Crystal material analysis device and method, and computer readable recording medium

Abstract

A crystal material analysis device and method and a computer-readable recording medium are disclosed. The crystal material analysis device includes: a graph creation unit for creating a loop graph, the loop graph having: intra-cell nodes indicating atoms in a unit cell of a crystal material; intra-cell edges indicating chemical bonds between atoms in the unit cell; and loop edges indicating virtual chemical bonds between atom X in the unit cell and atom Y in the unit cell: atom Y in the unit cell corresponds to atom Y' in an adjacent unit cell adjacent to the unit cell, wherein atom Y' has a chemical bond with atom X; and an analysis unit for analyzing the crystal material by using the graph.

Description

Technical Field

[0001] The embodiments discussed herein relate to a crystal material analysis apparatus, a crystal material analysis method, and a crystal material analysis program that can be used for analysis of a crystal material. Background Art

[0002] Computerized evaluation, prediction, inference, etc. are used, for example, to design new chemicals, predict the properties of existing chemicals, and search for new uses for existing chemicals.

[0003] For example, in the field of organic chemistry, Fig.29 (acetic acid) and Fig.30 (methyl acetate) is shown in Figure 1. The structure of a molecule, such as atoms and bonding relationships between atoms, is represented by a graph using nodes (spheres) and edges (rods). Then, material search or design is performed by using graph similarity evaluation of the graph or by machine learning using the graph as input data.

[0004] However, in the case of crystalline materials, the unit cell repeats periodically almost infinitely. Therefore, the size of a graph used to represent a crystal structure cannot usually be determined. Therefore, it is not easy to represent a crystalline material using a graph and perform analysis such as similarity evaluation.

[0005] As a related art, Japanese Laid-Open Patent Publication No. 2011-170444 is disclosed.

[0006] The object of the present application is to provide a crystal material analysis device, a crystal material analysis method, and a crystal material analysis program that can be used to analyze a crystal material. Summary of the invention

[0007] According to one aspect of the embodiment, a crystal material analysis device includes: a graph creation unit for creating a loop graph, the loop graph having: intra-cell nodes indicating atoms in a unit cell of a crystal material; intra-cell edges indicating chemical bonds between atoms in the unit cell; and loop edges indicating virtual chemical bonds between atom X in the unit cell and atom Y in the unit cell: atom Y in the unit cell corresponds to atom Y' in an adjacent unit cell adjacent to the unit cell, wherein atom Y' has a chemical bond with atom X; and an analysis unit for analyzing the crystal material by using the graph.

[0008] According to an aspect of an embodiment, a crystal material analysis device that can be used for analyzing a crystal material may be provided.

[0009] Furthermore, according to an aspect of the embodiment, a crystal material analysis method that can be used for analysis of a crystal material may be provided.

[0010] Furthermore, according to an aspect of the embodiment, a crystal material analysis program that can be used for analysis of a crystal material may be provided. BRIEF DESCRIPTION OF THE DRAWINGS

[0011] Figure 1 is a diagram showing a configuration example of a crystal material analysis device of the present application;

[0012] Figure 2 is a diagram showing another configuration example of the crystal material analysis device of the present application;

[0013] Figure 3 is a diagram showing another configuration example of the crystal material analysis device of the present application;

[0014] Figure 4 is a diagram showing an exemplary functional configuration as an embodiment of the crystal material analysis device of the present application;

[0015] Figure 5 is a diagram showing an exemplary functional configuration as another embodiment of the crystal material analysis device of the present application;

[0016] Figure 6 is a diagram showing an exemplary functional configuration as another embodiment of the crystal material analysis device of the present application;

[0017] Figure 7 is a schematic diagram showing an example of a crystal structure of a crystalline material;

[0018] Figure 8 An example of a diagram showing a unit cell;

[0019] Fig. 9 is a schematic diagram showing another example of the crystal structure of a crystalline material;

[0020] Fig.10 yes Figure 7 a diagram of a unit cell of a crystal structure in (circuit diagram), the diagram being created by drawing according to the techniques of the present application;

[0021] Fig.11 yes Fig. 9 a diagram of a unit cell of a crystal structure in (circuit diagram), the diagram being created by drawing according to the techniques of the present application;

[0022] Fig.12 is a flowchart for analyzing a crystal structure using an example of the first embodiment of the technology disclosed in this application;

[0023] Fig.13A is a (first) flow chart of an example of a loop diagram creation method;

[0024] Fig. 13Bis a (second) flow chart of an example of a loop diagram creation method;

[0025] Fig. 13C is a (third) flowchart of an example of a loop diagram creation method;

[0026] Fig.14A (1st) diagram for illustrating a comparison example between the degree of similarity in the case of a conventional graph and the degree of similarity in the case of a loop graph in the first embodiment;

[0027] Fig. 14B is a (second) diagram for illustrating a comparison example between the degree of similarity in the case of a conventional graph and the degree of similarity in the case of a loop graph in the first embodiment;

[0028] Fig. 14C (3rd) diagram for illustrating a comparison example between the degree of similarity in the case of a conventional graph and the degree of similarity in the case of a loop graph in the first embodiment;

[0029] Fig.15A FIG. 1 is a diagram for briefly illustrating an example of the second embodiment;

[0030] Fig. 15B FIG. 2 is a diagram for briefly illustrating an example of the second embodiment;

[0031] Fig. 15C FIG. 3 is a diagram for briefly illustrating an example of the second embodiment;

[0032] Fig.16A FIG. 1 is a diagram for illustrating the benefits of the second embodiment;

[0033] Fig. 16B FIG. 2 is a diagram for illustrating the benefits of the second embodiment;

[0034] Fig.17 is a flowchart for analyzing a crystal structure using an example of a second embodiment of the technology disclosed in the present application;

[0035] Fig.18A FIG. 1 is a diagram for illustrating a working example of the second embodiment;

[0036] Fig.18B FIG. 2 is a diagram for illustrating a working example of the second embodiment;

[0037] Fig.18C FIG. 3 is a diagram for illustrating a working example of the second embodiment;

[0038] Fig.19A FIG. 4 is a diagram for illustrating a working example of the second embodiment;

[0039] Fig.19B FIG. 5 is a diagram for illustrating a working example of the second embodiment;

[0040] Fig.19C FIG. 6 is a diagram for illustrating a working example of the second embodiment;

[0041] Fig. 20A FIG. 7 is a diagram for illustrating a working example of the second embodiment;

[0042] Fig. 20B FIG. 8 is a diagram for illustrating a working example of the second embodiment;

[0043] Fig. 20C FIG. 9 is a diagram for illustrating a working example of the second embodiment;

[0044] Fig.21A FIG. 10 is a diagram for illustrating a working example of the second embodiment;

[0045] Fig.21B FIG. 11 is a diagram for illustrating a working example of the second embodiment;

[0046] Fig. 21C FIG. 12 is a diagram for illustrating a working example of the second embodiment;

[0047] Fig.22A is a (first) schematic diagram for illustrating a copy of the diagram in the third embodiment;

[0048] Fig. 22B is a (second) schematic diagram for illustrating a copy of the diagram in the third embodiment;

[0049] Fig.23A is a diagram (1st) for illustrating an example of how to determine the number of times a unit cell is to be replicated to create a host lattice;

[0050] Fig. 23B is a (second) diagram for illustrating an example of how to determine the number of times a unit cell is to be replicated to create a host lattice;

[0051] Fig.24 is a flow chart for analyzing a crystal structure using an example of a third embodiment of the technology disclosed in the present application;

[0052] Fig.25A FIG. 1 is a diagram for illustrating a working example of the third embodiment;

[0053] Fig.25B FIG. 2 is a diagram for illustrating a working example of the third embodiment;

[0054] Fig.25C FIG. 3 is a diagram for illustrating a working example of the third embodiment;

[0055] Fig.26 It is a conceptual diagram of the graphs (simple graph, expanded graph and loop graph) formed by unit cell A;

[0056] Fig. 27 It is a conceptual diagram of the graphs (simple graph, expanded graph and loop graph) formed by the unit cell B;

[0057] Fig.28 is a conceptual diagram of an extended graph formed by unit cells A with edges between extended nodes;

[0058] Fig.29 is the graph of acetic acid; and

[0059] Fig.30 This is the graph of methyl acetate. DETAILED DESCRIPTION

[0060] (Crystal material analysis device, crystal material analysis method, and crystal material analysis program)

[0061] The crystal material analysis device of the present application includes a graph creation unit and an analysis unit, and may also include a graph replication unit, a graph database, etc. depending on the situation.

[0062] The crystal material analysis method of the present application includes executing a graph creation process and an analysis process by a computer, and also includes executing a graph copy process and the like according to circumstances.

[0063] The crystal material analysis program of the present application causes a computer to execute graph creation and analysis, and also execute graph copying and the like as appropriate.

[0064] The crystal material analysis device of the present application executes, for example, the crystal material analysis method of the present application.

[0065] The crystal material analysis method of the present application is performed by, for example, the crystal material analysis program of the present application.

[0066] The crystal material analysis device includes, for example, a memory and a processor, and may also include other units as appropriate.

[0067] The processor is coupled to the memory.

[0068] The processor is configured to perform, for example, a graph creation process.

[0069] The processor is configured to perform, for example, a graph replication process.

[0070] The processor is configured to perform, for example, analytical processing.

[0071] The processor is, for example, a central processing unit (CPU), a graphics processing unit (GPU), or a combination thereof.

[0072] In this application, a graph has nodes and edges, a node is data about an atom, and an edge is data about a chemical bond between two atoms.

[0073] The diagram has nodes indicating atoms in one unit cell of the crystalline material (sometimes referred to hereinafter as "intra-cell nodes").

[0074] The diagram has edges that indicate chemical bonds between atoms in the unit cell (sometimes referred to hereinafter as "intra-cell edges").

[0075] The graph may have an edge (hereinafter sometimes referred to as a "loop edge") indicating a virtual chemical bond between an atom X in a unit cell and an atom Y in a unit cell, the atom Y in the unit cell corresponding to an atom Y' in an adjacent unit cell (hereinafter sometimes referred to simply as an "adjacent unit cell") adjacent to the unit cell, wherein the atom Y' has a chemical bond with the atom X in the unit cell. Here, the atom Y in the unit cell corresponding to the atom Y' in the adjacent unit cell means an atom in the unit cell that overlaps with the atom Y' in the adjacent unit cell when the adjacent unit cell and the unit cell overlap so that the constituent atoms overlap.

[0076] The graph may have nodes (sometimes referred to hereinafter as "extension nodes") indicating atoms in neighboring unit cells that are adjacent to the unit cell, wherein the atoms have chemical bonds with atoms in the unit cell.

[0077] The graph may have edges indicating chemical bonds between atoms corresponding to nodes within the unit cell and atoms corresponding to extended nodes (hereinafter sometimes referred to as “extension edges”).

[0078] The graph may have an edge indicating a chemical bond between two atoms corresponding to an expansion node (hereinafter sometimes referred to as an “edge between expansion nodes”).

[0079] The graph is stored in, for example, a graph database.

[0080] The graph creation unit creates a graph.

[0081] In the graph creation process, a graph is created.

[0082] A graph has nodes and edges, where nodes are data about atoms and edges are data about chemical bonds between two atoms. A graph is an abstract data type consisting of a set of nodes (vertices) and a set of edges (lines) representing the link relationship between nodes. A graph is represented by G = (V, E), where V is a set of nodes and E is a set of edges. V is a finite set, and E is a set of sets consisting of two elements selected from V.

[0083] For example, nodes within a unit cell and extended nodes have data such as atom type, atom valence, and atom charge.

[0084] For example, the edges within the unit cell, the edges of the loops, and the edges of the extensions have data such as bond type, bond angle, bond distance, and bond order. The bond angle and bond distance are provided as coordinate data about, for example, atoms or chemical bonds.

