it is also possible to have Fig. 9A , Fig. 9B to Fig. 11 setting items or functions not shown in FIG. 12.

[0134] [Measurement Method]

[0135] The X-ray diffraction apparatus 200 is provided with a sample S, and an angle meter is driven on the basis of control by the control apparatus 300 under prescribed conditions. In addition, X-rays are made incident on the sample, and diffraction X-rays generated from the sample are detected. Thereby, diffraction data are acquired. The X-ray diffraction apparatus 200 transmits the acquired diffraction data and the like as measurement data to the control apparatus 300.

[0136] [Decomposition Method]

[0137] (Explanation of Basic Flow of Non-negative Matrix Factorization)

[0138] Fig. 12 is a flowchart showing one example of the action of the processing apparatus 400. Fig. 12 One example of the basic action of non-negative matrix factorization and correction of basis distribution maps is shown. First, the processing apparatus 400 acquires a measurement distribution map (step S1). Next, setting of parameters is performed (step S2). The parameters to be set are the number of basis distribution maps to be decomposed (the value of the hyperparameter), parameters required for optimization such as the optimization method. The parameters can be parameters input by a user, or can be parameters determined and set by the processing apparatus 400 from the measurement distribution map or information related to the measurement distribution map.

[0139] Next, the matrix W is updated (step S3). Next, the matrix B is updated (step S4). The update of the matrix W and the update of the matrix B are performed by creating a matrix including the measurement distribution map and optimizing the coefficient matrix W and the basis matrix B. The update of the matrix W and the update of the matrix B include the initial setting, calculation. In a case where there is a corrected basis distribution map, the update of the matrix W and the update of the matrix B are performed by setting the corrected basis distribution map as the basis matrix and optimizing the coefficient matrix W and the basis matrix B. The update of the matrix W and the update of the matrix B can be collectively referred to as performing non-negative matrix factorization.

[0140] Next, an index is calculated for the basis distribution pattern of each row of the basis matrix B (step S5). Next, the basis distribution pattern is classified into a plurality of groups (step S6). The classification of the basis distribution pattern is performed only in the initial cycle, and in the cycle after the 2nd cycle, the initial classification can be directly used. Next, at least one group of the plurality of groups is subjected to index-based correction (step S7). The corrected basis distribution pattern is referred to as a corrected basis distribution pattern. Next, it is determined whether or not an end condition is satisfied (step S8). In the case where the end condition is not satisfied (step S8 - "No"), the process returns to step S3, the corrected basis distribution pattern is set as the basis matrix, and non-negative matrix factorization is performed.

[0141] On the other hand, in the case where the end condition is satisfied (step S8 - "Yes"), the result is output as needed (step S9) and the process ends. It can also be configured to store only the result and output it in the case where an instruction is given from the user. In this way, it is possible to perform non-negative matrix factorization on a plurality of measured distribution patterns of X-ray powder diffraction and correct at least a part of the basis distribution pattern.

[0142] The end condition can adopt various conditions. For example, the number of cycles can be set and used as the end condition. In addition, the amount of change in the corrected basis distribution pattern before and after the cycle, the amount of change in part or all of the index, the amount of change in part or all of the coefficient matrix, the amount of change in part or all of the basis matrix, the degree of agreement of the calculated distribution pattern corresponding to one or a plurality of measured distribution patterns, and the like can be defined, a threshold value thereof is set, and in the case where the threshold value is exceeded or is below the threshold value, the process ends. In addition, the amount of change refers to the size or proportion of the fluctuation. In addition, the calculated distribution pattern refers to one distribution pattern obtained by multiplying a certain row of the coefficient matrix corresponding to one measured distribution pattern and the basis matrix. In addition, in the case where a known distribution pattern is used as an initial value of the basis distribution pattern or the like, it is sometimes expected that a result close to the target result can be obtained without performing the cycle process. In such a case, it is also possible to end until step S7. Fig. 12

[0143] (Explanation of the flow in the case where the number of basis distribution patterns is set)

[0144] Fig. 13 is a flowchart showing a modification example of the action of the processing device 400. Fig. 13 ​One example of the action in the case where the number of basis distribution maps is set is shown. In the explanation of the flowchart hereafter, the characteristic actions are explained in detail, and the explanation of the actions already explained is sometimes omitted. Steps T1 to T5 are the same as the above-described steps S1 to S5. Next, the processing device 400 sets the number of basis distribution maps included in the group that performs the correction based on the index (step T6). In the case where the number of basis distribution maps is set based on the index, the setting of the number of basis distribution maps needs to be performed after step T5. In this case, in the cycle after the second time, the setting of the number of basis distribution maps is skipped. In addition, in the case where the setting of the number of basis distribution maps is not performed based on the index, the setting of the number of basis distribution maps can be performed, for example, at the same time as the setting of the parameters. The subsequent steps T7 to T10 are the same as the above-described steps S6 to S9.

