Information processing method, information processing system, and program

Abstract

This information processing method is executed by a computer and comprises: a step (S101) for acquiring actual spectrum information indicating an actual spectrum which is obtained by actually measuring a material as the object for a search; a step (S101) for acquiring material information related to the composition of the material; steps (S102, S103) for generating, on the basis of the material information, a plurality of candidate structure information items related to a plurality of candidate structures which are candidates for a crystal structure the material has, and acquiring computed spectrum information indicating a computed spectrum corresponding to each of the plurality of candidate structures; steps (S103 to S107) for generating structure information regarding a crystal structure on the basis of a correlation between the actual spectrum information and the computed spectrum information; and a step (S108) for outputting the generated structure information.

Description

Information processing method, information processing system, and program

[0001] The present disclosure relates to an information processing method for identifying a crystal structure.

[0002] The physical properties of a material are primarily determined by its crystal structure. Therefore, a method for identifying the crystal structure of an unknown material is desired. For example, Non-Patent Document 1 discloses a method for identifying the crystal structure using the Rietveld method.

[0003] Furthermore, for example, Non-Patent Document 2 discloses a method for identifying a crystal structure using density functional theory.

[0004] Furthermore, for example, Patent Document 1 discloses a method for searching for substances having predetermined properties using spectral information.

[0005] JP 2021-149449 A

[0006] MCCUSKER, L. B. , et al. Rietveld refinement guidelines. Journal of Applied Crystallography, 1999, 32.1: 36-50. OGANOV, Artem R. ; GLASS, Colin W. Crystal structure prediction using ab initio evolutionary techniques: Principles and applications. The Journal of chemical physics, 2006, 124.24: 244704.

[0007] The present disclosure provides an information processing method and the like that facilitates efficient and accurate identification of unknown crystal structures.

[0008] An information processing method according to one aspect of the present disclosure is an information processing method executed by a computer, and includes the steps of acquiring actual spectrum information indicating an actual spectrum obtained by actually measuring a material to be searched for, acquiring material information regarding the composition of the material, generating, based on the material information, a plurality of candidate structure information regarding a plurality of candidate structures that are candidates for a crystal structure of the material, and acquiring calculated spectrum information indicating a calculated spectrum corresponding to each of the plurality of candidate structures, generating structural information regarding the crystal structure based on a correlation between the actual spectrum information and the calculated spectrum information, and outputting the generated structural information.

[0009] According to the present disclosure, it is easy to efficiently and accurately identify unknown crystal structures.

[0010] FIG. 1 is a block diagram showing an overall configuration including an information processing system according to a first embodiment. FIG. 2 is a flowchart showing an outline of the operation of the information processing system according to the first embodiment. FIG. 3 is a diagram showing an example of a list of candidate structure information. FIG. 4 is an explanatory diagram of a method for generating candidate structure information. FIG. 5 is a diagram showing a specific example of candidate structure information. FIG. 6 is a diagram showing another specific example of candidate structure information. FIG. 7 is a flowchart showing an example of calculation of a calculated spectrum. FIG. 8 is a diagram showing an example of a discrete spectrum and a continuous spectrum. FIG. 9 is an explanatory diagram of the similarity between an actual spectrum and a calculated spectrum. FIG. 10 is an explanatory diagram of structural optimization performed by the information processing system according to the first embodiment. FIG. 11 is a flowchart showing an example of an optimization process performed by the information processing system according to the first embodiment. FIG. 12 is a block diagram showing an overall configuration including an information processing system according to a second embodiment. FIG. 13 is a flowchart showing an outline of the operation of the information processing system according to the second embodiment. FIG. 14 is a flowchart showing an example of energy calculation. FIG. 15 is a diagram showing an example of a list of energy of candidate structures. FIG. 16 is a flowchart showing an example of an optimization process performed by the information processing system according to the second embodiment. FIG. 17 is an explanatory diagram of structural optimization performed by the information processing system according to the second embodiment. FIG. 18 is a diagram showing an image displayed on a display unit in an information processing system according to embodiment 2. FIG. 19 is a flowchart showing an outline of the operation of an information processing system according to comparative example 1. FIG. 20 is a flowchart showing an outline of the operation of an information processing system according to comparative example 2. FIG. 21 is a histogram showing the similarity between the actual spectrum and the calculated spectrum of a structure group structurally optimized in example 1. FIG. 22 is a histogram showing the similarity between the actual spectrum and the calculated spectrum of a structure group structurally optimized in example 2. FIG. 23 is a histogram showing the similarity between the actual spectrum and the calculated spectrum of a structure group structurally optimized in comparative example 1. FIG. 24 is a histogram showing the similarity between the actual spectrum and the calculated spectrum of a structure group structurally optimized in comparative example 2. FIG. 25 is a diagram comparing the actual spectrum with the calculated spectrum for the structure with the highest similarity in each of examples 1 and 2 and comparative examples 1 and 2.Figure 26 shows an example of one or more pieces of structural information. Figure 27 shows an example of information contained in the "Output" area of ​​Figure 18.

[0011] (Findings that led to the present disclosure) Conventionally, identification of a crystal structure has been performed by analyzing an X-ray diffraction pattern of an unknown material obtained through an experiment. Non-Patent Document 1 discloses a method for identifying a crystal structure using the Rietveld method. However, in identifying a crystal structure using the conventional Rietveld method, it is necessary to start identifying the crystal structure from one candidate structure that is thought to be closest to the actual crystal structure. In addition, the parameters of the candidate structure must have values ​​close to the parameters of the actual crystal structure, making it difficult to apply to unknown crystal structures.

[0012] Furthermore, with the recent development of simulation technology, a method for identifying a thermodynamically stable crystal structure has come into use, for example, by performing energy calculations on a large number of crystal structures using density functional theory. That is, identification is possible by selecting, from a group of a large number of obtained crystal structures, a crystal structure that is thought to be closest to the crystal structure of an unknown material obtained in an experiment. Non-Patent Document 2 discloses a crystal structure identification method using density functional theory. However, in identifying a crystal structure using density functional theory, it is necessary to calculate the energy for a large number of crystal structures, which results in high computational costs. Furthermore, since the number of crystal structures to be calculated is limited, it is difficult to identify the correct crystal structure.

[0013] Furthermore, Patent Document 1 discloses a method for searching for a substance having predetermined properties using spectral information. More specifically, actual measurement information including synthesis conditions, physical properties, and spectral information of a substance having predetermined properties is acquired, and the properties of the substance to be optimized are output. Therefore, in Patent Document 1, optimization processing must be performed using information on the synthesis conditions and physical properties of the substance other than spectral information. Furthermore, the output search results for the substance do not include information on the crystal structure.

[0014] The inventors of the present application have found that it is possible to efficiently and accurately identify unknown crystal structures by performing an optimization process using the similarity between an experimentally obtained X-ray diffraction pattern (actual spectrum) of an unknown material and a computationally calculated X-ray diffraction pattern (calculated spectrum).Furthermore, they have found that it is possible to output a structure with low energy that is close to the experimentally synthesized structure by performing an optimization process using the spectral similarity and energy information of the crystal structure.

[0015] Here, the term "spectrum" refers to a group of components that can be measured for a crystal structure. Examples include, but are not limited to, an X-ray diffraction pattern, an X-ray absorption pattern, NMR (Nuclear Magnetic Resonance), or an optical absorption spectrum. The actual spectrum is a spectrum obtained by measuring an experimentally obtained crystal structure. The calculated spectrum refers to a spectrum calculated from a crystal structure generated in a crystal structure generation process.

[0016] In order to solve the above-described problems, an information processing method according to one aspect of the present disclosure is an information processing method executed by a computer, and includes the steps of acquiring actual spectrum information indicating an actual spectrum obtained by actually measuring a material to be searched for, acquiring material information regarding the composition of the material, generating, based on the material information, a plurality of pieces of candidate structure information regarding a plurality of candidate structures that are candidates for a crystal structure of the material, and acquiring calculated spectrum information indicating a calculated spectrum corresponding to each of the plurality of candidate structures, generating structural information regarding the crystal structure based on a correlation between the actual spectrum information and the calculated spectrum information, and outputting the generated structural information.

[0017] This makes it easier to identify unknown crystal structures efficiently and accurately.

[0018] Furthermore, for example, in the step of generating the structural information, structural optimization may be performed on two or more of the plurality of candidate structures using the actual spectrum and the calculated spectrum, and the structural information may indicate a structure obtained by the structural optimization.

[0019] This makes it easier to identify unknown crystal structures efficiently and accurately.

[0020] Furthermore, the structural optimization may be performed using a similarity between the actual spectrum and the calculated spectrum, and the structural information may indicate a structure, of two or more structures obtained by the structural optimization, whose similarity is equal to or greater than a predetermined threshold value.

[0021] This makes it possible to extract all candidate structures whose similarity is equal to or greater than a predetermined threshold. If there are multiple candidate structures whose similarity is equal to or greater than a predetermined threshold, the multiple structures can be compared, making it possible to identify the unknown crystal structure with greater accuracy.

[0022] Furthermore, the structural optimization may be performed by changing at least one of the lattice constant of the candidate structure and the positions of atoms of the candidate structure, and the structural optimization may be performed such that a second similarity between the actual spectrum and the calculated spectrum of the structure obtained by the structural optimization is higher than a first similarity between the actual spectrum and the calculated spectrum of the candidate structure before the structural optimization is performed.

[0023] This makes it possible to improve the accuracy of identifying an unknown crystal structure by performing structural optimization using known information on at least one of the lattice constants and atomic positions.

[0024] Furthermore, the structural optimization may be performed one or more times on the target candidate structure until a first convergence condition is satisfied, and the first convergence condition may be at least one of the second similarity being equal to or greater than a first threshold and the difference between the second similarity and the first similarity being equal to or less than a second threshold that is smaller than the first threshold.

[0025] This makes it easier to identify unknown crystal structures efficiently and accurately.

[0026] The structural optimization may be performed by a gradient descent method using the similarity between the actual spectrum and the calculated spectrum.

[0027] This makes it easier to identify unknown crystal structures efficiently and accurately.

[0028] The information processing method may further include a step of acquiring energy information indicating an energy calculated for each of the plurality of candidate structures, and the structural optimization may be performed using the actual spectrum information, the calculated spectrum information, and the energy information.

[0029] This makes it possible to avoid atomic arrangements that are highly similar but energetically unstable, and to optimize the structure to a crystal structure that is low in energy and highly similar, that is, a structure that is close to the unknown crystal structure of the material being searched for.