[0085] Intra-cell edges, loop edges and extension edges are preferably created by, for example, Voronoi tessellation between nodes.

[0086] Voronoi tessellation is a technique that partitions the nearest neighbor region of each node by drawing perpendicular bisectors on the lines connecting adjacent nodes.

[0087] Here, a Voronoi diagram and a Voronoi tessellation will be briefly described.

[0088] The Voronoi graph is a graph in which a plurality of points (generators) are arranged at optional positions in a specific metric space, and regions are divided based on other points closest to the generator in the same metric space. In addition, such division of regions is called a Voronoi tessellation. The division pattern is determined only based on the positions of the generators.

[0089] In the case of schematically representing a unit cell of a crystal material including chemical bonds, the chemical bonds in the unit cell of the crystal material are usually not uniquely determined. However, creating edges (inner edges of the unit cell, loop edges, and extended edges) by Voronoi tessellation makes it possible to uniquely determine the edges (inner edges of the unit cell, loop edges, and extended edges). Therefore, the edges for multiple crystal materials can be uniquely determined, and this improves the accuracy of the analysis of the crystal material.

[0090] In addition, intra-cell edges, loop edges, and extended edges may be created, for example, based on the standard ionic radius of atoms. For example, the following rule may be applied: an edge is created between nodes if d≤a(r1+r2)+b is satisfied, where d is the distance between any two nodes, and r1 and r2 are the ionic radii of the nodes. Here, a is a constant equal to or greater than 0, and b is a constant. The constants are preferably 1.0≤a≤1.2 and But it is not limited to these values.

[0091] As a method for creating the unit cell inner edges, loop edges, and extended edges, one or both of the above two methods, the Voronoi tessellation method and the method using the standard ionic radius, can be freely selected. In the case where both methods are selected, for example, among the unit cell inner edges, loop edges, and extended edges that can be determined by the Voronoi tessellation, only those unit cell inner edges, loop edges, and extended edges that are regarded as unit cell inner edges, loop edges, and extended edges in the method using the standard ionic radius of atoms can be created as unit cell inner edges, loop edges, and extended edges.

[0092] The crystalline material is not particularly limited and can be appropriately selected according to the purpose. Examples of the crystalline material include organic compounds, inorganic compounds, proteins, polymers and the like.

[0093] The graph copying unit copies the graph.

[0094] In the graph copy process, the graph is copied.

[0095] The method of copying the diagram is not particularly limited and can be appropriately selected according to the purpose.

[0096] The analysis unit analyzes the crystal material by using a graph.

[0097] In the analytical process, the crystal material is analyzed by using a graph.

[0098] Examples of the analysis of crystal materials include analysis of similarities in crystal structures between a plurality of crystal materials, prediction of characteristics of crystal materials, and the like.

[0099] The method for analyzing the similarity of the crystal structures between a plurality of crystal materials is not particularly limited and can be appropriately selected according to the purpose, as long as the similarity between the crystal structure of one crystal material and the crystal structure of another crystal material is analyzed by using a graph according to the technology of the present application. Examples thereof include a method of calculating a score for the degree of similarity and determining that the larger the score, the higher the similarity, etc.

[0100] The method of calculating the score for the similarity degree is not particularly limited and can be appropriately selected according to the purpose. Examples thereof include the following methods (1), (2), and the like.

[0101] (1) Fingerprint method

[0102] (2) A technique for analyzing the similarity between compounds by searching for a substructure shared by the compounds by solving the maximum independent set problem in a conflict graph represented by an Ising model equation using an annealing machine or the like (for example, see Non-Patent Document X below)

[0103] Non-patent document

[0104] In the fingerprint method, for example, whether a substructure of a query compound is included in a compound to be compared is represented by 0 or 1, and the degree of similarity is evaluated.

[0105] The maximum independent set problem is this problem: In a given graph G(V, E), among the vertex sets Among them, a set having no lines (edges) between vertices in V' (independent set) and having a maximum size is obtained in graph theory.

[0106] Note that the method of calculating the score for the degree of similarity is not limited to these methods. For example, the score for the degree of similarity can be calculated based on cosine similarity, correlation coefficient, correlation function, edit distance (also called Levenshtein distance), etc. related to the calculation of the degree of similarity.

[0107] The method for predicting the characteristics of the crystal material is not particularly limited and can be appropriately selected according to the purpose, as long as the method for predicting the characteristics of the crystal material is a method for predicting the characteristics of the crystal material by using a graph according to the technology of the present application. Examples of the method include predicting the characteristics by using a learning model, etc.

[0108] Examples of predicting characteristics by using a learning model include a method of creating a learning model by machine learning and predicting characteristics of a crystal material by using the learning model, and the like.

[0109] Examples of machine learning include supervised learning, unsupervised learning, etc.

[0110] The learning method in the case of creating a learning model by machine learning is not particularly limited and can be appropriately selected according to the purpose.

[0111] The training data in machine learning includes, for example, a graph according to the technology of the present application and data on the characteristics of a crystal material corresponding to the graph.

[0112] The property is not particularly limited and can be appropriately selected according to the purpose, and may be a chemical property or a physical property. Specific examples of the property include electrical conductivity, ion conductivity, discharge potential, relative dielectric constant, thermal conductivity, specific heat, and the like.

[0113] For example, in the case of supervised learning, learning is performed using a training data set including a graph of a specific crystal material and characteristics of the crystal material as labels.

[0114] In addition, in order to predict characteristics, the graph (graph structure data) according to the technology of the present application can be processed and used. For example, the graph can be converted into a tensor so that the graph structure data can be learned with high accuracy by using machine learning (e.g., deep learning) technology.

[0115] Here, a tensor means data expressed as a multi-dimensional array in which concepts such as a matrix and a vector have been generalized.

[0116] The crystal material analysis procedure disclosed in the present application may be recorded in a recording medium such as an internal hard disk or an external hard disk, or may be recorded in a recording medium such as a compact disk read-only memory (CD-ROM), a digital versatile disk read-only memory (DVD-ROM), a magneto-optical (MO) disk, or a universal serial bus (USB) flash drive.

[0117] In addition, in the case where the crystal material analysis program disclosed in the present application is recorded in a recording medium as described above, the program can be used directly, or can be installed on a hard disk and then used by a recording medium reader included in a computer system, depending on the situation. In addition, the crystal material analysis program disclosed in the present application can be recorded in an external storage area (another computer, etc.) that can be accessed from a computer system via an information communication network. In this case, the crystal material analysis program of the present application recorded in the external storage area can be used directly, or can be installed on a hard disk and then used from the external storage area via an information communication network, depending on the situation.

[0118] Note that the crystal material analysis program of the present application may be divided for each of any of the processes and then recorded in a plurality of recording media.

[0119] The recording medium disclosed in the present application is obtained by recording the crystal material analysis procedure of the present application.

[0120] The recording medium is computer-readable.

[0121] The recording medium is not particularly limited and can be appropriately selected according to the purpose. Examples of the recording medium include an internal hard disk, an external hard disk, a CD-ROM, a DVD-ROM, an MO disk, a USB flash drive, and the like.

[0122] Furthermore, the recording medium may include a plurality of recording media in which the crystal material analysis program disclosed in the present application is recorded after being divided for each of any of the processes.

[0123] The recording medium may be transient or non-transitory.

[0124] Figure 1 An exemplary hardware configuration of the crystal material analysis device of the present application is shown.

[0125] In the crystal material analysis device 10 , for example, a control unit 11 , a memory 12 , a storage unit 13 , a display unit 14 , an input unit 15 , an output unit 16 , and an input / output (I / O) interface unit 17 are connected to one another via a system bus 18 .

[0126] The control unit 11 performs arithmetic operations (for example, four arithmetic operations, comparison operations, and arithmetic operations for simulated annealing), hardware and software operation control, and the like.

[0127] The control unit 11 is not particularly limited and can be appropriately selected according to the purpose; for example, the control unit 11 may be a CPU.

[0128] The graph creation unit, the graph copying unit, and the analysis unit of the crystal material analysis device disclosed in the present application can be realized by the control unit 11 , for example.

[0129] The memory 12 is a memory such as a random access memory (RAM) or a read only memory (ROM). The RAM stores an operating system (OS), application programs, etc. read from the ROM and the storage unit 13, and is used as a main memory and a work area of ​​the control unit 11.

[0130] The storage unit 13 is a device that stores various types of programs and data, and may be, for example, a hard disk. The storage unit 13 stores programs to be executed by the control unit 11, data to be used when executing the programs, an OS, etc. For example, a graph database is stored in the storage unit 13.

[0131] Furthermore, the crystal material analysis program disclosed in the present application is stored in, for example, the storage unit 13 , loaded into the RAM (main memory) of the memory 12 , and executed by the control unit 11 .

[0132] The display unit 14 is a display device, and may be, for example, a display device such as a cathode ray tube (CRT) monitor or a liquid crystal panel.

[0133] The input unit 15 is a device for inputting various types of data, and may be, for example, a keyboard, a pointing device (eg, a mouse, etc.), or the like.

[0134] The output unit 16 is a device for outputting various types of data, and may be, for example, a printer or the like.

[0135] The I / O interface unit 17 is an interface for connecting various external devices. The I / O interface unit 17 enables data input and output on, for example, a CD-ROM, a DVD-ROM, an MO disk, a USB flash drive, and the like.

[0136] Figure 2 FIG. 2 shows another exemplary hardware configuration of the crystal material analysis device disclosed in the present application.

[0137] Figure 2 The crystal material analysis device shown is an example of a case where a cloud type crystal material analysis device is adopted and the control unit 11 is independent of the storage unit 13 and the like. Figure 2 In the illustrated example, a computer 30 including a storage unit 13 and the like is connected to a computer 40 including the control unit 11 via network interface units 19 and 20 .

[0138] The network interface units 19 and 20 are hardware that performs communication using the Internet.

[0139] Figure 3 FIG. 2 shows another exemplary hardware configuration of the crystal material analysis device disclosed in the present application.

[0140] Figure 3 The crystal material analysis device shown is an example of a case where a cloud type crystal material analysis device is adopted and the storage unit 13 is independent of the control unit 11 and the like. Figure 3 In the illustrated example, a computer 30 including the control unit 11 and the like is connected to a computer 40 including the storage unit 13 via network interface units 19 and 20 .

[0141] Figure 4 An exemplary functional configuration as an embodiment of the crystal material analysis device disclosed in the present application is shown.

[0142] Figure 4 The illustrated crystal material analysis device 1A includes a map creation unit 2 and an analysis unit 4 .

[0143] Figure 5 An exemplary functional configuration as another embodiment of the crystal material analysis device disclosed in the present application is shown.

[0144] Figure 5 The illustrated crystal material analysis device 1B includes a graph creation unit 2 , an analysis unit 4 , and a graph database 5 .

[0145] Figure 6 An exemplary functional configuration as an embodiment of the crystal material analysis device disclosed in the present application is shown.

[0146] Figure 6The illustrated crystal material analysis device 1C includes a map creation unit 2 , a map reproduction unit 3 , and an analysis unit 4 .

[0147] (First Embodiment)

[0148] A crystal material analysis device according to a first embodiment of the disclosed technology includes a map creation unit and an analysis unit.

[0149] A crystal material analysis method according to a first embodiment of the disclosed technology includes a computer-executed map creation process and an analysis process.

[0150] The crystal material program according to the first embodiment of the disclosed technology includes causing a computer to perform map creation and analysis.

[0151] The graph creation unit creates a graph having intra-cell nodes, intra-cell edges, and loop edges (hereinafter sometimes referred to as a “loop graph”).

[0152] In the graph creation process, a cycle graph is created.

[0153] The analysis unit analyzes the crystal material by using a graph.

[0154] In the analytical process, the crystal material is analyzed by using a graph.

[0155] For example, in graph creation, a first loop graph of a unit cell of a first crystal material is created as a loop graph and a second loop graph of a unit cell of a second crystal material is created as a loop graph.