[0145] (Explanation of the flow in the case where a dendrogram is created)

[0146] Fig. 14 is a flowchart showing a modification example of the action of the processing device 400. Fig. 14 One example of the action in the case where a dendrogram is created is shown. First, the processing device 400 acquires the measurement distribution maps (step U1). Step U1 is the same as step S1.

[0147] Next, the creation of the dendrogram is performed (step U2). The dendrogram is created by calculating the statistics between the acquired plurality of measurement distribution maps. Next, the selection of the cluster is performed (step U3). The cluster can be selected by the user or by the processing device 400. By selecting the cluster as a group of similar distribution maps from the dendrogram, the resolution is improved.

[0148] Next, the setting of the parameters is performed (step U4). Next, the non-negative matrix factorization is performed (step U5). Step U5 is a step in which steps S3 to S8 are summarized. Then, the result is output as needed (step U6) and the process ends. In this way, the dendrogram can be created, the non-negative matrix factorization can be performed after the selection of the cluster, and at least a part of the basis distribution maps can be corrected.

[0149] (Explanation of the flow of the modification example when qualitative analysis is performed or quantitative analysis is further performed)

[0150] Fig. 15 is a flowchart showing a modification example of the action of the processing device 400. Fig. 15A modification of the action in the case where qualitative analysis or further quantitative analysis is performed after correction of at least a part of the basis distribution pattern by non-negative matrix factorization is shown. The steps of acquiring the measurement distribution pattern (step Vl) to the step of performing non-negative matrix factorization (step V5) are the same as steps Ul to U5.

[0151] Next, peak search is performed (step V6). The peak search is performed on a selected one of the basis distribution patterns of the result of non-negative matrix factorization. The selection of the basis distribution pattern can be performed by the user or by the processing device 400. In addition, a d-value-intensity list is created for each basis distribution pattern on which peak search is performed. It is preferable that peak search be performed on all of the basis distribution patterns except for the basis distribution pattern judged to be background.

[0152] Next, qualitative analysis is performed (step V7). The qualitative analysis can be performed by performing search matching based on the created d-value-intensity list. It can also be configured so as to return to step V4 and perform non-negative matrix factorization again from the setting of the parameters in the case where the result of search matching is that no distribution pattern with a degree of agreement of a prescribed value or more is found.

[0153] Next, quantitative analysis is performed (step V8). The quantitative analysis determines the content ratio of the substance determined by the qualitative analysis using various methods. For example, the DD (Direct Derivation) method, the RIR method, the Rietveld method, or the like can be used. Then, the result is output as needed (step V9) and the process ends. In this way, non-negative matrix factorization can be performed on a plurality of measurement distribution patterns of X-ray powder diffraction, at least a part of the basis distribution pattern can be corrected, and then qualitative analysis can be performed, and quantitative analysis can be performed using it.

[0154] In the flowchart of Fig. 15 , the qualitative analysis of step V7 can be followed by not performing quantitative analysis but outputting the result as needed (step V9) and ending. In this way, non-negative matrix factorization can be performed on a plurality of measurement distribution patterns of X-ray powder diffraction, at least a part of the basis distribution pattern can be corrected, and then qualitative analysis can be performed.

[0155] The order of the steps of the above-described flowcharts is not fixed and can be changed or the processing can be performed in parallel as long as the processing is performed correctly. In addition, each flowchart can be combined with another flowchart and applied.

[0156] [Examples, Comparative Examples]

[0157] (Example 1)

[0158] Using the system 100 configured as described above, X-ray diffraction data were measured for the mixture of indomethacin for samples 1 to 101. For the measured profiles of samples 1 to 90 among the measured samples, the base profiles of indomethacin α form, indomethacin γ form, and amorphous substance were calculated using the method of the present application. Specifically, non-negative matrix factorization was performed with the hyperparameter set to 3 and the end condition set to 200 iterations, the base profile of the profile considered to be amorphous substance was corrected, and thus each base profile was calculated.

[0159] (Comparative Example 1)

[0160] For the same measured profiles, non-negative matrix factorization was performed using the alternating least squares method as the existing method with the hyperparameter set to 3, and the base profiles of indomethacin α form, indomethacin γ form, and amorphous substance were calculated.