[0030] The structural optimization may be performed by a gradient descent method using a score, which is an index that combines the similarity between the actual spectrum and the calculated spectrum and the energy.

[0031] This makes it possible to avoid atomic arrangements that are highly similar but energetically unstable, and to optimize the structure to a crystal structure that is low in energy and highly similar, that is, a structure that is close to the unknown crystal structure of the material being searched for.

[0032] Furthermore, the structural optimization may be performed one or more times on the candidate structure until a second convergence condition is satisfied, and the second convergence condition may be a predetermined condition based on the score.

[0033] This makes it possible to avoid atomic arrangements that are highly similar but energetically unstable, and to optimize the structure to a crystal structure that is low in energy and highly similar, that is, a structure that is close to the unknown crystal structure of the material being searched for.

[0034] The actual spectrum and the calculated spectrum may be spectra obtained by X-ray diffraction.

[0035] This makes it easier to accurately reproduce a crystalline structure, which is a three-dimensional periodic structure.

[0036] Furthermore, an information processing method according to one aspect of the present disclosure is an information processing method executed by a computer, and includes the steps of generating structural information regarding the crystalline structure based on a correlation between actual spectral information indicating an actual spectrum obtained by actually measuring a material to be searched for and calculated spectral information indicating a calculated spectrum calculated for each of a plurality of candidate structures that are candidates for the crystalline structure of the material, and outputting the generated structural information.

[0037] This makes it easier to identify unknown crystal structures efficiently and accurately.

[0038] Moreover, an information processing system according to one aspect of the present disclosure includes a display unit that displays a first image that accepts input of material information regarding the composition of a material to be searched for and actual spectrum information indicating an actual spectrum obtained by actually measuring the material, and a display control unit that causes the display unit to display a second image that represents structural information regarding a crystal structure of the material, which is generated based on the input material information and the actual spectrum information.

[0039] This allows users to easily confirm the results of efficient and accurate identification of unknown crystal structures, and also allows users to identify unknown crystal structures using their own knowledge.

[0040] Furthermore, a program according to one aspect of the present disclosure causes a computer to execute the following steps: acquiring actual spectrum information indicating an actual spectrum obtained by actually measuring a material to be searched; acquiring material information regarding the composition of the material; generating, based on the material information, a plurality of candidate structure information regarding a plurality of candidate structures that are candidates for a crystal structure of the material, and acquiring calculated spectrum information indicating a calculated spectrum corresponding to each of the plurality of candidate structures; generating structural information regarding the crystal structure based on a correlation between the actual spectrum information and the calculated spectrum information; and outputting the generated structural information.

[0041] This makes it easier to identify unknown crystal structures efficiently and accurately.

[0042] Furthermore, the information processing method of the present disclosure can be realized as a computer program that causes a computer to execute the characteristic processes included in the information processing method of the present disclosure. Needless to say, such a computer program can be distributed on a computer-readable non-transitory recording medium such as a CD-ROM or via a communication network such as the Internet.

[0043] Hereinafter, the embodiments will be specifically described with reference to the drawings.

[0044] The embodiments described below are all comprehensive or specific examples of the present disclosure. The numerical values, shapes, materials, components, component placement and connection configurations, steps, step order, etc. shown in the following embodiments are merely examples and are not intended to limit the present disclosure. Furthermore, among the components in the following embodiments, components that are not described in the independent claims that represent the highest concepts are described as optional components. Furthermore, in all embodiments, the respective contents can be combined. Furthermore, each figure is a schematic diagram and is not necessarily an exact illustration. Furthermore, the same components are designated by the same reference numerals in each figure.

[0045] Furthermore, the information processing system according to the embodiment of the present disclosure may be configured so that all components are included in one computer, or may be configured as a system in which multiple components are distributed across multiple computers.

[0046] (First Embodiment) Hereinafter, an information processing system 100 (information processing method or program) according to a first embodiment of the present disclosure will be described in detail with reference to the drawings. FIG. 1 is a block diagram showing an overall configuration including the information processing system 100 according to the first embodiment. The information processing system 100 is configured as a computer such as a personal computer or a server. That is, the information processing system 100 may be realized by cloud computing, for example. In the first embodiment, the information processing system 100 will be described as a stationary computer.

[0047] The information processing system 100 includes a processing unit 10 and a storage unit 16. The processing unit 10 includes an acquisition unit 11, a candidate structure information generation unit 12, a calculated spectrum calculation unit 13, an optimization unit 14, and an output unit 15. The information processing system 100 is also connected to an input unit 2, a display control unit 30, and a display unit 3. The input unit 2, the display control unit 30, and the display unit 3 are configured by an information terminal used by a user, such as a smartphone, a tablet terminal, or a personal computer.

[0048] The input unit 2 is an input interface that accepts user input and is configured, for example, with a keyboard, a touch sensor, a touchpad, or a mouse. The input unit 2 accepts input operations by the user and outputs a signal corresponding to the input operation to the information processing system 100. In the present disclosure, the display unit 3 and the input unit 2 are configured independently of each other, but they may be configured integrally like a touch panel. In the present disclosure, the information processing system 100 does not include the display unit 3 or the input unit 2, but may include these.

[0049] The input unit 2 receives input of material information on the material to be searched for and actual spectrum information indicating an actual spectrum obtained by actually measuring the material to be searched for. In the first embodiment, the material information is the composition formula of the material to be searched for.

[0050] In the first embodiment, the actual spectrum is an X-ray diffraction pattern obtained by performing X-ray diffraction on the material to be searched. Similarly, the calculated spectrum, which will be described later, is also an X-ray diffraction pattern. The X-ray diffraction pattern is characterized by a three-dimensional periodic atomic arrangement pattern. Therefore, by performing structural optimization (described later) to increase the degree of agreement (i.e., similarity) between the actual spectrum and the calculated spectrum, it is possible to obtain a three-dimensional periodic atomic arrangement, i.e., a crystal structure, similar to the crystal structure obtained experimentally.

[0051] The display control unit 30 causes the display unit 3 to display images and the like based on information output from the output unit 15 of the information processing system 100 .

[0052] The display unit 3 displays images and the like under the control of the display control unit 30. The display unit 3 is, for example, a liquid crystal display, a plasma display, an organic EL (Electro-Luminescence) display, or the like, but is not limited to these.

[0053] The acquisition unit 11 acquires material information and real spectrum information. The acquisition unit 11 is the entity that executes the step of acquiring material information and the step of acquiring real spectrum information in the information processing method of the present disclosure. Specifically, the acquisition unit 11 acquires material information and real spectrum information input by a user via the input unit 2. For example, the user performs an operation to input material information and real spectrum information while viewing a first image displayed on the display unit 3 that accepts input of material information and real spectrum information.

[0054] The candidate structure information generating unit 12 generates candidate structure information regarding a plurality of candidate structures that are candidates for the crystal structure of the material, based on the material information acquired by the acquiring unit 11. The candidate structure information generating unit 12 is responsible for executing part of the step of acquiring calculated spectrum information in the information processing method of the present disclosure. Details of the processing executed by the candidate structure information generating unit 12 will be described later.

[0055] The calculated spectrum calculation unit 13 calculates a calculated spectrum corresponding to each of the plurality of candidate structures. The calculated spectrum calculation unit 13 is an entity that executes the step of acquiring calculated spectrum information in the information processing method of the present disclosure. Details of the processing executed by the calculated spectrum calculation unit 13 will be described later.

[0056] The optimization unit 14 generates structural information regarding the crystal structure of the material to be searched, based on the correlation between the actual spectrum information acquired by the acquisition unit 11 and the calculated spectrum information calculated by the calculated spectrum calculation unit 13. The optimization unit 14 is the entity that executes the step of generating structural information in the information processing method of the present disclosure.

[0057] In the first embodiment, the optimization unit 14 performs structural optimization on at least one of the multiple candidate structures using the actual spectrum and the calculated spectrum. The structural information indicates one or more structures obtained by the structural optimization. Here, the structure obtained by the structural optimization is considered to be the same as or similar to the unknown crystal structure of the material being searched for. In other words, the structure obtained by the structural optimization is a globally and locally stable structure. More specifically, the structural optimization is performed by a gradient descent method using the similarity between the actual spectrum and the calculated spectrum. The structural information indicates the structure with the highest similarity among the one or more structures obtained by the structural optimization, in other words, the structure considered to be closest to the unknown crystal structure of the material being searched for. Details of the structural optimization will be described later.

[0058] The output unit 15 outputs the image, etc. to the display control unit 30, thereby displaying the image, etc. on the display unit 3. The output unit 15 also outputs the structural information generated by the optimization unit 14. The output unit 15 is the entity that executes the step of outputting the structural information in the information processing method of the present disclosure. Specifically, the output unit 15 outputs the structural information by displaying a second image representing the structural information generated by the optimization unit 14 on the display unit 3.

[0059] The storage unit 16 is a recording medium that stores the material information and actual spectrum information acquired by the acquisition unit 11, multiple candidate structure information related to multiple candidate structures generated by the candidate structure information generation unit 12, calculated spectrum information calculated by the calculated spectrum calculation unit 13, and structure information indicating the structure related to the crystal structure generated by the optimization unit 14. The recording medium is, for example, a hard disk drive, a RAM (Random Access Memory), a ROM (Read Only Memory), or a semiconductor memory. Note that such a recording medium may be volatile or non-volatile.

[0060] [Operation] The following describes the operation (that is, the information processing method) of the information processing system 100 according to Embodiment 1. Fig. 2 is a flowchart showing an outline of the operation of the information processing system 100 according to Embodiment 1.

[0061] (Step S101) The acquisition unit 11 acquires material information and actual spectrum information. In step S101 (input step), the composition formula of the material to be searched for and the measured actual spectrum are input. The composition formula of the material to be searched for may be a composition formula predicted from the raw materials, or may be a composition formula identified by elemental analysis. When the total number of all elements included in the composition formula AaBb... (= a + b + ...) is relatively large, the crystal structure corresponding to the composition formula is complex. A is an element, a is the number of element A, B is an element, b is the number of element B, ..., a is an integer of 1 or more, b is an integer of 1 or more, .... The information processing method of the present disclosure is capable of handling composition formulas in which the total number exceeds 100. An example of a composition formula in which the total number exceeds 100 is Ca. ４０ Ti ４０ O １２０If a composition formula having a relatively large total value is treated by the density functional theory, the calculation cost will be high. In other words, the density functional theory cannot realistically handle a composition formula having a relatively large total value. On the other hand, in the information processing method of the present disclosure, in the first embodiment, it is not necessary to perform an energy calculation in the first place, and in the second embodiment described later, it is not necessarily necessary to use the density functional theory for the energy calculation, so it is possible to handle a composition formula having a relatively large total value.