[0156] For example, in the analysis, the similarity between the first crystal material and the second crystal material is analyzed by using the first loop graph and the second loop graph.

[0157] The analysis of similarities involves solving the maximum independent set problem in the conflict graph represented by the Ising model equation, for example using an annealing machine.

[0158] A conflict graph is created based on the following rule: an edge is created between two nodes when two nodes are compared and the two nodes are not identical to each other, and an edge is not created between the two nodes when the two nodes are compared and the two nodes are identical to each other, wherein each of the nodes is a combination of one of the node atoms constituting a unit cell of a first crystalline material expressed in the graph and one of the node atoms constituting a unit cell of a second crystalline material expressed in the graph.

[0159] For example, the maximum independent set in the conflict graph can be searched by using a Hamiltonian function, where minimization means searching for the maximum independent set. More specifically, for example, the search can be performed by using a Hamiltonian function (H) indicated by the following formula (A).

[0160] [Mathematical formula 1]

[0161]

[0162] Here, in the above formula (A), n represents the number of nodes in the conflict graph, and b i Represents the numerical value indicating the deviation of the i-th node.

[0163] In addition, when there is an edge between the i-th node and the j-th node, w ij has a positive non-zero value, and when there is no edge between the i-th node and the j-th node, w ij Has zero.

[0164] In addition, x i represents a binary variable indicating that the i-th node has either 0 or 1, and x j represents a binary variable indicating whether the jth node has 0 or 1.

[0165] Note that α and β represent positive numbers.

[0166] The annealing machine is not particularly limited and can be appropriately selected according to the purpose as long as the annealing machine is a computer that adopts an annealing method that searches for the ground state of the energy function represented by the Ising model. Examples of annealing machines include quantum annealing machines, semiconductor annealing machines using semiconductor technology, machines that perform simulated annealing performed by software using a CPU or GPU, etc. In addition, for example, a digital annealer (registered trademark) can be used as an annealing machine.

[0167] Here, the benefits of the first embodiment will be described.

[0168] Figure 7 It is a schematic diagram of the crystal structure of a crystalline material. Figure 7 The crystalline material in has nine different types of atoms (atom A to atom I) in the unit cell.

[0169] Crystal structures consist of infinite repetitions of unit cells. Therefore, crystal structures cannot usually be represented by graphs. Even when the graph is restricted to a certain size, a very large number of nodes and edges are used.

[0170] On the other hand, even in the case where a unit cell is represented by a graph, only one crystal structure cannot be represented by the graph, and in some cases, the graph may be caused to include a plurality of crystal structures. An example of this case will be described.

[0171] exist Figure 7 In FIG. 1 , the crystal structure 100X of the crystal material has a unit cell 100 including atoms A to I as a repeating unit. Note that in Figure 7 , the dashed lines at the top, bottom, left and right sides mean repeating unit cells 100.

[0172] When represented by the figure Figure 7 In the crystal structure 100X unit cell 100, the diagram is usually like Figure 8 shown.

[0173] Figure 8 is an example of a diagram of a unit cell 100 . Figure 8 The graph in FIG. 1 includes: a node 101A indicating atom A (a node within the unit cell); a node 101B indicating atom B (a node within the unit cell); and an edge 102 indicating a chemical bond between atom A and atom B (an edge within the unit cell). Note that although the reference numerals are omitted, Figure 8 The graph in also includes 7 intra-cell nodes and 11 intra-cell edges.

[0174] Here, examples of the crystal structure having a unit cell of 100 as a repeating unit are shown in FIG. Figure 7 In addition to the crystal structure 100X, Fig. 9 The crystal structure of 100Y, etc. Note that Fig. 9 , the dashed lines at the top, bottom, left and right sides mean repeating unit cells 100.

[0175] Then, in conjunction with Figure 8 The graph in Figure 7 In the same way as in the crystal structure 100X of the unit cell 100, by Figure 8 The graph in Fig. 9 The crystal structure of the unit cell of 100Y.

[0176] Then, Figure 8 The diagram in is not a diagram that represents only one crystal structure.

[0177] On the other hand, in the case of the graph created in the first embodiment of the technology of the present application, Figure 7 The crystal structure corresponding to the diagram is as follows Fig.10 Loop diagram shown. Fig.10 is with Figure 7 A loop diagram associated with 100 units of the unit cell of the crystal structure.

[0178] Fig.10 The loop diagram in includes: node 101A (intra-cell node) indicating atom A in unit cell 100; node 101B (intra-cell node) indicating atom B in unit cell 100; node 101C (intra-cell node) indicating atom C in unit cell 100, and also includes six intra-cell nodes without figure marks.

[0179] also, Fig.10The loop graph in has an edge 102 (an intra-cell edge) indicating a bonding relationship between an atom A and an atom B in the unit cell 100, and also has 11 intra-cell edges without reference numerals.

[0180] also, Fig.10 The cycle graph in has a total of six cycle edges. Two of the cycle edges are edge 111 and edge 112. Note that in Fig.10 In the loop graph, the edge 111 on the left and the edge 111 on the right are the same loop edge. Fig.10 In the cycle graph of , edge 112 at the top and edge 112 at the bottom are the same cycle edge.

[0181] Edge 111 (loop edge) indicates a virtual chemical bond between atom A in unit cell 100 and atom C in unit cell 100, and atom C in unit cell 100 corresponds to atom C in an adjacent unit cell that has a chemical bond with atom A in unit cell 100. Note that edge 111 also indicates a virtual chemical bond between atom C in unit cell 100 and atom A in unit cell 100, and atom A in unit cell 100 corresponds to atom A in an adjacent unit cell that has a chemical bond with atom C in unit cell 100.

[0182] Edge 112 (loop edge) indicates a virtual chemical bond between atom A in unit cell 100 and atom G in unit cell 100, which corresponds to atom G in an adjacent unit cell that has a chemical bond with atom A in unit cell 100. Note that edge 112 also indicates a virtual chemical bond between atom G in unit cell 100 and atom A in unit cell 100, which corresponds to atom A in an adjacent unit cell that has a chemical bond with atom G in unit cell 100.

[0183] By setting loop edges in the graph in this way, it is possible to obtain a graph including information on the repeated structure of unit cells (information on how unit cells are arranged) without increasing the number of nodes in the graph.

[0184] On the other hand, in the case of the graph created in the first embodiment of the technology of the present application, Fig. 9 The crystal structure corresponding to the diagram is as follows Fig.11 Loop diagram shown. Fig.11 is with Fig. 9 A loop diagram associated with 100 units of the unit cell of the crystal structure.

[0185] Here, Fig.11 The loop diagram in Fig.10 The loop graph in has a total of six loop edges in the same way. Then, two of the loop edges are edge 111' and edge 112'. Note that in Fig.11In the loop graph, the edge 111' on the left and the edge 111' on the right are the same loop edge. Fig.11 In the cycle graph of , the edge 112' at the top and the edge 112' at the bottom are the same cycle edge.

[0186] Edge 111′ (loop edge) indicates a virtual chemical bond between atom A in unit cell 100 and atom C in unit cell 100, and atom C in unit cell 100 corresponds to atom C in an adjacent unit cell that has a chemical bond with atom A in unit cell 100. Note that edge 111′ also indicates a virtual chemical bond between atom C in unit cell 100 and atom A in unit cell 100, and atom A in unit cell 100 corresponds to atom A in an adjacent unit cell that has a chemical bond with atom C in unit cell 100.

[0187] Edge 112' (loop edge) indicates a virtual chemical bond between atom A in unit cell 100 and atom I in unit cell 100, where atom I in unit cell 100 corresponds to atom I in an adjacent unit cell that has a chemical bond with atom A in unit cell 100. Note that edge 112' also indicates a virtual chemical bond between atom I in unit cell 100 and atom A in unit cell 100, where atom A in unit cell 100 corresponds to atom A in an adjacent unit cell that has a chemical bond with atom I in unit cell 100.

[0188] Here, edge 111 and edge 111' are the same edge, but edge 112 and edge 112' are different edges. Due to the difference between edge 112 and edge 112', Fig.10 The loop diagram and Fig.11 The loop graph in is a different graph.

[0189] In summary, in Figure 8 When a diagram shown expresses a unit cell, the diagram does not represent only one crystal structure.

[0190] On the other hand, in the drawing technique of the first embodiment, two or more crystal structures having the same unit cell but different crystal structures can be represented by different drawings.

[0191] In the case where two or more crystal structures having different crystal structures can be represented by different graphs, the analysis accuracy of the analysis of crystal materials (eg, analysis of similarities between crystal materials, prediction of characteristics of crystal materials, etc.) can be improved.

[0192] In addition, the number of nodes may affect the number of bits of the calculator, and the smaller the number of nodes, the better. On the other hand, the number of edges may affect the accuracy of the analysis, and the larger the number of edges, the better. Here, compared with the usual graph that does not include loop edges, the loop graph allows the number of edges to be increased without increasing the number of nodes.

[0193] Therefore, loop diagrams are expected to improve the analysis accuracy without increasing the number of bits of a calculator.

[0194] Therefore, the mapping technique of the first embodiment is used for analysis of crystal materials using computer technology.

[0195] Will refer to Fig.12 The shown flowchart briefly describes the crystal material analysis method in the first embodiment.

[0196] First, crystal structure data is extracted from another database (S1). The other database is not particularly limited and can be appropriately selected according to the purpose. Examples of other databases include the Inorganic Crystal Structure Database (ICSD) and the like. Note that the number and type of fragments of the crystal structure data to be extracted are not particularly limited and can be appropriately selected according to the purpose. For example, only crystal structure data about chemicals with specific elements can be extracted.

[0197] Next, using the extracted crystal structure data, a loop graph is created by mapping according to the technology of the present application, and a graph database including the loop graph is created (S2). For example, the loop graph is created according to a flowchart described later.

[0198] Next, the crystal structure is analyzed using the loop graph in the graph database (S3). Examples of the analysis include similarity evaluation. The similarity evaluation is performed by solving the maximum independent set problem in the conflict graph represented by the Ising model equation, for example, using an annealing machine. This method can be performed, for example, with reference to the following non-patent literature:

[0199] Non-patent literature: Maritza Hernandez, Arman Zaribafiyan, Maliheh Aramon, Mohammad Naghibi "A Novel Graph-based Approach for Determining MolecularSimilarity".ArXiv:1601.06693(https: / / arxiv.org / pdf / 1601.06693.pdf)

[0200] Therefore, the similarity of crystal structures can be evaluated, which is one of the analyses of crystal structures.

[0201] Here, an example of a loop diagram creation method will be described using a flowchart. FIG. 13A to FIG. 13C is a flowchart of an example of a loop diagram creation method.

[0202] First, crystal material data is read ( S101 ).

[0203] Next, the relative coordinates of all atoms in a single unit cell are calculated (S102). Thus, the relative positional relationship of all atoms is obtained.

[0204] Next, all atoms in a single unit cell are represented as nodes of a graph (S103). These nodes are intra-unit cell nodes.

[0205] Next, for the combination of two atoms (A and B), i.e., a specific atom (atom A) among all atoms in a single unit cell and another atom (atom B) except the specific atom, determine whether the distance between A and B is suitable as a bond distance (S106). Then, if suitable, node A and node B are bonded (S107). In other words, an edge is set between node A and node B. The edge is an edge within the unit cell. Thereafter, S106 is performed for all combinations of a specific atom (atom A) and another atom B (S105 and S108). If not suitable, no edge is set between node A and node B, and S106 is performed for all combinations of a specific atom (atom A) and another atom B (S105 and S108).