[0161] Fig. 16A 、 Fig. 16B are coordinate graphs each showing the base profiles of Example 1 and Comparative Example 1. According to Fig. 16A It is known that the base profile of the profile considered to be amorphous substance in Example 1 is wide and smooth. In contrast, according to Fig. 16B It is known that the base profile of the profile considered to be amorphous substance in Comparative Example 1 can be observed to have a fine peak, and has a characteristic different from the actually measured profile of amorphous substance.

[0162] Next, using each base profile calculated in Example 1 or Comparative Example 1, quantitative analysis was performed on the content ratio of indomethacin α form, indomethacin γ form, and amorphous substance for samples 91 to 101. In addition, samples 91 to 101 are mixtures of which the content ratio of each component is known, and the content ratio of each is set as Ground truth (true data). Fig. 17A to Fig. 17C is a coordinate graph each showing the true content ratio of samples 91 to 101, the analysis result by Example 1, and the analysis result by Comparative Example 1.

[0163] The residual sum of squares error (MSE) of the analysis result of Example 1 or Comparative Example 1 and the true content ratio was calculated. As a result, the MSE of Example 1 was 57.30, and the MSE of Comparative Example 1 was 60.57. It is known from this that the analysis result of the method of the present application is closer to the true content ratio than the analysis result of the existing method. That is, it is confirmed that the method of the present application also has high precision in quantitative analysis.

[0164] (Example 2)

[0165] Next, trehalose was placed on the sample stage of the same system 100 capable of changing temperature and humidity, and a plurality of X-ray diffraction data were measured while changing the temperature and humidity over time. Fig. 18 is a graph showing the time change of the temperature and humidity of the environment in which the sample was placed in Example 2 and Comparative Example 2. For the measurement profile, the base profiles of the amorphous (amorphous), dihydrate, anhydrous α, and anhydrous β of trehalose were calculated using the method of the present application. Specifically, non-negative matrix factorization was performed with the hyperparameter set to 4 and the end condition set to 200 iterations, and the base profile of the profile considered to be amorphous was corrected to thereby calculate each base profile.

[0166] (Comparative Example 2)

[0167] For the same measurement profile, non-negative matrix factorization was performed using the alternating least squares method with the hyperparameter set to 4, and the base profiles of the amorphous, dihydrate, anhydrous α, and anhydrous β of trehalose were calculated.

[0168] Fig. 19 is a graph showing the base profile of the amorphous of Example 2 and Comparative Example 2, respectively. According to Fig. 19 It was found that in Example 2, the base profile of the amorphous was also wide and smooth. In contrast, it was found that the base profile of the amorphous of Comparative Example 2 could be observed to have a fine peak, having a different characteristic from the actually measured profile of the amorphous.

[0169] The change in the content ratio of trehalose over time was calculated using each base profile calculated in Example 2 or Comparative Example 2. Fig. 20A 、 Fig. 20B is a graph showing the analysis results of Example 2 and the analysis results of Comparative Example 2, respectively. Regarding trehalose, the following is known. (1) When the dihydrate is heated at 140°C, it is converted to anhydrous β. (2) When the dihydrate is heated under ordinary humidity, a transition to amorphous is observed. (3) When the amorphous is heated, it is converted to anhydrous β at 150°C. (4) When anhydrous β is heated, it melts at 210°C and is converted to amorphous. Based on these, it was confirmed that the accuracy of the quantitative analysis of Example 2, which does not become anhydrous β at a temperature of 140°C or higher, is higher than that of Comparative Example 2, in which anhydrous β is observed at a temperature of 100°C or lower.

[0170] Based on the above results, it was confirmed that the processing device, system, method, and program of the present application can improve the accuracy of the decomposition by performing non-negative matrix factorization on the measurement profile of the X-ray powder diffraction and correcting at least a part of the base profile.

[0171] The functions of the elements disclosed in the specification can be implemented using a general purpose processor, a special purpose processor, an integrated circuit, ASICs (Application Specific Integrated Circuits), FPGAs (Field Programmable Gate Arrays), existing circuits, and / or a circuit or processing circuitry including a combination of them that is programmed to perform the functions disclosed using one or more programs stored in one or more memories and other methods. The processor includes transistors, other circuits, and thus is considered a circuit or processing circuitry. The processor can also be a programmed processor that executes programs stored in a memory. In the present disclosure, a circuit, unit, or mechanism is hardware that performs the recited function or is hardware that is programmed in a manner to perform the recited function. The hardware is the hardware disclosed in the specification, as long as it is programmed or constructed in a manner to perform the recited function, and can be any hardware.