[0062] If the composition formula of the material to be searched for is unknown, multiple composition formulas can be input. In this case, the information processing method of the present disclosure performs structural optimization on each of the multiple input composition formulas, and the structure with the highest degree of match among the multiple structures obtained can be output as the final structural information. The multiple input composition formulas and the multiple obtained structures may have a one-to-one correspondence. In the following processing, it is assumed that one composition formula is input in S101.

[0063] (Step S102) The candidate structure information generating unit 12 generates multiple pieces of candidate structure information relating to multiple candidate structures based on the material information acquired by the acquiring unit 11. In step S102 (candidate structure information generating step), multiple pieces of candidate structure information relating to multiple candidate structures are generated using a space group used to describe the symmetry of a three-dimensional structure, for example, based on the composition formula of the material to be searched acquired by the acquiring unit 11. FIG. 3 is a diagram showing an example of a list of candidate structure information. The list shown in FIG. 3 includes, from the left, a column indicating the space group, a column indicating the number of the candidate structure, and a column indicating the lattice constant and site (i.e., the position to be occupied by an atom in a crystal structure) in the candidate structure. FIG. 3 shows a list of candidate structure information relating to a material to be searched, where the composition formula is "Ca ４ Ti ４ O １２3 shows a list of candidate structure information when the space group number is "2" or "3". In the example shown in FIG. 3, candidate structure information corresponding to space group number "2" or "3" can be generated, but candidate structure information corresponding to space group number "142" cannot be generated. A plurality of candidate structures and a plurality of candidate structure information correspond one-to-one. Each of the plurality of candidate structure information may include information indicating the lattice constant and information indicating the site in the candidate structure.

[0064] The candidate structure information generating unit 12 generates candidate structure information when all atoms included in the composition formula of the material to be searched can be arranged at any site in the crystal structure indicated by the space group, and does not generate candidate structure information when all atoms cannot be arranged.The candidate structure information generating unit 12 then generates multiple pieces of candidate structure information regarding multiple candidate structures by performing the above process for all space groups.

[0065] FIG. 4 is an explanatory diagram of a method for generating candidate structure information. The arrangement of multiple atoms contained in a composition formula is determined under the constraint that the same atom is arranged at all t sites in the crystal structure, and the number of t sites is s. In FIG. 4, circles, triangles, and diamonds respectively represent different types of atoms. (a) in FIG. 4 represents four a sites, four b sites, four c sites, and eight d sites contained in a crystal structure indicated by space group number "62". In other words, (s, t) = (4, a), (4, b), (4, c), (8, d). Here, if the composition formula of the material to be searched is "Ca ４ Ti ４ O １２ ", four Ca atoms, four Ti atoms, and twelve O atoms can be arranged in the crystal structure under the above constraints, and therefore the candidate structure information generating unit 12 can generate candidate structure information corresponding to the space group number "62". (b) of FIG. 4 shows six a sites, six b sites, and twelve c sites contained in the crystal structure indicated by the space group number "178". In other words, (s, t) = (6, a), (6, b), (12, c). Here, if the composition formula of the material to be searched is "Ca ４ Ti ４ O １２", under the above constraints, four Ca atoms, four Ti atoms, and twelve O atoms cannot be arranged in the crystal structure. Therefore, the candidate structure information generating unit 12 cannot generate candidate structure information corresponding to the space group number "178."

[0066] FIG. 5 is a diagram showing a specific example of candidate structure information. FIG. 6 is a diagram showing another specific example of candidate structure information. In both FIG. 5(a) and FIG. 6(a), the composition formula of the material to be searched is "Ca ４ Ti ４ O １２ 5B and 6B are diagrams showing examples of candidate structure information when the composition formula of the material to be searched is "Ca ４ Ti ４ O １２ FIG. 10 is a diagram showing an example of the lattice constants and sites of candidate structures when

[0067] Here, the candidate structure information generating unit 12 is not limited to the above method, and may generate multiple pieces of candidate structure information using, for example, the Markov chain Monte Carlo method. This method makes it possible to generate candidate structure information using a probability density based on energy. In each step of the Markov chain Monte Carlo method, the atomic positions or the parameters of the crystal lattice are changed. At this time, only one or more of the atomic positions or the parameters of the crystal lattice may be changed. This method evaluates the energy before and after the change, and determines whether to accept or reject the change. By repeating the above steps and generating one piece of candidate structure information every several hundred to several thousand times, for example, it is possible to generate candidate structure information from a probability density based on energy.

[0068] Furthermore, in the Markov chain Monte Carlo method, by controlling the rejection probability by introducing a temperature term, it is possible to control whether to generate a large number of locally stable candidate structure information or a wide variety of candidate structure information. For example, if even partial information on the crystal structure of the material to be searched for is available, generating a large number of locally stable candidate structure information enables efficient identification of unknown crystal structures. On the other hand, if no information on the crystal structure of the material to be searched for is available, prioritizing the generation of a wide variety of candidate structure information makes it possible to select the most suitable crystal structure from a larger number of candidate structures. In this way, when generating candidate structure information using the Markov chain Monte Carlo method, it is also possible to efficiently search for unknown crystal structures by switching modes depending on whether or not information on the crystal structure of the material to be searched for is available.

[0069] Alternatively, the candidate structure information generator 12 may generate multiple pieces of candidate structure information using, for example, a genetic algorithm. This method allows for efficient generation of diverse candidate structure information. A genetic algorithm generates a child structure from a parent structure. Generally, the initial parent structure is a random structure in which atoms are randomly arranged in a randomly generated crystal lattice. A genetic algorithm generates a child structure through a mutation or crossover operation using one or two parent structures. For example, a mutation operation is performed by swapping the positions of atoms, and a crossover operation is performed by splitting and combining two structures. Both the mutation and crossover operations require a small computational load and can significantly change a structure at once. Therefore, generating candidate structure information using a genetic algorithm allows for efficient generation of diverse candidate structure information.

[0070] The candidate structure information generating unit 12 may randomly generate a plurality of pieces of candidate structure information, or may generate a plurality of pieces of candidate structure information using information on other crystal structures.

[0071] Hereinafter, steps S103 to S106 correspond to the optimization process. In the optimization process, structural optimization is performed on each of the multiple candidate structures corresponding to the multiple candidate structure information generated in S102. Here, structural optimization of a candidate structure refers to optimizing the lattice constant of the candidate structure and the coordinates (positions) of each atom within the candidate structure. In other words, structural optimization is performed by changing at least one of the lattice constant of the target candidate structure and the position of the atom within the candidate structure. The coordinates of each atom are expressed, for example, in a Cartesian coordinate system, fractional coordinates relative to the lattice, or polar coordinates. Furthermore, a multi-dimensional space that includes information on the elements themselves in addition to spatial information within the crystal may be defined and used as the coordinates of each atom.

[0072] The above-mentioned structural optimization may be performed by "changing the lattice constant of the candidate structure," "changing the positions of atoms in the candidate structure," or "changing the lattice constant of the candidate structure and changing the positions of atoms in the candidate structure."

[0073] In the information processing system 100 (information processing method) according to the first embodiment, the optimization step is performed by a gradient descent method using the similarity between the actual spectrum and the calculated spectrum. That is, in the information processing system 100 according to the first embodiment, structural optimization of the candidate structure is performed so that the actual spectrum matches the calculated spectrum. The similarity between the spectra is evaluated using an error index or a similarity index.

[0074] Here, the error index is an index for evaluating the error between spectra, and the smaller the value, the higher the degree of similarity. The error index can be obtained by evaluating, for example, Euclidean distance, Mahalanobis distance, Manhattan distance, Chebyshev distance, or Minkowski distance for each measurement point of each spectrum. These distances can also be converted into mean absolute error (MAE), mean square error (MSE), mean square error (RMSE), root mean square error ratio (RMSPE), mean absolute error ratio (MAPE), or the like, and calculated as a single index for each pair of spectra.

[0075] The similarity index is an index for evaluating the similarity between spectra, and the larger the value, the higher the similarity is evaluated. Examples of similarity indexes that can be used include cosine similarity, Pearson's correlation coefficient, and deviation pattern similarity.

[0076] In the optimization process, only one of these error indexes and similarity indexes may be used, or multiple indexes may be used. When multiple indexes are used, the similarity can be evaluated by a weighted average in which a coefficient is assigned to each of the multiple indexes. In the first embodiment, the index (similarity) used in the optimization process is cosine similarity.

[0077] (Step S103) The calculated spectrum calculation unit 13 calculates a calculated spectrum for one of the candidate structures (or the structure after structural optimization) among the plurality of candidate structures corresponding to the plurality of candidate structure information generated by the candidate structure information generation unit 12. In step S103 (calculated spectrum calculation step), the procedure for calculating the calculated spectrum will be described using an example in which an X-ray diffraction pattern is used. Fig. 7 is a flowchart showing an example of calculating the calculated spectrum.

[0078] <Step S201> The calculated spectrum calculation unit 13 calculates an X-ray diffraction pattern for the candidate structure (or the structure after structural optimization). The intensity of the X-ray diffraction pattern can be determined by the following formula (1) for the crystal planes defined by Miller indices h, k, and l: ｈｋｌ is the spacing between crystal planes, and d ｈｋｌ The relationship between the angle θ and the Bragg angle can be calculated using the Bragg equation shown in equation (2) and the wavelength λ of the X-rays used.

[0079]

[0080] In formula (1), "h", "k", and "l" are elements of the lattice plane (hkl), and "f ｊ " is the atomic scattering factor of atom j, "x ｊ "," "y ｊ "," "z ｊ" are the x-, y-, and z-coordinates of atom j, respectively, and "F(hkl)" represents the crystal structure factor. Since the square of the crystal structure factor corresponds to the peak intensity, the diffraction intensity of the hkl reflection can be calculated from the atomic coordinates and the type of element. In other words, an X-ray diffraction pattern is a spectrum that closely reflects the atomic arrangement and element type within a crystal structure, and is a spectrum that is useful for identifying the crystal structure.