[0206] Next, determine whether there is already a bond equivalent to the bond between A and B' between a specific atom (atom A) in a single unit cell and any atom B' in an adjacent unit cell (S110). If there is not yet a bond equivalent to the bond between A and B', determine whether the distance between A and B' is suitable as a bond distance (S111). If the distance between A and B' is suitable as a bond distance, determine whether there is already a node corresponding to B' (S112). Thereafter, if there is not yet a node corresponding to B', add atom B' as an extended node (S113). Thereafter, bond node A and node B' (S114). In other words, set an edge between node A and node B'. As a result of the determination in S112, if there is already a node corresponding to B', bond node A and node B' (S114). If the result of the determination in S110 indicates that the distance between A and B' is not suitable as a bond distance, if the result of the determination in S111 indicates that a node corresponding to B' already exists, and after executing S114, the processing between S109 and S115 is performed on all combinations of a specific atom (atom A) and another atom B'.

[0207] The processing of S105 to S115 is performed for all atoms ( S104 and S116 ) corresponding to a specific atom A in a single unit cell.

[0208] Next, find the node A' that is equivalent to the expanded node B' in the unit cell (S118). Then, treat the expanded node B' as the node A' (S119). Then, the edge between the node A and the node A' becomes a loop edge. These processes are performed for all expanded nodes (S117 and S120).

[0209] Thus, a loop diagram is obtained.

[0210] Here, reference will be made to 14A to Fig. 14C A comparison example between the degree of similarity in the case of a normal graph and the degree of similarity in the case of a cycle graph is described.

[0211] Use as Fig.14A The crystal structure shown is composed of 12 different types of atoms A to L. Consider identifying Fig.14A The case of two types of unit cells, unit cell A and unit cell B, is shown.

[0212] In conventional plotting techniques, the plot created for cell A is Fig. 14B Figure A-1 shown, and the diagram created for unit cell B is Fig. 14B As shown in Figure B-1. As the maximum independent set problem in the conflict graph, Figure A-1 and Figure B-1 are represented by the Ising model equation and solved by the annealing machine. Then, six atoms (A, C, F, H, J, and L) are found as common atoms, and the degree of similarity obtained by formula (1-1) described later is 0.50.

[0213] On the other hand, when a loop diagram is created by the drawing technique of the first embodiment, the diagram created for unit cell A is Fig. 14C Figure A-2 shown in Figure 14C, and the figure created for unit cell B is Figure B-2 shown in Figure 14C. As the maximum independent set problem in the conflict graph, Figure A-2 and Figure B-2 are represented by the Ising model equation and solved by the annealer. Then, 12 atoms are found as common atoms, and the degree of similarity obtained by formula (1-1) described later is 1.00.

[0214] Unit cell A and unit cell B have the same crystal structure. Therefore, a similarity degree of 1.00 between the graph created for unit cell A and the graph created for unit cell B means that the calculation result is more accurate.

[0215] In this way, the loop diagram can be used to improve the accuracy of the analysis (eg, degree of similarity).

[0216] <Second Embodiment>

[0217] A crystal material analysis device according to a second embodiment of the disclosed technology includes a map creation unit, a map reproduction unit, and an analysis unit.

[0218] A crystal material analysis method according to a second embodiment of the disclosed technology includes a computer executing a map creation process, a map copy process, and an analysis process.

[0219] A crystal material program according to a second embodiment of the disclosed technology includes causing a computer to execute map creation, map copying, and analysis.

[0220] The graph creation unit creates a graph having intra-cell nodes and intra-cell edges.

[0221] In the graph creation process, a graph having intra-cell nodes and intra-cell edges is created.

[0222] In graph creation, a graph having intra-cell nodes, intra-cell edges, extended nodes, and extended edges (hereinafter sometimes referred to as an "extended graph") may be created. The extended graph may have edges between extended nodes.

[0223] In graph creation, you can create a loop graph.

[0224] Note that a graph having only intra-cell nodes as nodes and only intra-cell edges as edges may sometimes be referred to as a “simple graph” hereinafter.

[0225] The graph copying unit generates a copy graph by copying the graph.

[0226] In the graph copying process, a copied graph is generated by copying the graph.

[0227] The analysis unit analyzes the crystal material by using the replica map.

[0228] In the analytical process, the crystal material is analyzed by using the replica map.

[0229] For example, in graph creation, a first graph of a unit cell of a first crystal material is created as a graph and a second graph of a unit cell of a second crystal material is created as a graph.

[0230] For example, in the graph duplication, at least one of the first graph or the second graph is duplicated.

[0231] The copying of at least one of the first graph or the second graph is performed in such a manner as to minimize an absolute value of a difference between a total number of nodes in the plurality of first graphs after the copying and a total number of nodes in the plurality of second graphs after the copying.

[0232] For example, in the analysis, the similarity between the first crystal material and the second crystal material is analyzed by using any one of the first graph or the first integrated graph and any one of the second graph or the second integrated graph.

[0233] The first integrated graph is obtained by integrating a plurality of first copy graphs generated by copying the first graph with each other.

[0234] The second integrated graph is obtained by integrating a plurality of second copy graphs generated by copying the second graph with each other.

[0235] Here, the graph obtained by integrating the replicated graphs (hereinafter sometimes referred to as an "integrated graph") may be, for example, a graph in which a plurality of graphs obtained by replication are simply put together. In this case, there is no edge between the plurality of graphs.

[0236] In addition, the figure obtained by integrating the replicated figures may be a figure obtained by combining a plurality of figures obtained by replication, for example, through edges (hereinafter sometimes referred to as "edges between figures"). In this case, the edges between figures are preferably added between the plurality of figures so that the integrated figure matches the structure of the crystal material.

[0237] The analysis of similarities involves solving the maximum independent set problem in the conflict graph represented by the Ising model equation, for example using an annealing machine.

[0238] Here, an example of the second embodiment will be briefly described below.

[0239] The following describes a case in which each of the figures of two crystal materials is copied, but only one of the figures may be copied.

[0240] Assume that Fig.15A The case of analyzing two unit cells A and B shown. As for the analysis, the calculation of the degree of similarity is taken as an example. Here, the simple graph of unit cell A is called graph A. The simple graph of unit cell B is called graph B. In the case where the number of nodes in graph A is different from the number of nodes in graph B, the difference leads to a decrease in the degree of similarity. The reason will be described later.

[0241] Therefore, in order to reduce the difference between the number of nodes in graph A and the number of nodes in graph B, at least one of graph A or graph B is replicated. The replication is performed, for example, in the following manner: the absolute value of the difference between the total number of nodes in the replicated graph A and the total number of nodes in the replicated graph B is minimized.

[0242] For example, Figure A is copied four times, while Figure B is copied nine times.

[0243] As for the integrated graph obtained by integrating the replicated graphs, e.g. Fig. 15B As shown, graphs A can be combined, or graphs B can be combined. Combining here means setting an edge between graphs (between graphs A or between graphs B).

[0244] On the other hand, in the integrated graph, graph A may not be combined, or graph B may not be combined ( Fig. 15C ).

[0245] Then, analysis is performed using the integrated graph obtained by replicating the graph in this manner.

[0246] Note that, for example, the integrated diagrams of the second embodiment can be classified into the following combinations, for example, according to the structure of the diagram.

[0247] -2-1: In the integrated graph, there are bonds between graphs (edges between graphs) ( Fig. 15B ).

[0248] --2-1-1: The integrated graph is a simple graph.

[0249] --2-1-2: The integrated diagram is an extended diagram.

[0250] --2-1-3: The integration diagram is a loop diagram.

[0251] --2-2: In the integrated graph, there are no bonds (edges between graphs) between graphs. Fig. 15C ).

[0252] --2-2-1: Each graph in the integration diagram is a simple graph.

[0253] --2-2-2: Each graph in the integrated graph is an extended graph.

[0254] --2-2-3: Each graph in the integrated graph is a loop graph.

[0255] Here, the benefits of the second embodiment will be described.

[0256] Fig.16A and Fig. 16B is a schematic diagram of the unit cell.

[0257] Fig.16A The unit cell 200A in has nine different types of atoms (atom A to atom I).

[0258] Fig. 16B The unit cell 200B in includes 24 different types of atoms (atom A to atom X).

[0259] Here, by using Fig.16A The simple diagram of the unit cell 200A in Fig. 16B The similarity between the unit cell 200A and the unit cell 200B is calculated by using a simple graph composed of the unit cell 200B in FIG. When the similarity is calculated by using the maximum independent set, the similarity is usually obtained by, for example, the following formula (1).

[0260] [Mathematical formula 2]

[0261]

[0262] Here, in the above formula (1), S(G A ,G B) represents the degree of similarity between the unit cell A of the first crystal material expressed in the graph and the unit cell B of the second crystal material expressed in the graph, S(G A ,G B ) is expressed as 0 to 1, and means that the closer it is to 1, the higher the degree of similarity.

[0263] In addition, among the node atoms in the unit cell A represented by the diagram, V A represents the total number of node atoms in the unit cell A expressed in the graph, and V c A Represents the number of node atoms included in the maximum independent set in the conflict graph. Note that node atoms mean atoms at the vertices of molecules expressed in a graph.

[0264] In addition, among the node atoms in the unit cell B represented in the diagram, V B represents the total number of node atoms in the unit cell B expressed in the graph, and V c B Indicates the number of node atoms included in the maximum independent set in the conflict graph.

[0265] δ represents a number from 0 to 1.

[0266] Furthermore, in the above formula (1), max{A,B} means selecting either A or B having a larger value, and min{A,B} means selecting either A or B having a smaller value.

[0267] Here, a conflict graph is understood to be a graph created based on the following rule: when two nodes are compared and the two nodes are different from each other, an edge is created between the two nodes, and when two nodes are compared and the two nodes are the same as each other, no edge is created between the two nodes, wherein each of the nodes is a combination of one of the node atoms constituting a unit cell A in a first crystal material expressed in the graph and one of the node atoms constituting a unit cell B in a second crystal material expressed in the graph.

[0268] The above formula (1) can be simplified to the following formula (1-1): δ is 0.5.

[0269] [Mathematical formula 3]

[0270] Degree of similarity

[0271] Here, AB common represents the number of substructures shared by unit cell A and unit cell B. all represents the number of nodes in the graph of the unit cell A, and B all Represents the number of nodes in the graph of unit cell B.

[0272] In for Fig.16A All atoms in the unit cell 200A constitute the atoms in the unit cell 200A and Fig. 16B In the case of a substructure shared by atoms in the unit cell 200B in , the similarity degree is maximized. In this case, the numerical value of the similarity degree obtained according to formula (1-1) is 1 / 2[(9 / 9)+(9 / 24)]=0.675. This means that the difference between the number of atoms (the number of nodes) in the two unit cells reduces the similarity degree.

[0273] Therefore, in the second embodiment, at least one of the diagrams of the unit cells of the two crystal materials is copied in the diagram replication. By copying the diagram to reduce the difference between the number of atoms (the number of nodes) between the two unit cells to be compared, the reduction in the degree of similarity caused by the difference in the number of atoms (the number of nodes) can be avoided. Therefore, the accuracy of the analysis (e.g., the degree of similarity) can be improved.

[0274] Therefore, the mapping technique of the second embodiment is used for analysis of crystal materials using computer technology.

[0275] Will refer to Fig.17 The shown flowchart briefly describes the crystal material analysis method in the second embodiment.

[0276] First, crystal structure data is extracted from another database (S11). Other databases are not particularly limited and can be appropriately selected according to the purpose. Examples of other databases include inorganic crystal structure databases (ICSD) and the like. Note that the number and type of fragments of the crystal structure data to be extracted are not particularly limited and can be appropriately selected according to the purpose. For example, only crystal structure data about chemicals with specific elements can be extracted.

[0277] Next, using the extracted crystal structure data, a graph is created by mapping according to the technology of the present application, and a graph database including the graph is created ( S12 ).

[0278] Next, a copy graph is generated by copying the created graph (S13).

[0279] Next, the crystal structure is analyzed by using the replica graph (S14). Examples of the analysis include similarity evaluation. The similarity evaluation is performed, for example, by solving the maximum independent set problem in the conflict graph represented by the Ising model equation using an annealer or the like.