[0172] In addition, this application claims priority based on Japanese Patent Application No. 2024-124422 filed on July 31, 2024, and incorporates the entire contents of Japanese Patent Application No. 2024-124422 by reference into the present application.

Claims

1. A processing apparatus for processing the measured distribution pattern of X-ray powder diffraction, characterized in that, have: The distribution map acquisition unit acquires multiple distribution maps of X-ray powder diffraction. The decomposition unit performs non-negative matrix factorization on the measured distribution map and calculates the basis distribution map; The index calculation unit obtains the basis distribution map and calculates the convexity / concavity index based on the basis distribution map; A basal distribution map classification unit, which classifies the basal distribution map into multiple groups based on the index; as well as The basis distribution map correction unit performs correction on at least one of the plurality of groups based on the index and calculates the corrected basis distribution map.

2. The processing apparatus according to claim 1, characterized in that, The decomposition unit performs non-negative matrix factorization on the measured distribution map using the corrected basis distribution map as the initial condition.

3. The processing apparatus according to claim 1 or claim 2, characterized in that, The indicator is the relative total variation.

4. The processing apparatus according to claim 1 or claim 2, characterized in that, The plurality of groups consists of two groups, and the group that performs correction based on the index is the group that includes the substrate distribution map derived from the amorphous material.

5. The processing apparatus according to claim 1 or claim 2, characterized in that, It also includes a distribution map quantity setting unit, which sets the number of the base distribution maps included in the group for which correction based on the index is performed.

6. The processing apparatus according to claim 3, characterized in that, One of the corrections performed by the base map correction unit is to correct for a decrease in the value of the relative total variation.

7. The processing apparatus according to claim 1 or claim 2, characterized in that, It also includes a tree diagram creation unit, which calculates statistics among multiple measurement distribution maps and creates a tree diagram. The decomposition unit performs non-negative matrix factorization on clusters containing similar distribution groups selected by the processing device from the dendrogram or by the user.

8. The processing apparatus according to claim 1 or claim 2, characterized in that, It also has: The peak search unit performs a peak search on the basis distribution map after the nonnegative matrix factorization, and creates a d-value-intensity list; and The qualitative section uses the aforementioned d-value-intensity list for qualitative analysis.

9. The processing apparatus according to claim 8, characterized in that, It also includes a quantitative section, which performs quantitative analysis using the data that has undergone the qualitative analysis.

10. A system, characterized in that, Include: An X-ray diffraction apparatus comprising an X-ray generator, an X-ray detector, and a goniometer for controlling the rotation of the sample; and The processing apparatus according to claim 1 or claim 2.

11. A method for processing a measured distribution pattern of X-ray powder diffraction, characterized in that, Include: Steps for obtaining multiple distribution patterns from X-ray powder diffraction; The steps are: performing non-negative matrix factorization on the measured distribution map to calculate the basis distribution map; The steps include obtaining the basis distribution map and calculating the concavity / convexity index based on the basis distribution map; The step of classifying the baseline distribution map into multiple groups based on the aforementioned indicators; as well as The step of performing correction based on the index on at least one of the plurality of groups and calculating the corrected basis distribution map.

12. A program product for processing the distribution map of X-ray powder diffraction, characterized in that, To make the computer perform: Processing of multiple measured distribution patterns obtained from X-ray powder diffraction; The measured distribution map is subjected to non-negative matrix factorization to calculate the basis distribution map; Obtain the basis distribution map and calculate the concavity / convexity index based on the basis distribution map; The process of classifying the baseline distribution map into multiple groups based on the aforementioned indicators; as well as At least one of the plurality of groups is corrected based on the index, and the corrected basis distribution map is calculated.

13. A recording medium that is a computer-readable and non-transitory recording medium for recording a program for processing a measured distribution pattern of X-ray powder diffraction, characterized in that, The program causes the computer to execute: Processing of multiple measured distribution patterns obtained from X-ray powder diffraction; The measured distribution map is subjected to non-negative matrix factorization to calculate the basis distribution map; Obtain the basis distribution map and calculate the concavity / convexity index based on the basis distribution map; The process of classifying the baseline distribution map into multiple groups based on the aforementioned indicators; as well as At least one of the plurality of groups is corrected based on the index, and the corrected basis distribution map is calculated.

Images