[0081] <Step S202> Next, the calculated spectrum calculation unit 13 converts the discrete spectrum of the obtained X-ray diffraction pattern into a continuous spectrum. The discrete spectrum can be converted into a continuous spectrum by applying a Gaussian function, a Lorentzian function, a Pseudo-Voigt function, or the like. FIG. 8 shows examples of a discrete spectrum and a continuous spectrum. FIG. 8(a) shows the discrete spectrum of the X-ray diffraction pattern, and FIG. 8(b) shows the continuous spectrum obtained by converting the discrete spectrum shown in FIG. 8(a) using a Gaussian function (standard deviation: 0.3). In both FIG. 8(a) and FIG. 8(b), the vertical axis represents intensity, and the horizontal axis represents 2θ ("2θ" is the diffraction angle). The unit of 2θ is angle.

[0082] As will be described later, in the optimization process, the similarity between the calculated spectrum and the real spectrum, both of which are continuous spectra, is calculated. In this case, it is desirable to remove the background from the real spectrum. This is because removing the background makes the calculation of the similarity between the calculated spectrum and the real spectrum more accurate. It is also possible to convert the real spectrum, which is a continuous spectrum, into a discrete spectrum and then convert it back into a continuous spectrum, and then calculate the similarity. In this case, by making the conversion of the real spectrum to a continuous spectrum and the conversion of the calculated spectrum to a continuous spectrum under the same conditions, a more accurate calculation of the similarity is possible. This method enables the calculation of the similarity to be less dependent on noise in the measurement of the real spectrum.

[0083] In the optimization process, when calculating the similarity between the calculated spectrum and the real spectrum, both of which are discrete spectra, the real spectrum can be converted into a discrete spectrum by extracting peak positions and intensities. In this case, all peaks may be converted, or only some of the peaks may be converted. For example, if the measurement of the real spectrum contains a lot of noise, the influence of the noise can be suppressed by extracting only peaks whose intensities are above a certain level.

[0084] <Step S203> Next, the calculated spectrum calculation unit 13 performs normalization processing on the continuous spectrum of the converted calculated spectrum, thereby normalizing the intensity of the continuous spectrum of the calculated spectrum.

[0085] <Step S204> The calculated spectrum calculation unit 13 then outputs the normalized calculated spectrum, which is used to calculate the similarity in the optimization step.

[0086] The above-mentioned steps S201 to S204 are executed as step S103.

[0087] (Step S104) Returning to FIG. 2 , next, the optimization unit 14 calculates the similarity between the real spectrum, which is the measured spectrum acquired by the acquisition unit 11, and the calculated spectrum calculated by the calculated spectrum calculation unit 13. As already described, in the first embodiment, the optimization unit 14 evaluates the similarity between the real spectrum and the calculated spectrum using cosine similarity, which is a similarity index. Therefore, the similarity is expressed as a value between 0 and 1, and the larger the value, the more similar the real spectrum and the calculated spectrum are.

[0088] FIG. 9 is an explanatory diagram of the similarity between the actual spectrum and the calculated spectrum. The table shown in FIG. 9(a) includes, from left to right, a column indicating the candidate structure number, a column indicating the calculated spectrum, and a column indicating the similarity. FIG. 9(b) shows the actual spectrum. In the example shown in FIG. 9(a), the similarity between the calculated spectrum and the actual spectrum of the candidate structure "Structure 1" is relatively low, and the similarity between the calculated spectrum and the actual spectrum of the candidate structure "Structure 2" is relatively high. In the diagram showing the calculated spectrum shown in FIG. 9(a) and the diagram showing the actual spectrum shown in FIG. 9(b), the vertical axis represents intensity and the horizontal axis represents 2θ ("2θ" is the diffraction angle). The unit of 2θ is angle.

[0089] (Step S105) Next, the optimization unit 14 determines whether the calculated similarity satisfies a first convergence condition. Here, the first convergence condition is a condition that the calculated similarity is equal to or greater than a first threshold (e.g., 0.99) when structural optimization has not yet been performed. On the other hand, when structural optimization has been performed one or more times, the first convergence condition is at least one of the following: the second similarity is equal to or greater than the first threshold, and the difference between the second similarity and the first similarity is equal to or less than a second threshold (e.g., 0.01) that is smaller than the first threshold. When structural optimization has been performed one or more times, the first convergence condition may be "the second similarity is equal to or greater than the first threshold," "the difference between the second similarity and the first similarity is equal to or less than a second threshold that is smaller than the first threshold," or "the second similarity is equal to or greater than the first threshold, and the difference between the second similarity and the first similarity is equal to or less than the second threshold."

[0090] The first similarity is the similarity between the actual spectrum and the calculated spectrum of the candidate structure before structural optimization. The second similarity is the similarity between the actual spectrum and the calculated spectrum of the structure obtained by structural optimization. In other words, the second similarity is the similarity between the actual spectrum and the calculated spectrum calculated for the structure after the lattice constants and atomic positions of the candidate structure have been updated in step S106, which will be described later. Furthermore, if structural optimization has been performed multiple times, the second similarity is the similarity for the structure after the latest structural optimization, and the first similarity is the similarity for the structure after the structural optimization immediately before the latest structural optimization.

[0091] If the similarity satisfies the first convergence condition (step S105: Yes), the optimization unit 14 then executes step S107. On the other hand, if the similarity does not satisfy the first convergence condition (step S105: No), the optimization unit 14 then executes step S106. That is, if the similarity for the candidate structure or a structure obtained by structurally optimizing the candidate structure is equal to or greater than the first threshold, the optimization process ends. Also, if the difference between the second similarity and the first similarity for the candidate structure or a structure obtained by structurally optimizing the candidate structure is equal to or less than the second threshold (in other words, if the gradient, described below, is equal to or less than the threshold), the optimization process ends. Note that an upper limit on the number of iterations of the optimization process may be set. In this case, the process may proceed to S107 when the number of iterations of the optimization process reaches the upper limit.

[0092] In this way, the structural optimization is performed one or more times on the target candidate structure until the first convergence condition is satisfied or the upper limit number of repetitions of the optimization process is reached. Note that if the similarity between the candidate structures satisfies the first convergence condition, structural optimization may not be performed even once.

[0093] (Step S106) Next, the optimization unit 14 updates the lattice constants and atomic positions of the candidate structure (or the structure after structural optimization). First, the optimization unit 14 calculates a gradient with respect to the similarity in order to change the lattice constants and atomic positions of the candidate structure (or the structure after structural optimization) so as to improve the similarity (increase when similarity coordinates are used, decrease when error indices are used). The gradient can be calculated by partially differentiating the similarity with respect to each component of the lattice constants and atomic coordinates. Then, the optimization unit 14 updates the lattice constants and atomic positions of the candidate structure (or the structure after structural optimization) by applying an optimization algorithm described later using the calculated gradient. In the first embodiment, both the lattice constants and the atomic positions are updated, but only one of them may be updated. Furthermore, the atomic positions may be updated for all atomic positions or for only one atomic position. Then, the information processing system 100 (information processing method) returns to step S103 and executes the optimization process again.

[0094] The optimization algorithm may be a steepest descent method, a Newton method, a quasi-Newton method, a conjugate gradient method, or a derivative of these methods. Alternatively, the optimization algorithm may be a moving average of the gradient, or an algorithm such as Adagrad, Adadelta, or Adam that adaptively changes the learning rate in response to changes in the gradient.

[0095] FIG. 10 is an explanatory diagram of structural optimization by the information processing system 100 according to the first embodiment. In FIG. 10, the vertical axis represents similarity, and the horizontal axis represents structural space. In the example shown in FIG. 10, the pre-optimization structure before structural optimization is performed is located midway on the similarity surface, has a relatively low similarity, and is an unstable structure. On the other hand, the post-optimization structure after one or more structural optimizations along the gradient direction are performed is located in the valley of the similarity surface, has a relatively high similarity, and is a locally stable structure.

[0096] In this way, the structural optimization is performed along the gradient direction (i.e., the direction in which the similarity improves) so that the gradient is equal to or less than a threshold value. In other words, the structural optimization is performed so that the second similarity between the actual spectrum and the calculated spectrum of the structure obtained by structural optimization becomes higher than the first similarity between the actual spectrum and the calculated spectrum of the candidate structure before structural optimization.

[0097] The above-described optimization process is shown again in Fig. 11. Fig. 11 is a flowchart showing an example of the optimization process performed by the information processing system 100 according to the first embodiment.

[0098] <Step S301> First, the calculated spectrum calculation unit 13 calculates a calculated spectrum for one of the candidate structures (or the structure after structural optimization) corresponding to the plurality of pieces of candidate structure information generated by the candidate structure information generation unit 12. Step S301 is the same process as step S103 (see FIG. 2 ).

[0099] <Step S302> Next, the optimization unit 14 calculates the similarity between the real spectrum acquired by the acquisition unit 11 and the calculated spectrum calculated by the calculated spectrum calculation unit 13. Step S302 is the same process as step S104 (see FIG. 2).

[0100] <Step S303> Next, the optimization unit 14 determines whether the calculated similarity satisfies a first convergence condition. Step S303 is the same process as step S105 (see FIG. 2). If the similarity satisfies the first convergence condition (step S303: Yes), the optimization process ends. On the other hand, if the similarity does not satisfy the first convergence condition (step S303: No), the optimization unit 14 next executes step S304.

[0101] <Step S304> Next, the optimization unit 14 calculates the lattice constant and the gradient of the atomic positions of the candidate structure (or the structure after structural optimization). Step S304 is the same process as part of step S106 (see FIG. 2).

[0102] <Step S305> Next, the optimization unit 14 updates the lattice constants and atomic positions of the candidate structure (or the structure after structural optimization) by changing the lattice constants and atomic positions along the calculated gradient direction. Step S305 is the same process as part of step S106 (see FIG. 2). Then, the information processing system 100 (information processing method) returns to step S301 and executes the optimization process again.

[0103] (Step S107) Returning to FIG. 2 , the optimization unit 14 determines whether or not other candidate structures exist. If other candidate structures exist (step S107: No), the process returns to step S103, and the optimization process is performed on the other candidate structures. On the other hand, if other candidate structures do not exist (step S107: Yes), the information processing system 100 (information processing method) next executes step S108.

[0104] (Step S108) The output unit 15 outputs the structural information generated by the optimization unit 14. In step S108 (output step), the structural information obtained by the optimization step is output. The structural information includes information on the lattice constants and atomic positions of one or more structures generated by the optimization unit 14. The output format of the structural information is not particularly limited, and may be, for example, a simple list of parameters or a standardized format such as CIF (Crystalographic Information File). Here, the output unit 15 outputs the structural information by displaying a second image representing the structural information generated by the optimization unit 14 on the display unit 3.