[0280] Therefore, the similarity of crystal structures can be evaluated, which is one of the analyses of crystal structures.

[0281] Here, we will refer to 18A to 18C , FIG. 19A to FIG. 19C , FIG. 20A to FIG. 20C as well as FIG. 21A to FIG. 21C A working example of the second embodiment is described.

[0282] In this working example, we obtain Fig.18A The degree of similarity between the crystal material A represented by the unit cell A and the crystal material B represented by the unit cell B is shown. The crystal material A represented by the unit cell A has the following characteristics: Fig.18B The structure of the repeating unit cell A is shown. The crystal material B represented by the unit cell B has the following structure: Fig. 18C The structure of the repeating unit cell B is shown. Unit cells A and B are composed of 16 different types of atoms A to P.

[0283] according to Fig.18A The simple diagram created by the unit cell A shown is Fig.19A As shown in Figure A-1-1.

[0284] according to Fig.18A The simple diagram created by the unit cell B shown is Fig.19A As shown in Figure B-1.

[0285] As the maximum independent set problem in the conflict graph, Figure A-1-2 and Figure B-1 are represented by the Ising model equation and solved by the annealing machine. Then, 16 atoms are found as common atoms and the similarity degree obtained by the previously described formula (1-1) is 0.625 ( Fig.19A ). This example is for comparison.

[0286] On the other hand, as an example of the second embodiment, an integrated graph (graph A-1-2, no edges between graphs) obtained by replicating graph A-1-1 (simple graph) four times is created ( Fig.19B ). Then, as the maximum independent set problem in the conflict graph, Figure A-1-2 and Figure B-1 are represented by the Ising model equation and solved by the annealing machine. Then, 50 atoms are found as common atoms and the similarity degree obtained by the previously described formula (1-1) is 0.78 ( Fig.19B ).

[0287] Furthermore, as an example of the second embodiment, an integrated graph (graph A-1-3, graphs with edges between them) obtained by replicating the graph A-1-1 (simple graph) four times is created ( Fig.19C ). In this case, Figure A-1-3 and Figure B-1 are the same graph. Then, as the maximum independent set problem in the conflict graph, Figure A-1-3 and Figure B-1 are represented by the Ising model equation and solved by the annealing machine. Then, 64 atoms are found as common atoms and the similarity degree obtained by the previously described formula (1-1) is 1.00 ( Fig.19C ).

[0288] Next, a working example of the case where an extended graph is used will be described.

[0289] When based on Fig.18A When creating an expanded diagram of the unit cell A shown, we obtain Fig. 20A As shown in Figure A-2-1.

[0290] On the other hand, according to Fig.18A When creating an expanded diagram of the unit cell B shown, we obtain Fig. 20A As shown in Figure B-2.

[0291] Then, as the maximum independent set problem in the conflict graph, Figure A-2-1 and Figure B-2 are represented by the Ising model equation and solved by the annealing machine. Then, 28 atoms are found as common atoms and the similarity degree obtained by the previously described formula (1-1) is 0.583 ( Fig. 20A ). In this example, the figures are not copied, which makes this example different from the second embodiment.

[0292] On the other hand, as an example of the second embodiment, an integrated graph (graph A-2-2, no edges between graphs) obtained by replicating graph A-2-1 (expanded graph) four times is created ( Fig. 20B ). In this case, the integrated graph (Figure A-2-2) can be obtained by copying Figure A-2-1 (expanded graph) four times, or the integrated graph (Figure A-2-2) can be obtained by copying Figure A-1-1 (simple graph) four times and then converting each of them into an expanded graph. Then, as the maximum independent set problem in the conflict graph, Figure A-2-2 and Figure B-2 are represented by the Ising model equation and solved by the annealing machine. Then, 82 atoms are found as common atoms and the degree of similarity obtained by the previously described formula (1-1) is 0.75 ( Fig. 20B ).

[0293] Furthermore, as an example of the second embodiment, an integrated graph (Figure A-2-3, an extended graph with edges between graphs) obtained by replicating Figure A-1-1 (a simple graph) four times is created ( Fig. 20C ). In this case, the integrated graph (Figure A-2-3) can be obtained by, for example, copying Figure A-1-1 (simple graph) four times, and then combining Figure A-1-1, and converting the graph obtained by the combination into an extended graph. In this case, Figure A-2-3 and Figure B-2 are the same graph. Then, as the maximum independent set problem in the conflict graph, Figure A-2-3 and Figure B-2 are represented by the Ising model equation and solved by the annealing machine. Then, 96 atoms are found as common atoms and the degree of similarity obtained by the previously described formula (1-1) is 1.00 ( Fig. 20C ).

[0294] Next, a working example of the case where a loop graph is used will be described.

[0295] When based on Fig.18A When creating a loop diagram for the unit cell A shown in the figure, we obtain Fig.21A As shown in Figure A-3-1.

[0296] On the other hand, according to Fig.18A When creating the loop diagram for the unit cell B shown, we obtain Fig.21A As shown in Figure B-3.

[0297] Then, as the maximum independent set problem in the conflict graph, Figure A-3-1 and Figure B-3 are represented by the Ising model equation and solved by the annealing machine. Then, 11 atoms are found as common atoms and the similarity degree obtained by the previously described formula (1-1) is 0.42 ( Fig.21A ). In this example, the figures are not copied, which makes this example different from the second embodiment.

[0298] On the other hand, as an example of the second embodiment, an integrated graph (graph A-3-2, no edges between graphs) obtained by replicating graph A-3-1 (loop graph) four times is created ( Fig. 20B ). In this case, the integrated graph (Figure A-3-2) can be obtained by copying Figure A-3-1 (loop graph) four times, or the integrated graph (Figure A-3-2) can be obtained by copying Figure A-1-1 (simple graph) four times and then converting each of them into a loop graph. Then, as the maximum independent set problem in the conflict graph, Figure A-3-2 and Figure B-3 are represented by the Ising model equation and solved by the annealing machine. Then, 44 atoms are found as common atoms and the degree of similarity obtained by the previously described formula (1-1) is 0.68 ( Fig.21B ).

[0299] In addition, as an example of the second embodiment, an integrated graph (Figure A-3-3, a loop graph with edges between graphs) obtained by copying Figure A-1-1 (simple graph) four times is created. In this case, the integrated graph (Figure A-3-3) can be obtained in the following manner: for example, Figure A-1-1 (simple graph) is copied four times, and then Figure A-1-1 is combined, and the graph obtained by the combination is converted into a loop graph. In this case, Figure A-3-3 and Figure B-3 are the same graph. Then, as the maximum independent set problem in the conflict graph, Figure A-3-3 and Figure B-3 are represented by the Ising model equation and solved by an annealing machine. Then, 64 atoms are found as common atoms and the degree of similarity obtained by the previously described formula (1-1) is 1.00 ( Fig. 21C ).

[0300] <Third Embodiment>

[0301] A crystal material analysis device according to a third embodiment of the disclosed technology includes a map creation unit, a map copy unit, and an analysis unit.

[0302] A crystal material analysis method according to a third embodiment of the disclosed technology includes a computer executing a map creation process, a map copy process, and an analysis process.

[0303] A crystal material program according to a third embodiment of the disclosed technology includes causing a computer to execute map creation, map copying, and analysis.

[0304] The graph creation unit creates a graph, and the graph has intra-cell nodes and intra-cell edges.

[0305] In the graph creation process, a graph having intra-cell nodes and intra-cell edges is created.

[0306] In graph creation, you can create simple graphs.

[0307] In graph creation, you can create extended graphs.

[0308] In graph creation, you can create a loop graph.

[0309] In the graph creation, a graph is created for each of the first crystal material and the second crystal material.

[0310] The graph copying unit performs at least one of the first copying or the second copying.

[0311] In the graph copy process, at least one of the first copy or the second copy is performed.

[0312] In the first replication, the diagram of the unit cell of the second crystalline material is replicated so that the guest lattice, which is the unit cell of the first crystalline material, is adapted to the host lattice created by connecting a plurality of unit cells of the second crystalline material.

[0313] In the second replication, the diagram of the unit cell of the first crystalline material is replicated so that the guest lattice, which is the unit cell of the second crystalline material, is adapted to the host lattice created by connecting a plurality of unit cells of the first crystalline material.

[0314] It is sufficient if at least one of the first copy or the second copy is performed. Only the first copy may be performed, only the second copy may be performed, or both the first copy and the second copy may be performed.

[0315] Here, in a case where the unit cells of the first crystal material and the unit cells of the second crystal material are different in size, at least one of the first replication or the second replication is performed.

[0316] Note that the size of the unit cell is calculated based on information about, for example, the bond distances between nodes at the edges.

[0317] The analysis unit analyzes the crystal material.

[0318] In analytical processing, the crystalline material is analyzed.

[0319] In the analysis, a first comparison and a second comparison are performed.

[0320] The first comparison is a comparison between a figure consisting of a guest lattice of the first crystalline material and a figure consisting of a host lattice in which the guest lattice of the first crystalline material is adapted. Here, the host lattice is a host lattice consisting of one or more unit cells of the second crystalline material.

[0321] The second comparison is a comparison between a figure consisting of a guest lattice of the second crystalline material and a figure consisting of a host lattice in which the guest lattice of the second crystalline material is adapted. Here, the host lattice is a host lattice consisting of one or more unit cells of the first crystalline material.

[0322] The analysis is, for example, an analysis of similarities between the first crystal material and the second crystal material.

[0323] The graph corresponding to the host lattice composed of a plurality of unit cells is obtained by, for example, integrating the replicated graphs. For example, the graph corresponding to the host lattice composed of a plurality of unit cells may be, for example, a graph in which a plurality of graphs obtained by replication are simply put together. In this case, there are no edges between the plurality of graphs.

[0324] In addition, the graph obtained by integrating the replicated graphs can be a graph obtained by combining multiple graphs obtained by replication, for example, through edges between graphs. In this case, the edges between graphs are preferably added between multiple graphs so that the integrated graph matches the structure of the crystal material.

[0325] Fig.22A and Fig. 22B It is a schematic diagram for explaining the copying of a figure in the third embodiment. Fig.22A It is a schematic diagram for explaining the first replication. Fig. 22B It is a schematic diagram for explaining the second replication.

[0326] exist Fig.22A and Fig. 22B In FIG. 1 , A represents a unit cell of a first crystal material and B represents a unit cell of a second crystal material.

[0327] like Fig.22AAs shown, in the first replication, the diagram of the unit cell B is replicated six times so that the guest lattice A as the unit cell A is adapted to the host lattice B' created by connecting the six replicated unit cells B. Here, the entirety of the six replicated unit cells B is the host lattice B'.

[0328] like Fig. 22B As shown, in the second replication, the diagram of the unit cell A is replicated four times so that the guest lattice B as the unit cell B is adapted to the host lattice A' created by connecting the four replicated unit cells A. Here, the entirety of the four replicated unit cells A constitutes the host lattice A'.

[0329] Here, an example of how to determine the number of times a unit cell is to be replicated to create a host lattice will be described. Here, the case of a plane will be described, and this case is applicable to the case of three dimensions.

[0330] Consider the following case: In this case, the diagram of the unit cell B is replicated so that the guest lattice A is adapted to the host lattice B' created by connecting the unit cells B. In this case, Fig.23A As shown, the number of times the unit cell B is to be replicated is determined so that a circle (a sphere in the case of three dimensions) having a diameter corresponding to the longest diagonal of the guest lattice A is adapted to the host lattice B' created by connecting the unit cells B. Here, when considered in a plane, the circle is the smallest circle that can contain the guest lattice A. When considered in three dimensions, the sphere is the smallest sphere that can contain the guest lattice A. In addition, when considered in a plane, the host lattice B' is the smallest size that can contain the circle. When considered in three dimensions, the host lattice B' is the smallest size that can contain the sphere.