[0105] The output unit 15 may output one or more pieces of structural information determined in the optimization step. The output unit 15 may cause the display unit 3 to display the one or more pieces of structural information. Each of the one or more pieces of structural information may correspond to one piece of material information, i.e., one composition formula, input in step S101. In step S108 (output step), the one or more pieces of structural information may be output. Each of the one or more pieces of structural information may include information on lattice constants and atomic positions that determine each of one or more candidate structures that are one or more candidates for the crystal structure corresponding to the composition formula.

[0106] 26 is a diagram showing an example of one or more pieces of structural information. The one or more pieces of structural information are the first structural information, through the n-th structural information, where n is a natural number equal to or greater than 1.

[0107] The lattice constants include the lengths of sides a, b, and c of the unit cell, the angle γ between sides a and b, the angle α between sides b and c, and the angle β between side c and side a. In Figure 26, the length of side a is shown in column a, the length of side b in column b, and the length of side c in column c. In Figure 26, angle α is shown in column α, angle β in column β, and angle γ in column γ.

[0108] The positions of atoms are indicated by three-dimensional coordinates (x, y, z). In FIG. 26, the first structure information includes, as the atomic position information, d three-dimensional coordinates of atom A, e three-dimensional coordinates of atom B, and f three-dimensional coordinates of atom C, while the n-th structure information includes, as the atomic position information, d three-dimensional coordinates of atom A, e three-dimensional coordinates of atom B, and f three-dimensional coordinates of atom C. The three-dimensional coordinates of the d atoms A included in the first structure information are (x Ａ１１ , y Ａ１１ , z Ａ１１ ), ~, (x Ａ１ｄ , y Ａ１ｄ , z Ａ１ｄ )

[0109] As described above, in the first embodiment, the optimization process is performed using the correlation (similarity) between the X-ray diffraction pattern (actual spectrum) obtained by actually measuring the unknown material to be searched for and the X-ray diffraction patterns (calculated spectra) calculated for each of a plurality of candidate structures that are candidates for the crystal structure of the material. Therefore, in the first embodiment, it is easy to efficiently and accurately identify the unknown crystal structure.

[0110] (Embodiment 2) An overview of an information processing system 200 (information processing method or program) according to embodiment 2 of the present disclosure will be first described below. The information processing system 200 (information processing method) according to embodiment 2 uses an optimization method that uses both spectrum and energy, making it easy to efficiently and accurately identify unknown crystal structures. The differences between this optimization method and conventional methods will be described below.

[0111] In the conventional Rietveld method, candidate structure information about a candidate structure created by an analyst is input, and an X-ray diffraction pattern for the candidate structure is calculated. The calculated X-ray diffraction pattern is then compared with an X-ray diffraction pattern obtained experimentally, and an error is calculated. The analyst then modifies the candidate structure information about the candidate structure based on the obtained error and re-enters it. This series of processes is repeated until the error is acceptable, thereby identifying the crystal structure.

[0112] In conventional density functional theory (DFT) methods, analysts prepare a large number of candidate structure information and calculate their energies. Based on the obtained energies, analysts then prepare a large number of new candidate structure information and calculate their energies. These processes are repeated until the energy falls below an acceptable value, thereby identifying the crystal structure.

[0113] In other words, the identification of crystal structure by the Rietveld method is an optimization method using spectra, and the identification of crystal structure by density functional theory is an optimization method using energy.

[0114] In identifying crystal structures using the Rietveld method, it is generally necessary to input candidate structure information about candidate structures that are very close to the correct crystal structure, making it difficult to identify unknown crystal structures. Furthermore, in identifying crystal structures using density functional methods, there is a problem in that the resulting structure often differs from the structure actually obtained experimentally.

[0115] On the other hand, in the optimization method according to the second embodiment, the crystal structure is identified by an optimization algorithm that uses both the spectrum and the energy. This eliminates the need to input candidate structure information about candidate structures that are close to the correct crystal structure, and makes it possible to search for a structure that is similar to the spectrum obtained in an experiment, i.e., close to the correct crystal structure.

[0116] An information processing system 200 (information processing method or program) according to the second embodiment will be described in detail below with reference to the drawings. FIG. 12 is a block diagram showing an overall configuration including the information processing system 200 according to the second embodiment. As shown in FIG. 12, the information processing system 200 according to the second embodiment differs from the information processing system 100 according to the first embodiment in that the processing unit 10 further includes an energy calculation unit 17, and the optimization unit 14 further refers to the energy calculated by the energy calculation unit 17. Note that, hereinafter, a description of the configuration common to the information processing system 100 according to the first embodiment will be omitted.

[0117] The energy calculation unit 17 calculates the energy for each of the plurality of candidate structures corresponding to the plurality of candidate structure information generated by the candidate structure information generation unit 12. The energy calculation unit 17 is an entity that executes the step of acquiring energy information indicating the energy calculated for each of the plurality of candidate structures in the information processing method of the present disclosure. Details of the processing executed by the energy calculation unit 17 will be described later.

[0118] In the second embodiment, the optimization unit 14 performs structural optimization on at least one of the multiple candidate structures using the real spectrum information acquired by the acquisition unit 11, the calculated spectrum information calculated by the calculated spectrum calculation unit 13, and the energy information calculated by the energy calculation unit 17. That is, in the second embodiment, the structural optimization is performed using the real spectrum information, the calculated spectrum information, and the energy information. Furthermore, in the second embodiment, the structural optimization is performed by a gradient descent method using a score, which is an index combining the similarity between the real spectrum and the calculated spectrum and the energy. Details of the structural optimization will be described later.

[0119] [Operation] The following describes the operation (that is, the information processing method) of the information processing system 200 according to Embodiment 2. Fig. 13 is a flowchart showing an outline of the operation of the information processing system 200 according to Embodiment 2.

[0120] (Step S401) The acquisition unit 11 acquires material information and actual spectrum information. Step S401 is the same process as step S101 (see FIG. 2).

[0121] (Step S402) The candidate structure information generating unit 12 generates a plurality of pieces of candidate structure information regarding a plurality of candidate structures based on the material information acquired by the acquiring unit 11. Step S402 is the same process as step S102 (see FIG. 2).

[0122] Hereinafter, steps S403 to S407 correspond to the optimization step. In the information processing system 200 (information processing method) according to the second embodiment, the structural optimization in the optimization step is performed by a gradient descent method using a score, which is an index that combines the similarity between the actual spectrum and the calculated spectrum and the energy.

[0123] (Step S403) The calculated spectrum calculation unit 13 calculates a calculated spectrum for one of the candidate structures (or the structure after structural optimization) corresponding to the plurality of pieces of candidate structure information generated by the candidate structure information generation unit 12. Step S403 is the same process as step S103 (see FIG. 2).

[0124] (Step S404) The energy calculation unit 17 calculates the energy of the candidate structure (or the structure after structural optimization) that is the calculation target by the calculated spectrum calculation unit 13. The energy calculated in step S404 (energy calculation step) may be any amount that gives an order to a group of structures having the composition ratio of the material to be searched, and may be, for example, an amount obtained by calculating the cohesive energy or the formation energy on an atomic basis.

[0125] In the second embodiment, the energy calculation unit 17 calculates the energy using an interatomic potential. Here, the interatomic potential refers to a group of potentials that describe interactions between atoms. As the interatomic potential, for example, Lennard-Jones, Buckingham, Born-Mayer-Huggins, Stillinger-Weber, Tersoff, or Bond-Valence-Site-Energy can be used. Furthermore, it is also possible to use machine learning or deep learning to approximate an interatomic potential obtained by, for example, density functional theory, and this can also be used as an interatomic potential.

[0126] This method allows for high-speed energy calculations, making it easier to efficiently identify crystal structures. Generally, energy calculations using interatomic potentials can be performed much faster than energy calculations using density functional theory. Meanwhile, the accuracy of energy calculations using interatomic potentials is often inferior to that of density functional theory. However, in the information processing method disclosed herein, structural optimization is performed using both spectrum and energy, so the low accuracy of energy calculations using interatomic potentials is not an issue.

[0127] The procedure for calculating the energy using the interatomic potential will be described below. Fig. 14 is a flowchart showing an example of energy calculation.

[0128] <Step S501> The energy calculation unit 17 creates a list of pairs of two atoms for all atoms included in the candidate structure (or the structure after structural optimization). For example, assume that the candidate structure includes eight atoms, "p1", ..., "p8". In this case, the energy calculation unit 17 creates a list of pairs of two atoms, "p1-p2", "p1-p3", etc., for a total of 28 (= ８ C ２ ) Create a list of pairs.

[0129] <Step S502> Next, the energy calculation unit 17 calculates the distance between two atoms for each of all pairs included in the created list.

[0130] <Step S503> Next, the energy calculation unit 17 calculates the energy acting between the two atoms for each of all pairs included in the created list, based on the calculated distance between the two atoms and the atomic numbers of each of the two atoms.

[0131] <Step S504> Then, the energy calculation unit 17 calculates the energy of the candidate structure (or the structure after structural optimization) by summing up the energies of all pairs included in the created list. Here, the energy calculation unit 17 may simply sum up the energies between all atoms, or may sum up the energies weighted for each atom. For example, when optimizing only a pair of two specific atoms, such weighting can be used to prioritize the optimization of that pair of atoms.

[0132] FIG. 15 is a diagram showing an example of a list of the energies of candidate structures. The example shown in FIG. 15 is a list of candidate structures whose composition formula is "Ca ４ Ti ４ O １２ 15 is a list of energies of candidate structures when the energy calculation unit 17 calculates the energy of the candidate structure (unit: eV / atom).

[0133] 13 , the optimization unit 14 calculates the similarity between the real spectrum acquired by the acquisition unit 11 and the calculated spectrum calculated by the calculated spectrum calculation unit 13. Then, the optimization unit 14 calculates a weighted average of the calculated similarity and the energy calculated by the energy calculation unit 17, thereby calculating a score.