[0331] Furthermore, consider the case in which the diagram of the unit cell A is replicated so that the guest lattice B is adapted to the host lattice A' created by connecting the unit cells A. In this case, Fig. 23B As shown, the number of times the unit cell A is to be replicated is determined so that a circle (a sphere in the case of three dimensions) having a diameter corresponding to the longest diagonal of the guest lattice B is adapted to the host lattice A' created by connecting the unit cells A. Here, when considered in a plane, the circle is the smallest circle that can contain the guest lattice B. When considered in three dimensions, the sphere is the smallest sphere that can contain the guest lattice B. In addition, when considered in a plane, the host lattice A' is the smallest size that can contain the circle. When considered in three dimensions, the host lattice A' is the smallest size that can contain the sphere.

[0332] In the analysis, a diagram of a unit cell A (guest lattice A) of a first crystalline material is compared with a diagram of a host lattice B' composed of one or more unit cells B of a second crystalline material. In addition, in the analysis, a diagram of a unit cell B (guest lattice B) of a second crystalline material is compared with a diagram of a host lattice A' composed of one or more unit cells A of a first crystalline material.

[0333] Here, using Fig.22A The diagram consisting of the unit cell A (guest lattice A) in Fig.22A The degree of similarity between them is calculated by using a diagram of the main lattice B' composed of the six unit cells B in FIG.

[0334] In addition, using Fig. 22B The diagram composed of the unit cell B (guest lattice B) in Fig. 22B A diagram of the main lattice A' formed by the four unit cells A in is used to calculate the degree of similarity between them.

[0335] Here, in the calculation of the similarity degree using the maximum independent set, the similarity degree is obtained by, for example, the following equation (2).

[0336] [Formula 4]

[0337]

[0338] Here, in the above formula (2), S(G A ,G B ) represents the degree of similarity between the unit cell A of the first crystal material expressed in the graph and the unit cell B of the second crystal material expressed in the graph, S(G A ,G B ) is expressed as 0 to 1, and means that the closer it is to 1, the higher the degree of similarity.

[0339] In addition, V A represents the total number of node atoms in the guest lattice of the unit cell A expressed as a graph, and V c A' It represents the number of node atoms included in the maximum independent set in the conflict graph among the host lattice A' composed of one or more unit cells A expressed in the graph. Note that the node atom means an atom at a vertex of a molecule expressed in the graph.

[0340] In addition, V B represents the total number of node atoms in the guest lattice as a unit cell B expressed in the graph, and V c B' It represents the number of node atoms included in the maximum independent set in the conflict graph in the main lattice B' composed of one or more unit cells B expressed in the graph.

[0341] δ represents a number from 0 to 1.

[0342] In addition, in the above formula (2), max{A, B} means selecting either A or B having a larger value, and min{A, B} means selecting either A or B having a smaller value.

[0343] Here, a conflict graph is created based on the following rule: when two nodes are compared and the two nodes are different from each other, an edge is created between the two nodes, and when two nodes are compared and the two nodes are the same as each other, no edge is created between the two nodes, wherein each of the nodes is a combination of one of the node atoms constituting a unit cell A or a main lattice A' of a first crystal material expressed in the graph and one of the node atoms constituting a unit cell B or a main lattice B' of a second crystal material expressed in the graph.

[0344] The above formula (2) can be simplified to the following formula (2-1): δ is 0.5.

[0345] [Mathematical formula 5]

[0346]

[0347] Here, AB' common represents the number of substructures shared by the guest lattice A and the host lattice B'. common A represents the number of substructures shared by the guest lattice B and the host lattice A'. all represents the number of nodes in the graph of the unit cell A, and B all Represents the number of nodes in the graph of unit cell B.

[0348] In the case of the second embodiment, by duplicating the graph to reduce the difference in the number of atoms (number of nodes) between the two unit cells to be compared, the reduction in the degree of similarity caused by the difference in the number of atoms (number of nodes) can be avoided. However, in the case where the number of unit cells does not match after duplication, the degree of similarity does not become 1.

[0349] On the other hand, in the case of the third embodiment, when the previously described formula (2) or (2-1) for calculating the degree of similarity is used, the maximum value of the degree of similarity is 1 even when the sizes of the unit cell A and the unit cell B are different.

[0350] Therefore, in the third embodiment, compared with the second embodiment, the reduction in the degree of similarity caused by the difference in the number of atoms (the number of nodes) of the two unit cells to be compared can be further avoided. Therefore, compared with the second embodiment, the accuracy of the analysis (e.g., the degree of similarity) can be further improved.

[0351] Therefore, the mapping technique of the third embodiment is used for analysis of crystal materials using computer technology.

[0352] Note that, for example, the combinations of the guest lattice and the host lattice in the third embodiment can be classified into the following combinations according to the structures of the diagrams, for example.

[0353] -3-1: The diagram of the object lattice is a simple diagram.

[0354] --3-1-1: The diagram of the main lattice is a simple diagram.

[0355] --3-1-2: The diagram of the main lattice is an extended diagram.

[0356] --3-1-3: The diagram of the main lattice is a loop diagram.

[0357] -3-2: The diagram of the guest lattice is an expanded diagram.

[0358] --3-2-1: The diagram of the main lattice is a simple diagram.

[0359] --3-2-2: The diagram of the main lattice is an extended diagram.

[0360] --3-2-3: The diagram of the main lattice is a loop diagram.

[0361] -3-3: The diagram of the object lattice is a loop diagram.

[0362] --3-3-1: The diagram of the main lattice is a simple diagram.

[0363] --3-3-2: The diagram of the main lattice is an extended diagram.

[0364] --3-3-3: The diagram of the main lattice is a loop diagram.

[0365] Will refer to Fig.24 The flowchart shown in briefly describes the crystal material analysis method in the third embodiment.

[0366] First, crystal structure data is extracted from another database (S21). Other databases are not particularly limited and can be appropriately selected according to the purpose. Examples of databases include inorganic crystal structure databases (ICSD) and the like. Note that the number and type of fragments of the crystal structure data to be extracted are not particularly limited and can be appropriately selected according to the purpose. For example, only crystal structure data about chemicals having specific elements can be extracted.

[0367] Next, using the extracted crystal structure data, a graph is created by mapping according to the technology of the present application and a graph database including the graph is created ( S22 ).

[0368] Next, the created graph is copied (S23). Here, when the graph is copied, at least one of the first copy or the second copy is performed. In the first copy, the graph of the unit cell of the second crystal material is copied so that the guest lattice of the unit cell of the first crystal material is adapted to the host lattice created by connecting a plurality of unit cells of the second crystal material. In the second copy, the graph of the unit cell of the first crystal material is copied so that the guest lattice of the unit cell of the second crystal material is adapted to the host lattice created by connecting a plurality of unit cells of the first crystal material. Next, the crystal material is analyzed (S24). In the analysis, a first comparison and a second comparison are performed. The first comparison is a comparison between a graph consisting of a guest lattice of the first crystal material and a graph consisting of a host lattice in which the guest lattice of the first crystal material is adapted. Here, the host lattice is a host lattice consisting of one or more unit cells of the second crystal material. The second comparison is a comparison between a graph consisting of a guest lattice of the second crystal material and a graph consisting of a host lattice in which the guest lattice of the second crystal material is adapted. Here, the host lattice is a host lattice composed of one or more unit cells of the first crystal material. Examples of the analysis include similarity evaluation. The similarity evaluation is performed by solving the maximum independent set problem in the conflict graph represented by the Ising model equation, for example, using an annealer.

[0369] Therefore, the similarity of crystal structures can be evaluated, which is one of the analyses of crystal structures.

[0370] Here, we will refer to FIG. 25A to FIG. 25C A working example of the third embodiment is described.

[0371] In the working example, we obtain Fig.25A The degree of similarity between the crystal material A represented by the unit cell A and the crystal material B represented by the unit cell B is shown in FIG. The crystal material A represented by the unit cell A has a Fig.25B The structure of the unit cell A is repeated as shown. The crystal material B represented by the unit cell B has a structure in which Fig.25C The structure shown is repeated for unit cell B. Unit cell A and unit cell B are composed of 16 different types of atoms A to P.

[0372] Using the graph created by unit cell A and the graph created by unit cell B, the maximum independent set problem in the conflict graph is expressed by the Ising model equation and solved by the annealer. Then, the degree of similarity between the crystal material of unit cell A and the crystal material of unit cell B obtained by the above formula (2-1) is shown in the following Table 1.

[0373] [Table 1]

[0374]

[0375] Note that here, Fig.26 A simple diagram, an expanded diagram, and a loop diagram are shown in the case where unit cell A is used as guest cell A. Fig. 27 A simple diagram, an expanded diagram, and a loop diagram are shown in the case where unit cell B is used as guest cell B.

[0376] Note that the expanded graph does not have any edges between expanded nodes.

[0377] In addition, Table 2 shows the results of obtaining the degree of similarity in a similar manner to Table 1 for the case where the graph created by the unit cell A in the patterns 3-2-1, 3-2-2, and 3-2-3 shown in Table 1 is an extended graph having edges between extended nodes (patterns 3-2'-1, 3-2'-2, and 3-2'-3). Note that, Fig.28 A schematic diagram is shown of a case where a graph created by cell A is an extended graph having edges between extended nodes. Comparison between pattern 3-2-1 and pattern 3-2'-1, comparison between pattern 3-2-2 and pattern 3-2'-2, and comparison between pattern 3-2-3 and pattern 3-2'-3 indicate that when an extended graph having edges between extended nodes is used, the degree of similarity becomes higher.

[0378] [Table 2]

[0379]

[0380] The disclosed technology may also be configured as follows:

[0381] 1. A crystal material analysis device, comprising:

[0382] A graph creation unit, for creating a loop graph, the loop graph having: intra-unit cell nodes indicating atoms in a unit cell of a crystal material; intra-unit cell edges indicating chemical bonds between atoms in the unit cell; and loop edges indicating virtual chemical bonds between atom X in the unit cell and atom Y in the unit cell: atom Y in the unit cell corresponds to atom Y' in an adjacent unit cell adjacent to the unit cell, wherein atom Y' has a chemical bond with atom X; and

[0383] An analyzing unit analyzes the crystal material by using the map.

[0384] 2. The crystal material analysis device according to configuration 1, wherein:

[0385] The graph creation unit creates a first loop graph of a unit cell of a first crystal material as the loop graph and a second loop graph of a unit cell of a second crystal material as the loop graph, and

[0386] The analyzing unit analyzes similarity between the first crystal material and the second crystal material by using the first loop graph and the second loop graph.

[0387] 3. The crystal material analysis device according to configuration 2, wherein:

[0388] The similarity analysis includes: using an annealing machine to solve the maximum independent set problem in the conflict graph represented by the Ising model equation,

[0389] Wherein, the conflict graph is created based on the following rule: when two nodes are compared and the two nodes are different from each other, an edge is created between the two nodes, and when two nodes are compared and the two nodes are the same as each other, no edge is created between the two nodes, wherein each of the nodes is a combination of one of the node atoms constituting the unit cell of the first crystal material expressed in the graph and one of the node atoms constituting the unit cell of the second crystal material expressed in the graph.

[0390] 4. A method for analyzing crystal materials executed by a computer, the method comprising:

[0391] A graph creation process for creating a loop graph, the loop graph having: intra-unit cell nodes indicating atoms in a unit cell of a crystal material; intra-unit cell edges indicating chemical bonds between atoms in the unit cell; and loop edges indicating virtual chemical bonds between an atom X in the unit cell and an atom Y in the unit cell corresponding to an atom Y' in an adjacent unit cell adjacent to the unit cell, wherein the atom Y' has a chemical bond with the atom X; and

[0392] An analysis process is provided for analyzing the crystalline material by using the loop diagram.