[0134] (Step S406) Next, the optimization unit 14 determines whether the calculated score satisfies a second convergence condition. Here, the second convergence condition is a predetermined condition based on the score. For example, when structural optimization has not yet been performed, the second convergence condition is a condition that the calculated score is equal to or greater than a third threshold. On the other hand, when structural optimization has been performed one or more times, the second convergence condition is at least one of the following: the second score is equal to or greater than the third threshold, and the difference between the second score and the first score is equal to or less than a fourth threshold that is smaller than the third threshold. When structural optimization has been performed one or more times, the second convergence condition may be "the second score is equal to or greater than the third threshold," "the difference between the second score and the first score is equal to or less than a fourth threshold that is smaller than the third threshold," or "the second score is equal to or greater than the third threshold and the difference between the second score and the first score is equal to or less than the fourth threshold."

[0135] The first score is the score of the candidate structure before structural optimization is performed. The second score is the score of the structure obtained by structural optimization. In addition, when structural optimization is performed multiple times, the second score is the score of the structure after the latest structural optimization, and the first score is the score of the structure after the structural optimization immediately before the latest structural optimization.

[0136] If the score satisfies the second convergence condition (step S406: Yes), the optimization unit 14 then executes step S408. On the other hand, if the score does not satisfy the second convergence condition (step S406: No), the optimization unit 14 then executes step S407. That is, if the score for the candidate structure or a structure obtained by structurally optimizing the candidate structure is equal to or greater than the third threshold, the optimization process ends. Also, if the difference between the second score and the first score for the candidate structure or a structure obtained by structurally optimizing the candidate structure is equal to or less than the fourth threshold (in other words, if the gradient is equal to or less than the threshold), the optimization process ends.

[0137] In this way, the structural optimization is performed one or more times on the candidate structure until the second convergence condition is satisfied. Note that if the score for the candidate structure satisfies the second convergence condition, structural optimization may not be performed even once.

[0138] (Step S407) Next, the optimization unit 14 updates the lattice constants and atomic positions of the candidate structure (or the structure after structural optimization). First, the optimization unit 14 calculates a gradient with respect to the score in order to change the candidate structure (or the structure after structural optimization) so as to improve the score. The gradient can be calculated by partially differentiating the score with respect to each component of the lattice constants and atomic coordinates. Then, the optimization unit 14 updates the lattice constants and atomic coordinates of the candidate structure (or the structure after structural optimization) by applying the same optimization algorithm as in the first embodiment using the calculated gradient. In other words, the structural optimization is performed along the gradient direction (i.e., the direction in which the score improves) so that the gradient is equal to or less than the threshold. Then, the information processing system 200 (information processing method) returns to step S403 and executes the optimization process again.

[0139] The above-mentioned optimization process is shown again in Fig. 16. Fig. 16 is a flowchart showing an example of the optimization process performed by the information processing system 200 according to the second embodiment.

[0140] <Step S601> First, the calculated spectrum calculation unit 13 calculates a calculated spectrum for one of the candidate structures (or the structure after structural optimization) corresponding to the plurality of pieces of candidate structure information generated by the candidate structure information generation unit 12. Step S601 is the same process as step S403 (see FIG. 13 ).

[0141] <Step S602> Next, the optimization unit 14 calculates the similarity between the real spectrum acquired by the acquisition unit 11 and the calculated spectrum calculated by the calculated spectrum calculation unit 13. Step S602 is the same processing as part of step S405 (see FIG. 13 ).

[0142] <Step S603> Next, the energy calculation unit 17 calculates the energy of the candidate structure (or the structure after structural optimization) selected as the calculation target by the calculated spectrum calculation unit 13. Step S603 is the same process as step S404 (see FIG. 13 ). Note that the order of executing steps S602 and S603 may be reversed.

[0143] <Step S604> Next, the optimization unit 14 calculates a score by calculating a weighted average of the calculated similarity and the energy calculated by the energy calculation unit 17. Step S604 is the same process as step S405 (see FIG. 13 ).

[0144] <Step S605> Next, the optimization unit 14 determines whether the calculated score satisfies the second convergence condition. Step S605 is the same process as step S406 (see FIG. 13). If the score satisfies the second convergence condition (step S605: Yes), the optimization process ends. On the other hand, if the score does not satisfy the second convergence condition (step S605: No), the optimization unit 14 next executes step S606.

[0145] <Step S606> Next, the optimization unit 14 calculates the lattice constant and the gradient of the atomic positions of the candidate structure (or the structure after structural optimization). Step S606 is the same process as part of step S407 (see FIG. 13).

[0146] <Step S607> Next, the optimization unit 14 updates the lattice constants and atomic positions of the candidate structure (or the structure after structural optimization) by changing the lattice constants and atomic positions along the calculated gradient direction. Step S607 is the same process as part of step S407 (see FIG. 13 ). Then, the information processing system 200 (information processing method) returns to step S601 and executes the optimization process again.

[0147] (Step S408) Returning to FIG. 13 , the optimization unit 14 determines whether or not other candidate structures exist. If other candidate structures exist (step S408: No), the process returns to step S403, and the optimization process is performed on the other candidate structures. On the other hand, if other candidate structures do not exist (step S408: Yes), the information processing system 200 (information processing method) next executes step S409.

[0148] (Step S409) The output unit 15 outputs the structural information generated by the optimization unit 14. In step S409 (output step), one or more locally stable structures obtained by the optimization step are output as structural information. The structural information includes information on the lattice constants and atomic positions of the one or more structures generated by the optimization unit 14. The output format of the structural information is not particularly limited, and may be, for example, a simple list of parameters or a standardized format such as CIF (Crystalographic Information File). Here, the output unit 15 outputs the structural information by displaying a second image representing the structural information generated by the optimization unit 14 on the display unit 3.

[0149] The output unit 15 may output one or more pieces of structural information determined in the optimization step. The output unit 15 may cause the display unit 3 to display the one or more pieces of structural information. Each of the one or more pieces of structural information may correspond to one piece of material information, i.e., one composition formula, acquired in step S401. In step S409 (output step), the one or more pieces of structural information may be output. Each of the one or more pieces of structural information may include information on lattice constants and atomic positions that determine each of one or more candidate structures that are one or more candidates for the crystal structure corresponding to the composition formula.

[0150] As described above, in the second embodiment, the candidate structure is optimized so that it is thermodynamically stable and the actual spectrum matches the calculated spectrum. This allows for the identification of a more realistic crystal structure. In the second embodiment, the gradient is calculated for the score calculated from the weighted average of the similarity and energy. Therefore, by adjusting the coefficients of the similarity and energy when calculating the score, it is possible to optimize the candidate structure while balancing thermodynamic validity and spectral consistency. Below, the effect of using the gradient for the score, which is the sum of the spectral similarity and energy, is described.

[0151] FIG. 17 is an explanatory diagram of structural optimization by the information processing system 200 according to the second embodiment. In (a) of FIG. 17, the solid line represents the score surface, the dotted line represents the energy surface, and the dashed line represents the similarity surface. In the example shown in (a) of FIG. 17, two valleys exist on the similarity surface. When an optimized structure after one or more structural optimizations is located in one valley, the similarity is relatively high and the structure is locally stable, i.e., the correct structure. However, when the optimized structure is located in the other valley, the similarity is relatively low and the structure appears locally stable at first glance, but it is an incorrect structure.

[0152] Here, the actual spectrum of an X-ray diffraction pattern is generally obtained from a crystal structure with high symmetry. Therefore, a crystal structure having a calculated spectrum that shows a high similarity to the actual spectrum has an atomic arrangement aligned like the correct structure shown in FIG. 17(a). Therefore, a group of atoms with a random initial arrangement is optimized in a direction that aligns the atomic arrangement by an optimization operation using the gradient of similarity. In this case, on the similarity surface, as shown in FIG. 17(b), the structure is not optimized along the gradient toward the correct structure, but along the gradient toward the incorrect structure, resulting in multiple atoms overlapping at the same coordinates. Such an atomic arrangement is energetically very unstable and therefore should not occur in practice.

[0153] On the other hand, in the score surface, as shown in (c) of Figure 17, structural optimization is performed along a gradient toward the correct structure. That is, in structural optimization using a gradient with respect to a score obtained by adding together energy and similarity, an arrangement in which multiple atoms overlap is disadvantageous in terms of score, so the gradient direction is not a direction toward the incorrect structure but a direction toward the correct structure. As a result, in the second embodiment, it is possible to avoid atomic arrangements that are highly similar but energetically unstable, and it is possible to perform structural optimization to a crystal structure that is low in energy and highly similar, that is, a structure that is close to the unknown crystal structure of the material being searched for.

[0154] In the second embodiment, an optimization step using only similarity may be additionally performed on the structure that has been optimized using the score, thereby further increasing the similarity of the finally obtained crystal structure.

[0155] (User Interface) The user interface of the information processing system 200 according to the second embodiment will be described below with reference to the drawings. FIG. 18 is a diagram showing an image displayed on the display unit 3 in the information processing system 200 according to the second embodiment. In FIG. 18, the "Spectrum Input" area corresponds to the first image. Also, an area including the "Spectrum Input" area, the "Structure Generation Condition Setting" area, and the "Optimization Condition Setting" area may correspond to the first image. Also, in FIG. 18, the "Output" area corresponds to the second image.

[0156] The "Spectrum Input" area displays a text box for entering the composition formula of the material, a text box for entering the number of atoms contained in the crystal structure, a button for selecting and uploading X-ray diffraction pattern data obtained in an experiment, a check box for selecting whether or not to perform conversion to a continuous spectrum, and a check box for selecting whether or not to perform normalization processing.

[0157] The "Structure Generation Condition Setting" area displays a pull-down menu for selecting a method for generating candidate structure information for candidate structures, and a text box for inputting the number of candidate structure information for the candidate structures to be generated.

[0158] The "optimization condition setting" area displays text boxes for inputting weighting coefficients for energy and similarity when calculating the score, a pull-down menu for selecting an interatomic potential, a pull-down menu for selecting an index for evaluating similarity, a pull-down menu for selecting a convergence condition, and a text box for inputting a threshold value for the convergence condition.

[0159] The "Output" area displays a list of one or more structures that have been structurally optimized and an image of the structure selected by the user. The image is of the CaTiO structure identified by the structure ID = 004 in FIG. 18. ３ The list includes, from left to right, a column displaying an identification number (ID) for each structure, a column showing the score of the structure, and a column showing whether the structure satisfies the convergence condition. Here, if a structure does not satisfy the convergence condition (i.e., "False"), this corresponds to, for example, a case where the convergence condition is not satisfied even after performing structural optimization a predetermined number of times or more.