[0393] 5. The crystal material analysis method according to configuration 4, wherein:

[0394] In the graph creation process, a first loop graph of a unit cell of a first crystal material is created as the loop graph and a second loop graph of a unit cell of a second crystal material is created as the loop graph, and

[0395] In the analysis process, similarity between the first crystal material and the second crystal material is analyzed by using the first loop graph and the second loop graph.

[0396] 6. The crystal material analysis method according to configuration 5, wherein:

[0397] The similarity analysis includes: using an annealing machine to solve the maximum independent set problem in the conflict graph represented by the Ising model equation,

[0398] Wherein, the conflict graph is created based on the following rule: when two nodes are compared and the two nodes are different from each other, an edge is created between the two nodes, and when two nodes are compared and the two nodes are the same as each other, no edge is created between the two nodes, wherein each of the nodes is a combination of one of the node atoms constituting the unit cell of the first crystal material expressed in the graph and one of the node atoms constituting the unit cell of the second crystal material expressed in the graph.

[0399] 7. A computer-readable recording medium storing a program for causing a computer to execute a crystal material analysis process, the crystal material analysis process comprising:

[0400] Creating a loop graph, the loop graph having: intra-unit cell nodes indicating atoms in a unit cell of a crystal material; intra-unit cell edges indicating chemical bonds between atoms in the unit cell; and loop edges indicating virtual chemical bonds between atom X in the unit cell and atom Y in the unit cell: atom Y in the unit cell corresponding to atom Y' in an adjacent unit cell adjacent to the unit cell, wherein atom Y' has a chemical bond with atom X; and

[0401] The crystalline material is analyzed by using the loop diagram.

[0402] 8. The computer-readable recording medium according to configuration 7, wherein:

[0403] In the loop graph creation, a first loop graph of a unit cell of a first crystal material is created as the loop graph and a second loop graph of a unit cell of a second crystal material is created as the loop graph, and

[0404] In the analysis, similarity between the first crystal material and the second crystal material is analyzed by using the first loop graph and the second loop graph.

[0405] 9. The computer-readable recording medium according to configuration 8, wherein:

[0406] The similarity analysis includes: using an annealing machine to solve the maximum independent set problem in the conflict graph represented by the Ising model equation,

[0407] Wherein, the conflict graph is created based on the following rule: when two nodes are compared and the two nodes are different from each other, an edge is created between the two nodes, and when two nodes are compared and the two nodes are the same as each other, no edge is created between the two nodes, wherein each of the nodes is a combination of one of the node atoms constituting the unit cell of the first crystal material expressed in the graph and one of the node atoms constituting the unit cell of the second crystal material expressed in the graph.

[0408] 10. A crystal material analysis device, comprising:

[0409] A graph creation unit, configured to create a graph having: intra-unit cell nodes indicating atoms in a unit cell of a crystal material; and intra-unit cell edges indicating chemical bonds between atoms in the unit cell;

[0410] A graph duplication unit, which generates a duplicate graph by duplicating the graph; and

[0411] An analyzing unit analyzes the crystal material by using the replica image.

[0412] 11. The crystal material analysis device according to configuration 10, wherein:

[0413] the map creation unit creates a first map of a unit cell of a first crystal material as the map and a second map of a unit cell of a second crystal material as the map,

[0414] The graph copying unit copies at least one of the first graph or the second graph, and

[0415] The analyzing unit analyzes the similarity between the first crystal material and the second crystal material by using any one of the first graph or the first integrated graph and any one of the second graph or the second integrated graph, wherein the first integrated graph is obtained by integrating a plurality of first replicated graphs generated by replicating the first graph, and the second integrated graph is obtained by integrating a plurality of second replicated graphs generated by replicating the second graph.

[0416] 12. The crystal material analysis device according to configuration 11, wherein:

[0417] The similarity analysis includes: using an annealing machine to solve the maximum independent set problem in the conflict graph represented by the Ising model equation,

[0418] Wherein, the conflict graph is created based on the following rule: when two nodes are compared and the two nodes are different from each other, an edge is created between the two nodes, and when two nodes are compared and the two nodes are the same as each other, no edge is created between the two nodes, wherein each of the nodes is a combination of one of the node atoms constituting the unit cell of the first crystal material expressed in the graph and one of the node atoms constituting the unit cell of the second crystal material expressed in the graph.

[0419] 13. The crystal material analysis device according to configuration 11 or 12, wherein:

[0420] The copying of at least one of the first graph or the second graph is performed in such a manner that an absolute value of a difference between a total number of nodes in the plurality of the first graphs after copying and a total number of nodes in the plurality of the second graphs after copying is minimized.

[0421] 14. A method for analyzing crystal materials executed by a computer, the method comprising:

[0422] A graph creation process for creating a graph having: intra-unit cell nodes indicating atoms in a unit cell of a crystalline material; and intra-unit cell edges indicating chemical bonds between atoms in the unit cell;

[0423] a graph replication process for generating a replication graph by replicating the graph; and an analysis process for analyzing the crystal material by using the replication graph.

[0424] 15. The crystal material analysis method according to configuration 14, wherein:

[0425] In the graph creation process, a first graph of a unit cell of a first crystal material is created as the graph and a second graph of a unit cell of a second crystal material is created as the graph,

[0426] In the graph copying process, at least one of the first graph or the second graph is copied, and

[0427] In the analysis process, the similarity between the first crystal material and the second crystal material is analyzed by using any one of the first graph or the first integrated graph and any one of the second graph or the second integrated graph, wherein the first integrated graph is obtained by integrating a plurality of first replicated graphs generated by replicating the first graph, and the second integrated graph is obtained by integrating a plurality of second replicated graphs generated by replicating the second graph.

[0428] 16. The crystal material analysis method according to configuration 15, wherein:

[0429] The similarity analysis includes: using an annealing machine to solve the maximum independent set problem in the conflict graph represented by the Ising model equation,

[0430] Wherein, the conflict graph is created based on the following rule: when two nodes are compared and the two nodes are different from each other, an edge is created between the two nodes, and when two nodes are compared and the two nodes are the same as each other, no edge is created between the two nodes, wherein each of the nodes is a combination of one of the node atoms constituting the unit cell of the first crystal material expressed in the graph and one of the node atoms constituting the unit cell of the second crystal material expressed in the graph.

[0431] 17. The crystal material analysis method according to configuration 15 or 16, wherein:

[0432] The copying of at least one of the first graph or the second graph is performed in such a manner that an absolute value of a difference between a total number of nodes in the plurality of the first graphs after copying and a total number of nodes in the plurality of the second graphs after copying is minimized.

[0433] 18. A computer-readable recording medium storing a program for causing a computer to execute a crystal material analysis process, the crystal material analysis process comprising:

[0434] creating a graph having: intra-unit-cell nodes indicating atoms in a unit cell of a crystalline material; and intra-unit-cell edges indicating chemical bonds between atoms in the unit cell;

[0435] generating a duplicate graph by duplicating the graph; and

[0436] The crystalline material is analyzed by using the replica map.

[0437] 19. The computer-readable recording medium according to configuration 18, wherein:

[0438] In the graph creation, a first graph of a unit cell of a first crystalline material is created as the graph and a second graph of a unit cell of a second crystalline material is created as the graph,

[0439] In the graph duplication, at least one of the first graph or the second graph is duplicated, and

[0440] In the analysis, the similarity between the first crystal material and the second crystal material is analyzed by using any one of the first graph or the first integrated graph and any one of the second graph or the second integrated graph, wherein the first integrated graph is obtained by integrating a plurality of first replicated graphs generated by replicating the first graph, and the second integrated graph is obtained by integrating a plurality of second replicated graphs generated by replicating the second graph.

[0441] 20. The computer-readable recording medium according to configuration 19, wherein:

[0442] The similarity analysis includes: using an annealing machine to solve the maximum independent set problem in the conflict graph represented by the Ising model equation,

[0443] Wherein, the conflict graph is created based on the following rule: when two nodes are compared and the two nodes are different from each other, an edge is created between the two nodes, and when two nodes are compared and the two nodes are the same as each other, no edge is created between the two nodes, wherein each of the nodes is a combination of one of the node atoms constituting the unit cell of the first crystal material expressed in the graph and one of the node atoms constituting the unit cell of the second crystal material expressed in the graph.

[0444] 21. The computer-readable recording medium according to configuration 19 or 20, wherein:

[0445] The copying of at least one of the first graph or the second graph is performed in such a manner that an absolute value of a difference between a total number of nodes in the plurality of the first graphs after copying and a total number of nodes in the plurality of the second graphs after copying is minimized.

[0446] 22. A crystal material analysis device, comprising:

[0447] A graph creation unit, for creating a graph for the first crystal material and the second crystal material, the graph having: intra-unit cell nodes indicating atoms in one unit cell of the crystal material; and intra-unit cell edges indicating chemical bonds between atoms in the unit cell;

[0448] a graph duplication unit that performs at least one of a first duplication in which a graph of a unit cell of the second crystal material is duplicated in such a manner that a guest lattice of a unit cell of the first crystal material is adapted to a host lattice created by connecting a plurality of unit cells of the second crystal material, or a second duplication in which a graph of a unit cell of the first crystal material is duplicated in such a manner that a guest lattice of a unit cell of the second crystal material is adapted to a host lattice created by connecting a plurality of unit cells of the first crystal material; and

[0449] An analysis unit analyzes the crystal material by performing a first comparison between a graph consisting of a guest lattice of the first crystal material and a graph consisting of a host lattice consisting of one or more unit cells of the second crystal material that is adapted to the guest lattice of the first crystal material, and also performing a second comparison between a graph consisting of a guest lattice of the second crystal material and a graph consisting of a host lattice consisting of one or more unit cells of the first crystal material that is adapted to the guest lattice of the second crystal material.

[0450] 23. The crystal material analysis device according to configuration 22, wherein:

[0451] The first replication replicates a diagram of a unit cell of the second crystalline material in such a way that a sphere having a diameter corresponding to the longest diagonal of the guest lattice of the first crystalline material fits into the host lattice, and

[0452] The second replication replicates a diagram of a unit cell of the first crystalline material in such a way that a sphere having a diameter corresponding to the longest diagonal of the guest lattice of the second crystalline material fits into the host lattice.

[0453] 24. The crystal material analysis device according to configuration 22 or 23, wherein:

[0454] The analyzing unit analyzes similarity between the first crystal material and the second crystal material by using the first comparison and the second comparison.

[0455] 25. The crystal material analysis device according to configuration 24, wherein:

[0456] The similarity analysis includes: using an annealing machine to solve the maximum independent set problem in the conflict graph represented by the Ising model equation,

[0457] Wherein, the conflict graph is created based on the following rule: when two nodes are compared and the two nodes are different from each other, an edge is created between the two nodes, and when two nodes are compared and the two nodes are the same as each other, no edge is created between the two nodes, wherein each of the nodes is a combination of one of the node atoms constituting the unit cell of the first crystal material expressed in the graph and one of the node atoms constituting the unit cell of the second crystal material expressed in the graph.

[0458] 26. The crystal material analysis device according to configuration 25, wherein:

[0459] The analyzing unit uses the following formula (2) to obtain the degree of similarity between the first crystal material and the second crystal material based on the maximum independent set that has been searched out,

[0460] [Mathematical formula 1]

[0461]

[0462] Among them, in the above formula (2),

[0463] G A represents the first crystalline material,

[0464] G B represents the second crystalline material,

[0465] S(G A ,G B) represents the degree of similarity between the first crystal material and the second crystal material expressed in a graph, and is represented by 0 to 1, and means that the closer to 1, the higher the degree of similarity,

[0466] V A represents the total number of node atoms in the guest lattice of the unit cell of the first crystalline material expressed as a graph,

[0467] V c A' represents the number of node atoms included in the maximum independent set of the conflict graph among the node atoms in the host lattice composed of one or more unit cells of the first crystalline material expressed in the graph,

[0468] V B represents the total number of node atoms in the guest lattice of the unit cell of the second crystalline material expressed as a graph,

[0469] V c B' represents the number of node atoms included in the maximum independent set of the conflict graph among the node atoms in the host lattice composed of one or more unit cells of the second crystalline material expressed in the graph, and

[0470] δ represents a number from 0 to 1.