[0160] When the user selects the download button included in the "output" area in Fig. 18, the processing unit 10 receives a signal indicating that the download button has been selected. When the processing unit 10 receives the selection signal, the processing unit 10 downloads the composition CaTiO identified by structure ID = 004. ３ The display control unit 30 then sends an instruction to the display control unit 30 to display on the display unit 3 the lattice constant and sites (i.e., atomic positions) of the crystal structure corresponding to the structure ID=004. When the display control unit 30 receives the instruction, the display control unit 30 displays the lattice constant and sites (i.e., atomic positions) of the crystal structure corresponding to the structure ID=004. ３ The lattice constants and sites (i.e., atomic positions) of the crystal structure corresponding to the structure ID=004 are displayed on the display unit 3. The display format of the lattice constants and sites of the crystal structure may be the format shown in FIG. 5(b). ３ The display unit 3 may display the values ​​of the lattice constants a, b, c, α, β, and γ of the corresponding crystal structure, the three-dimensional coordinates of one Ca atom, the three-dimensional coordinates of one Ti atom, and the three-dimensional coordinates of each of the three O atoms.

[0161] The list displayed in the "Output" area is ｉ The information may include a plurality of i, where i is a natural number between 2 and n, and n is the number of candidate structures. ｉ = [Structure ID ｉ ,Score ｉ , structure ID ｉ Information on whether the candidate structure identified by satisfies the convergence condition or not, structure ID ｉThe lattice constant and structure ID of the candidate structure identified by ｉ For example, the information ４ Structure ID included in ４ 004, Information ４ Scores included in ４ is 0.999.

[0162] If the candidate structure identified by structure IDi does not satisfy the convergence condition (i.e., if the "Convergence" column in the list included in the "Output" area of ​​Figure 18 indicates False), the list does not include multiple lattice constants of the candidate structure identified by structure IDi, and does not include the respective positions of multiple atoms included in the candidate structure identified by structure IDi.

[0163] The "output" area in FIG. 18 may include the information shown in FIG. 27. FIG. 27 is a diagram showing an example of information included in the "output" area in FIG. 18. FIG. 27 shows the lattice constants of a crystal structure corresponding to a structure ID and the positions of atoms included in the crystal structure. The information shown in FIG. 27 includes one or more structure IDs. Each of one or more candidate structures that correspond one-to-one to the one or more structure IDs satisfies the convergence condition. The explanation of the lattice constants and the positions of atoms in FIG. 27 can be understood by referring to the explanation of the lattice constants and the positions of atoms in FIG. 26.

[0164] After the user inputs desired parameters in the "Spectrum Input" area, the "Structure Generation Condition Setting" area, and the "Optimization Condition Setting" area, the user selects the "Start" icon, which causes the information processing system 200 to execute a series of processes and display the processing results in the "Output" area.

[0165] (Examples) Below, an example (Example 1) of the information processing system 100 according to embodiment 1 and an example (Example 2) of the information processing system 200 according to embodiment 2 will be described, along with comparisons with an example (Comparative Example 1) of the information processing system according to Comparative Example 1 and an example (Comparative Example 2) of the information processing system according to Comparative Example 2.

[0166] 19 is a flowchart showing an outline of the operation of the information processing system according to Comparative Example 1. The information processing system according to Comparative Example 1 differs from the information processing system 100 according to Embodiment 1 in that it calculates energy instead of calculating a calculated spectrum, and performs structural optimization so that the energy satisfies a convergence condition (i.e., is equal to or less than a threshold value).

[0167] In the flow shown in FIG. 19 , step S701 is the same process as step S101 (see FIG. 2 ), except that real spectrum information is not acquired. Also, step S702 is the same process as step S102 (see FIG. 2 ). Also, the optimization process (steps S703 to S705) differs from the optimization process (steps S103 to S106 (see FIG. 2 )) of the information processing system 100 according to embodiment 1 in that it is performed by gradient descent using energy instead of the similarity between the real spectrum and the calculated spectrum. Also, step S706 is the same process as step S107 (see FIG. 2 ). Also, step S707 is the same process as step S108 (see FIG. 2 ).

[0168] 20 is a flowchart showing an outline of the operation of the information processing system according to Comparative Example 2. The information processing system according to Comparative Example 2 uses a genetic algorithm to determine a candidate structure from an initial structure group, which is an initial structure group consisting of a plurality of structures after structural optimization obtained by the information processing system according to Comparative Example 1. The processing after determining the candidate structure is the same as that of the information processing system according to Comparative Example 1.

[0169] In the flow shown in FIG. 20 , step S708 is a process of acquiring the above-mentioned initial structure group. Step S709 is a process of forming a population of relatively low energy from the acquired multiple initial structure groups. Step S710 is a process of determining a predetermined number (here, 20) of candidate structures from the formed population. In step S710, operations such as atom swapping, displacement or inversion of atomic positions, or displacement of lattice constants are performed. Steps S709 and S710 may be performed not only once, but also multiple times repeatedly.

[0170] Example 1 First, an example (Example 1) of the information processing system 100 according to the first embodiment will be described.

[0171] [Acquisition of real spectrum] Ca ４ Ti ４ O １２ Orthorhombic CaTiO ３ From the X-ray diffraction pattern, a group of peaks with intensities of 1 / 100 or more of the most intense peak were extracted. A Gaussian function (standard deviation: 0.5) was applied to these peak positions to obtain a continuous pattern (continuous spectrum) from 0 to 90°. This was normalized by the intensity of the most intense peak to obtain the actual spectrum.

[0172] [Determination of candidate structures] For each of the space groups Nos. 2-230, Ca ４ Ti ４ O １２ The initial atomic arrangement and lattice constant were randomly generated from parameters that satisfied the symmetry of the space group. ４ Ti ４ O １２ If the space group could not be reproduced with the composition of the compound, the space group was excluded. By this procedure, a total of 129 candidate structures were determined (i.e., information on 129 candidate structures was generated).

[0173] [Calculation of Calculated Spectrum] An X-ray diffraction pattern was calculated for the candidate structure (or the structure after structural optimization), and a Gaussian function (standard deviation: 0.5) was applied to obtain a continuous pattern (continuous spectrum) from 0 to 90°. This was normalized by the intensity of the strongest peak to obtain a calculated spectrum.

[0174] [Structural optimization] Atomic positions and lattice constants were updated using the gradient descent method for spectral similarity. The atomic positions and lattice constants were updated using the Adam algorithm. Structural optimization was performed until the standard deviation of similarity over the most recent 10 steps reached 1E-06. If the convergence condition (first convergence condition) was not satisfied after 1000 steps, the calculation was terminated, and the structure obtained in the final step was used as the final structure after structural optimization.

[0175] Example 2 Next, an example (second example) of the information processing system 200 according to the second embodiment will be described.

[0176] In the same manner as in Example 1, the actual spectrum was acquired, the candidate structure was determined (that is, candidate structure information was generated), and the calculated spectrum was calculated.

[0177] [Energy Calculation] The energy of the candidate structure (or the structure after structural optimization) was calculated using Bond-Valence-Site-Energy. The screening factor, which indicates the contribution of the Coulomb potential, was set to 0.7.

[0178] [Structural optimization] The atomic positions and lattice constants were updated using the gradient descent method for the score obtained by calculating the weighted average of the energy and spectral similarity. The atomic positions and lattice constants were updated using the Adam algorithm. Structural optimization was performed until the standard deviation of the scores for the most recent 10 steps reached 1E-06. If the convergence condition (second convergence condition) was not satisfied after 1000 steps, the calculation was terminated, and the structure obtained in the final step was used as the final structure after structural optimization.

[0179] Comparative Example 1 Next, an example of an information processing system according to Comparative Example 1 (Comparative Example 1) will be described.

[0180] [Determination of Candidate Structures] 129 candidate structures were determined (that is, information on 129 candidate structures was generated) by the same process as in Examples 1 and 2.

[0181] [Energy Calculation] The energy of the candidate structure (or the structure after structural optimization) was calculated by the same process as in Example 2.

[0182] [Structure optimization] Atomic positions and lattice constants were updated using the gradient descent method for energy. The atomic positions and lattice constants were updated using the Adam algorithm. Structural optimization was performed until the standard deviation of the energy for the most recent 10 steps was 1E-06 or less. If the convergence condition was not met within 1000 steps, the calculation was terminated, and the structure obtained in the final step was used as the final structure after structural optimization.

[0183] <Comparative Example 2> Next, an example of an information processing system according to Comparative Example 2 (Comparative Example 2) will be described. In Comparative Example 2, the structure of the structural optimization of Comparative Example 1 was used as an initial structure group, and 200 candidate structures were determined using a genetic algorithm (i.e., 200 pieces of candidate structure information were generated). The processing in Comparative Example 2 was the same as that of Comparative Example 1, except for the determination of the candidate structures (i.e., the generation of candidate structure information).

[0184] [Determination of Candidate Structures] Candidate structures were determined using a genetic algorithm (i.e., candidate structure information was generated using a genetic algorithm). The structure group optimized in Comparative Example 1 was used as an initial structure group. 20 child structures were generated from the population of the initial structure group with low energy after structural optimization. This was repeated 10 times to determine a total of 200 candidate structures (i.e., 200 pieces of candidate structure information were generated).

[0185] <Results> Fig. 21 is a histogram showing the similarity between the actual spectrum and the calculated spectrum of the structure group that was structurally optimized in Example 1. As shown in Fig. 21, the calculated spectrum of 79% of the structures in the structure group has a cosine similarity with the actual spectrum of 0.8 or more, which indicates that the calculated spectrum has converged to a structure similar to the actual crystal structure. In addition, the cosine similarity reached a maximum of 0.992, indicating that the orthorhombic CaTiO ３ It reproduced the unique tilt of the skeleton.

[0186] 22 is a histogram showing the similarity between the actual spectrum and the calculated spectrum of the structure group optimized in Example 2. As shown in FIG. 22, the calculated spectrum of 81% of the structures in the structure group has a cosine similarity with the actual spectrum of 0.8 or more, indicating that the calculated spectrum has converged to a structure similar to the actual crystal structure. In addition, the cosine similarity reaches a maximum of 0.998, indicating that the orthorhombic CaTiO ３ The unique tilt of the skeleton was reproduced. As such, it can be seen that the use of the information processing method of the present disclosure enables efficient identification of the crystal structure.