[0471] 27. A method for analyzing crystal materials executed by a computer, the method comprising:

[0472] A graph creation process for creating a graph for a first crystalline material and a second crystalline material, the graph having: intra-unit cell nodes indicating atoms in a unit cell of the crystalline materials; and intra-unit cell edges indicating chemical bonds between atoms in the unit cells;

[0473] a graph replication process for performing at least one of a first replication in which a graph of a unit cell of the second crystal material is replicated in such a manner that a guest lattice of the unit cell of the first crystal material is adapted to a host lattice created by connecting a plurality of unit cells of the second crystal material, or a second replication in which a graph of a unit cell of the first crystal material is replicated in such a manner that a guest lattice of the unit cell of the second crystal material is adapted to a host lattice created by connecting a plurality of unit cells of the first crystal material; and

[0474] Analysis processing for analyzing the crystalline material by performing a first comparison between a map consisting of a guest lattice of the first crystalline material and a map consisting of a host lattice consisting of one or more unit cells of the second crystalline material adapted to the guest lattice of the first crystalline material, and also performing a second comparison between a map consisting of a guest lattice of the second crystalline material and a map consisting of a host lattice consisting of one or more unit cells of the first crystalline material adapted to the guest lattice of the second crystalline material.

[0475] 28. The crystal material analysis method according to configuration 27, wherein:

[0476] The first replication replicates a diagram of a unit cell of the second crystalline material in such a way that a sphere having a diameter corresponding to the longest diagonal of the guest lattice of the first crystalline material fits into the host lattice, and

[0477] The second replication replicates a diagram of a unit cell of the first crystalline material in such a way that a sphere having a diameter corresponding to the longest diagonal of the guest lattice of the second crystalline material fits into the host lattice.

[0478] 29. The crystal material analysis method according to configuration 27 or 28, wherein:

[0479] In the analyzing process, similarity between the first crystal material and the second crystal material is analyzed by using the first comparison and the second comparison.

[0480] 30. The crystal material analysis method according to configuration 29, wherein:

[0481] The similarity analysis includes: using an annealing machine to solve the maximum independent set problem in the conflict graph represented by the Ising model equation,

[0482] Wherein, the conflict graph is created based on the following rule: when two nodes are compared and the two nodes are different from each other, an edge is created between the two nodes, and when two nodes are compared and the two nodes are the same as each other, no edge is created between the two nodes, wherein each of the nodes is a combination of one of the node atoms constituting the unit cell of the first crystal material expressed in the graph and one of the node atoms constituting the unit cell of the second crystal material expressed in the graph.

[0483] 31. The crystal material analysis method according to configuration 30, wherein:

[0484] In the analysis process, based on the maximum independent set that has been searched, the following formula (2) is used to obtain the degree of similarity between the first crystal material and the second crystal material:

[0485] [Mathematical formula 2]

[0486]

[0487] Among them, in the above formula (2),

[0488] G A represents the first crystalline material,

[0489] G B represents the second crystalline material,

[0490] S(G A ,G B ) represents the degree of similarity between the first crystal material and the second crystal material expressed in a graph, and is represented by 0 to 1, and means that the closer to 1, the higher the degree of similarity,

[0491] V A represents the total number of node atoms in the guest lattice of the unit cell of the first crystalline material expressed as a graph,

[0492] V c A' represents the number of node atoms included in the maximum independent set of the conflict graph among the node atoms in the host lattice composed of one or more unit cells of the first crystalline material expressed in the graph,

[0493] V B represents the total number of node atoms in the guest lattice of the unit cell of the second crystalline material expressed as a graph,

[0494] V c B' represents the number of node atoms included in the maximum independent set of the conflict graph among the node atoms in the host lattice composed of one or more unit cells of the second crystalline material expressed in the graph, and

[0495] δ represents a number from 0 to 1.

[0496] 32. A computer-readable recording medium storing a program for causing a computer to execute a crystal material analysis process, the crystal material analysis process comprising:

[0497] Creating a graph for the first crystalline material and the second crystalline material, the graph having: intra-unit cell nodes indicating atoms in a unit cell of the crystalline material; and intra-unit cell edges indicating chemical bonds between atoms in the unit cells;

[0498] performing at least one of a first replication in which a diagram of a unit cell of the second crystal material is replicated in such a manner that a guest lattice of the unit cell of the first crystal material is adapted to a host lattice created by connecting a plurality of unit cells of the second crystal material, or a second replication in which a diagram of a unit cell of the first crystal material is replicated in such a manner that a guest lattice of the unit cell of the second crystal material is adapted to a host lattice created by connecting a plurality of unit cells of the first crystal material; and

[0499] The crystalline material is analyzed by performing a first comparison between a graph consisting of a guest lattice of the first crystalline material and a graph consisting of a host lattice consisting of one or more unit cells of the second crystalline material adapted to the guest lattice of the first crystalline material, and also performing a second comparison between a graph consisting of a guest lattice of the second crystalline material and a graph consisting of a host lattice consisting of one or more unit cells of the first crystalline material adapted to the guest lattice of the second crystalline material.

[0500] 33. The computer-readable recording medium according to configuration 32, wherein:

[0501] The first replication replicates a diagram of a unit cell of the second crystalline material in such a way that a sphere having a diameter corresponding to the longest diagonal of the guest lattice of the first crystalline material fits into the host lattice, and

[0502] The second replication replicates a diagram of a unit cell of the first crystalline material in such a way that a sphere having a diameter corresponding to the longest diagonal of the guest lattice of the second crystalline material fits into the host lattice.

[0503] 34. The computer-readable recording medium according to configuration 32 or 33, wherein:

[0504] In the analysis, similarity between the first crystal material and the second crystal material is analyzed by using the first comparison and the second comparison.

[0505] 35. The computer-readable recording medium according to configuration 34, wherein:

[0506] The similarity analysis includes: using an annealing machine to solve the maximum independent set problem in the conflict graph represented by the Ising model equation,

[0507] Wherein, the conflict graph is created based on the following rule: when two nodes are compared and the two nodes are different from each other, an edge is created between the two nodes, and when two nodes are compared and the two nodes are the same as each other, no edge is created between the two nodes, wherein each of the nodes is a combination of one of the node atoms constituting the unit cell of the first crystal material expressed in the graph and one of the node atoms constituting the unit cell of the second crystal material expressed in the graph.

[0508] 36. The computer-readable recording medium according to configuration 35, wherein:

[0509] In the analysis, based on the maximum independent set that has been searched, the following formula (2) is used to obtain the degree of similarity between the first crystal material and the second crystal material:

[0510] [Mathematical formula 3]

[0511]

[0512] Among them, in the above formula (2),

[0513] G A represents the first crystalline material,

[0514] G B represents the second crystalline material,

[0515] S(G A ,G B ) represents the degree of similarity between the first crystal material and the second crystal material expressed in a graph, and is represented by 0 to 1, and means that the closer to 1, the higher the degree of similarity,

[0516] V A represents the total number of node atoms in the guest lattice of the unit cell of the first crystalline material expressed as a graph,

[0517] V c A' represents the number of node atoms included in the maximum independent set of the conflict graph among the node atoms in the host lattice composed of one or more unit cells of the first crystalline material expressed in the graph,

[0518] V B represents the total number of node atoms in the guest lattice of the unit cell of the second crystalline material expressed as a graph,

[0519] V c B'represents the number of node atoms included in the maximum independent set of the conflict graph among the node atoms in the host lattice composed of one or more unit cells of the second crystalline material expressed in the graph, and

[0520] δ represents a number from 0 to 1.

Claims

1. A crystal material analysis device, comprising: A graph creation unit, configured to create a loop graph, the loop graph having: intra-unit cell nodes indicating atoms in one unit cell of a crystal material; Internal edges of the unit cell, which indicate chemical bonds between atoms in the unit cell; and a loop edge indicating a virtual chemical bond between an atom X in the unit cell and an atom Y in the unit cell: the atom Y in the unit cell corresponds to an atom Y' in an adjacent unit cell adjacent to the unit cell, wherein the atom Y' has a chemical bond with the atom X; and An analyzing unit analyzes the crystal material by using the map, wherein, The graph creation unit creates a first loop graph of a unit cell of a first crystal material as the loop graph and a second loop graph of a unit cell of a second crystal material as the loop graph, and The analyzing unit analyzes similarity between the first crystal material and the second crystal material by using the first loop graph and the second loop graph, and wherein, The similarity analysis includes: using an annealing machine to solve the maximum independent set problem in a conflict graph represented by the Ising model equation, wherein the conflict graph is created based on the following rule: when two nodes are compared and the two nodes are not identical to each other, an edge is created between the two nodes, and when two nodes are compared and the two nodes are identical to each other, no edge is created between the two nodes, wherein each of the nodes is a combination of one of the node atoms constituting the unit cell of the first crystal material expressed in the graph and one of the node atoms constituting the unit cell of the second crystal material expressed in the graph.

2. A method for analyzing crystal materials executed by a computer, the method comprising: A graph creation process for creating a loop graph having: intra-unit cell nodes indicating atoms in one unit cell of a crystalline material; Internal edges of the unit cell, which indicate chemical bonds between atoms in the unit cell; and a loop edge indicating a virtual chemical bond between an atom X in the unit cell and an atom Y in the unit cell: the atom Y in the unit cell corresponds to an atom Y' in an adjacent unit cell adjacent to the unit cell, wherein the atom Y' has a chemical bond with the atom X; and Analytical processing for analyzing the crystalline material by using the loop diagram, wherein, In the graph creation process, a first loop graph of a unit cell of a first crystal material is created as the loop graph and a second loop graph of a unit cell of a second crystal material is created as the loop graph, and In the analysis process, similarity between the first crystal material and the second crystal material is analyzed by using the first loop graph and the second loop graph, and wherein, The similarity analysis includes: using an annealing machine to solve the maximum independent set problem in a conflict graph represented by the Ising model equation, wherein the conflict graph is created based on the following rule: when two nodes are compared and the two nodes are not identical to each other, an edge is created between the two nodes, and when two nodes are compared and the two nodes are identical to each other, no edge is created between the two nodes, wherein each of the nodes is a combination of one of the node atoms constituting the unit cell of the first crystal material expressed in the graph and one of the node atoms constituting the unit cell of the second crystal material expressed in the graph.

3. A computer-readable recording medium storing a program for causing a computer to execute a crystal material analysis process, the crystal material analysis process comprising: creating a loop graph having: intra-unit-cell nodes indicating atoms in one unit cell of a crystalline material; Internal edges of the unit cell, which indicate chemical bonds between atoms in the unit cell; and a loop edge indicating a virtual chemical bond between an atom X in the unit cell and an atom Y in the unit cell: the atom Y in the unit cell corresponds to an atom Y' in an adjacent unit cell adjacent to the unit cell, wherein the atom Y' has a chemical bond with the atom X; and The crystalline material is analyzed by using the loop diagram, wherein, In the loop graph creation, a first loop graph of a unit cell of a first crystal material is created as the loop graph and a second loop graph of a unit cell of a second crystal material is created as the loop graph, and In the analysis, similarity between the first crystal material and the second crystal material is analyzed by using the first loop graph and the second loop graph, and wherein, The similarity analysis includes: using an annealing machine to solve the maximum independent set problem in a conflict graph represented by the Ising model equation, wherein the conflict graph is created based on the following rule: when two nodes are compared and the two nodes are not identical to each other, an edge is created between the two nodes, and when two nodes are compared and the two nodes are identical to each other, no edge is created between the two nodes, wherein each of the nodes is a combination of one of the node atoms constituting the unit cell of the first crystal material expressed in the graph and one of the node atoms constituting the unit cell of the second crystal material expressed in the graph.

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