[0187] Fig. 23 is a histogram showing the similarity between the actual spectrum and the calculated spectrum of the structure group structurally optimized in Comparative Example 1. As shown in Fig. 23, the maximum cosine similarity between the calculated spectrum and the actual spectrum is 0.31, which indicates that the calculated spectrum converges to a structure different from the actual crystal structure.

[0188] Fig. 24 is a histogram showing the similarity between the actual spectrum and the calculated spectrum of the structure group structurally optimized in Comparative Example 2. As shown in Fig. 24, the maximum cosine similarity between the calculated spectrum and the actual spectrum is 0.33, which indicates that the calculated spectrum converges to a structure different from the actual crystal structure.

[0189] FIG. 25 is a diagram comparing the actual spectra with the calculated spectra for the structures with the highest similarity in Examples 1 and 2 and Comparative Examples 1 and 2. As shown in FIG. 25, it can be seen that the calculated spectra for Examples 1 and 2 have spectral shapes that are almost completely identical to the actual spectra. On the other hand, it can be seen that the calculated spectra for Comparative Examples 1 and 2 have shapes that are completely different from the actual spectra. In FIG. 25, the vertical axis represents intensity, and the horizontal axis represents 2θ ("2θ" is the diffraction angle). The unit of 2θ is angle.

[0190] From the above results, it is difficult to obtain a structure close to the actual crystal structure even if many candidate structures are optimized when identifying the crystal structure without using calculated spectra, as in Comparative Examples 1 and 2. On the other hand, it is possible to efficiently identify the actual crystal structure when identifying the crystal structure using calculated spectra, as in Examples 1 and 2.

[0191] (Modifications) The information processing system (information processing method) according to one or more aspects of the present disclosure has been described above based on each embodiment, but the present disclosure is not limited to those embodiments. Various modifications conceivable by a person skilled in the art to the above embodiments may also be included in the present disclosure, as long as they do not deviate from the spirit of the present disclosure. Furthermore, the present disclosure may also include a configuration constructed by combining components of multiple different embodiments.

[0192] For example, in each of the above-described embodiments, the information processing systems 100 and 200 display the first image or the second image on the display unit 3, but are not limited to this. For example, the information processing systems 100 and 200 may output information included in the first image or the second image without displaying the first image or the second image itself on the display unit 3.

[0193] Furthermore, in each of the above-described embodiments, the information processing systems 100 and 200 are configured with the processing unit 10 and the storage unit 16, but are not limited to this. For example, the information processing system according to the first embodiment may be configured with the display control unit 30 and the display unit 3, as shown by "100A" in Fig. 1. For example, the information processing system according to the second embodiment may be configured with the display control unit 30 and the display unit 3, as shown by "200A" in Fig. 12.

[0194] In each of the above embodiments, each component may be configured with dedicated hardware, or may be realized by executing a software program suitable for that component. Each component may be realized by a program execution unit such as a CPU (Central Processing Unit) or a processor reading and executing a software program recorded on a recording medium such as a hard disk or semiconductor memory.

[0195] The following cases are also included in this disclosure:

[0196] (1) The at least one device is specifically a computer system comprising a microprocessor, ROM (Read Only Memory), RAM (Random Access Memory), a hard disk unit, a display unit, a keyboard, a mouse, etc. A computer program is stored in the RAM or hard disk unit. The at least one device achieves its function when the microprocessor operates in accordance with the computer program. Here, the computer program is composed of a combination of multiple instruction codes that indicate commands to a computer to achieve a predetermined function.

[0197] (2) Some or all of the components constituting at least one of the above devices may be configured as a single system LSI (Large Scale Integration). A system LSI is an ultra-multifunctional LSI manufactured by integrating multiple components on a single chip, and specifically, is a computer system configured to include a microprocessor, ROM, RAM, etc. A computer program is stored in the RAM. The system LSI achieves its functions by the microprocessor operating in accordance with the computer program.

[0198] (3) Some or all of the components constituting at least one of the above devices may be configured as an IC card or a standalone module that can be attached to the device. The IC card or module is a computer system composed of a microprocessor, ROM, RAM, etc. The IC card or module may include the above-mentioned ultra-multifunctional LSI. The IC card or module achieves its functions when the microprocessor operates in accordance with a computer program. This IC card or module may be tamper-resistant.

[0199] (4) The present disclosure may be embodied as the methods described above, a computer program that implements these methods on a computer, or a digital signal that includes the computer program.

[0200] The present disclosure may also be a computer program or a digital signal recorded on a computer-readable recording medium, such as a flexible disk, a hard disk, a CD (Compact Disc)-ROM, a DVD, a DVD-ROM, a DVD-RAM, a BD (Blu-ray (registered trademark) Disc), a semiconductor memory, etc. Alternatively, the present disclosure may be a digital signal recorded on such a recording medium.

[0201] The present disclosure may also be applied to transmitting a computer program or digital signal via a telecommunications line, a wireless or wired communication line, a network such as the Internet, data broadcasting, or the like.

[0202] Furthermore, the program or digital signal may be recorded on a recording medium and transferred, or the program or digital signal may be transferred via a network or the like, so that the program or digital signal may be implemented by another independent computer system.

[0203] (Other 1) In the present disclosure, at least one of A and B means "A", "B", or "A and B".

[0204] (Other 2) Modifications of the embodiment of the present disclosure may be as follows.

[0205] a method being performed by one or more processors configured to execute instructions stored in one or more memories, the method including: acquiring first spectral information indicating a first spectrum obtained by measuring a material having a crystalline structure (e.g., S101); acquiring a composition formula for the material (e.g., S101); generating a plurality of first information indicating a plurality of first candidates for the crystalline structure based on the composition formula (e.g., S102); calculating second spectral information corresponding to second spectra corresponding to each of the plurality of first candidates based on the plurality of first information, thereby calculating a plurality of second spectral information indicating a plurality of second spectra in one-to-one correspondence with the plurality of first information (e.g., S103); generating one or more pieces of structural information indicating one or more candidate structures that are one or more second candidates for the crystalline structure based on a correlation between each of the plurality of second spectral information and the first spectral information (e.g., S104 to S107, S103); and outputting the generated one or more pieces of structural information (e.g., S108).

[0206] The present disclosure is useful in identifying the crystal structure of unknown materials.

[0207] REFERENCE SIGNS LIST 10 Processing unit 11 Acquisition unit 12 Candidate structure information generation unit 13 Calculated spectrum calculation unit 14 Optimization unit 15 Output unit 16 Storage unit 17 Energy calculation unit 2 Input unit 3 Display unit 30 Display control unit 100, 200 Information processing system 100A, 200A Information processing system

Claims

1. A method of information processing performed by a computer, The steps include: obtaining real spectral information showing the actual spectrum obtained by actually measuring the material to be investigated; A step of obtaining material information regarding the composition of the aforementioned material, The steps include generating a plurality of candidate crystal structure information relating to a plurality of candidate crystal structures that are candidates for the crystal structure of the material based on the material information, and obtaining computational spectral information showing the computational spectrum corresponding to each of the plurality of candidate crystal structures, A step of generating crystal structure information relating to the crystal structure based on the correlation between the actual spectral information and the calculated spectral information, The step of outputting the generated crystal structure information includes, Information processing methods.

2. In the step of generating the crystal structure information, the actual spectrum and the calculated spectrum are used to perform structural optimization on two or more candidate crystal structures from the plurality of candidate crystal structures. The crystal structure information indicates the structure obtained by the structural optimization. The information processing method according to claim 1.

3. The structural optimization is performed using the similarity between the actual spectrum and the calculated spectrum. The crystal structure information indicates a structure among two or more structures obtained by the structural optimization whose similarity is above a predetermined threshold. The information processing method according to claim 2.

4. The structural optimization is performed by changing at least one of the lattice constant of the candidate crystal structure and the positions of the atoms in the candidate crystal structure. The structural optimization is performed such that the second similarity between the actual spectrum and the calculated spectrum of the structure obtained by the structural optimization is higher than the first similarity between the actual spectrum and the calculated spectrum of the candidate crystal structure before the structural optimization is performed. The information processing method according to claim 2 or 3.

5. The aforementioned structural optimization is performed one or more times on the target candidate crystal structure until the first convergence condition is satisfied. The first convergence condition is at least one of the following: the second similarity is greater than or equal to the first threshold, and the difference between the second similarity and the first similarity is less than or equal to a second threshold that is smaller than the first threshold. The information processing method according to claim 4.

6. The aforementioned structural optimization is performed by a gradient descent method using the similarity between the real spectrum and the calculated spectrum. The information processing method according to claim 2 or 3.

7. The process further includes the step of obtaining energy information indicating the energy calculated for each of the aforementioned plurality of candidate crystal structures, The structural optimization is performed using the actual spectral information, the calculated spectral information, and the energy information. The information processing method according to claim 2 or 3.

8. The structural optimization is performed by a gradient descent method using a score, which is an index that combines the similarity between the real spectrum and the calculated spectrum with the energy. The information processing method according to claim 7.

9. The aforementioned structural optimization is performed one or more times on the target candidate crystal structure until the second convergence condition is met. The second convergence condition is a predetermined condition based on the score. The information processing method according to claim 8.

10. The actual spectrum and the calculated spectrum are spectra obtained by X-ray diffraction. The information processing method according to any one of claims 1 to 3.

11. A method of information processing performed by a computer, A step of generating crystal structure information relating to the crystal structure based on the correlation between actual spectral information showing the actual spectrum obtained by actually measuring the material to be searched and computed spectral information showing the computed spectrum calculated for each of a plurality of candidate crystal structures that are candidates for the crystal structure of the material, The step of outputting the generated crystal structure information includes, Information processing methods.

12. The system includes a display control unit that displays a first image on the display unit which accepts input material information relating to the composition of the material to be searched and actual spectral information showing the actual spectrum obtained by actually measuring the material, and then displays a second image on the display unit which represents crystal structure information relating to the crystal structure of the material, generated based on the input material information and actual spectral information. Information processing system.

13. The steps include: obtaining real spectral information showing the actual spectrum obtained by actually measuring the material to be investigated; A step of obtaining material information regarding the composition of the aforementioned material, The steps include generating a plurality of candidate crystal structure information relating to a plurality of candidate crystal structures that are candidates for the crystal structure of the material based on the material information, and obtaining computational spectral information showing the computational spectrum corresponding to each of the plurality of candidate crystal structures, A step of generating crystal structure information relating to the crystal structure based on the correlation between the actual spectral information and the calculated spectral information, The steps include: outputting the generated crystal structure information, and causing a computer to perform these steps. program.