Computing device, method and program

Abstract

A calculation device, method, and program for calculating a correlation function from a structural model are provided. [Solution] A computing device 100 that calculates a correlation function from a structural model includes a structural model acquisition unit 110 that acquires the structural model including multiple types of atoms in space, an atomic species setting unit 120 that sets a specific atomic species in the structural model, and a correlation function calculation unit 130 that calculates the correlation function, which is the ratio between a first radial distribution function and a second radial distribution function, wherein the first radial distribution function is a radial distribution function between atoms of the specific atomic species and atoms of the specific atomic species, and the second radial distribution function is a radial distribution function between atoms of the specific atomic species and atoms of two or more atomic species including the specific atomic species.

Description

Technical Field

[0001] The present invention relates to a computing device, a method, and a program for calculating a correlation function from a structural model.

Background Art

[0002] In recent years, with the development of analysis methods such as the RMC method, it has become possible to analyze a range larger than the unit cell. As a result, information that could not be obtained by conventional analysis using a unit cell can now be obtained. One such piece of information is the information on the particle positions in the structural model.

[0003] However, conventionally, there has been no method for evaluating the mixing state of neighboring atoms in a structural model other than discussing it using the partial correlation two-body distribution function g(r) from the estimated structural model. Since understanding the mixing state of neighboring atoms in a structural model advances the understanding of the properties of materials, such information is important.

[0004] Non-Patent Document 1 discloses a method for estimating S(Q) of the mixing state of a binary system by actual measurement. It also discloses a thermodynamic formula that can examine the concentration and temperature dependence of various types of mixtures (regular, disorder-order type, athermal, etc.).

[0005] Non-Patent Document 2 discloses that an analysis of the dipole correlation of water as a function of temperature and density and in the presence of a simple ionic solute was performed using molecular dynamics simulation and an empirical potential. Non-Patent Document 2 defines a spatial correlation function of dipole-dipole and discusses its characteristics.

Prior Art Documents

Non-Patent Documents

[0006]

Non-Patent Document 1

Non-Patent Document 2

Summary of the Invention

Problems to be Solved by the Invention

[0007] However, the methods described in Non-Patent Document 1 and Non-Patent Document 2 do not consider expressing the mixing state of neighboring atoms in the structural model.

[0008] As a result of intensive research, the inventors have discovered that the mixing state of neighboring atoms in the structural model can be represented by calculating a correlation function, which is the ratio of two types of radial distribution functions focused on specific atomic species. Further, by analyzing the calculated correlation function, it has been found that the mixing state of neighboring atoms in the structural model can be evaluated, and the present invention has been completed.

[0009] The present invention has been made in view of such circumstances, and an object thereof is to provide a computing device, a method, and a program for calculating a correlation function from a structural model.

Means for Solving the Problems

[0010] (1) To achieve the above object, the computing device of the present invention has taken the following means. That is, the computing device according to one aspect of the present invention is a computing device that calculates a correlation function from a structural model, and includes a structural model acquisition unit that acquires the structural model including a plurality of types of atoms in space, an atomic species setting unit that sets a specific atomic species in the structural model, and a correlation function calculation unit that calculates the correlation function which is the ratio of the first radial distribution function and the second radial distribution function. The first radial distribution function is the radial distribution function between atoms of the specific atomic species, and the second radial distribution function is the radial distribution function between atoms of the specific atomic species and atoms of two or more atomic species including the specific atomic species.

[0011] (2) Further, the computing device according to one aspect of the present invention further includes a display unit that displays the correlation function.

[0012] (3) Further, in the computing device according to one aspect of the present invention, the display unit superimposes and displays the correlation function and the atomic number ratio of the specific atomic species in the structural model.

[0013] (4) Further, in the computing device according to one aspect of the present invention, the display unit simultaneously displays the correlation function of the specific atomic species and the correlation function of an atomic species different from the specific atomic species.

[0014] (5) Further, the computing device according to one aspect of the present invention further includes a plane determination unit that determines a specific plane in the structural model, and the correlation function calculation unit calculates the correlation function in the specific plane.

[0015] (6) Further, the computing device according to one aspect of the present invention further includes an evaluation unit that evaluates the regularity of the atomic arrangement in the structural model based on the correlation function.

[0016] (7) Further, the computing device according to one aspect of the present invention further includes an index calculation unit that calculates an index based on the correlation function, and the evaluation unit evaluates the regularity of the atomic arrangement based on the index.

[0017] (8) Also, in the computing device according to one aspect of the present invention, the index is the variance or standard deviation of the correlation function.

[0018] (9) Also, in the computing device according to one aspect of the present invention, the index is calculated based on the ratio of the correlation function to the number of atoms of the specific atomic species in the structural model.

[0019] (10) Also, in the computing device according to one aspect of the present invention, the structural model is a model generated by the RMC method.

[0020] (11) Also, a method according to one aspect of the present invention is a method for calculating a correlation function from a structural model, the method including: obtaining the structural model including a plurality of types of atoms in space; setting a specific atomic species in the structural model; and calculating the correlation function that is a ratio between a first radial distribution function and a second radial distribution function, wherein the first radial distribution function is a radial distribution function between atoms of the specific atomic species, and the second radial distribution function is a radial distribution function between atoms of the specific atomic species and atoms of two or more types of atomic species including the specific atomic species.

[0021] (12) Also, a program according to one aspect of the present invention is a program for calculating a correlation function from a structural model, the program causing a computer to execute: a process of obtaining the structural model including a plurality of types of atoms in space; a process of setting a specific atomic species in the structural model; and a process of calculating the correlation function that is a ratio between a first radial distribution function and a second radial distribution function, wherein the first radial distribution function is a radial distribution function between atoms of the specific atomic species, and the second radial distribution function is a radial distribution function between atoms of the specific atomic species and atoms of two or more types of atomic species including the specific atomic species.

Brief Description of the Drawings

[0022]

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Mode for Carrying Out the Invention

[0023] Next, embodiments of the present invention will be described with reference to the drawings. For ease of understanding of the description, the same reference numerals are assigned to the same components in each drawing, and overlapping descriptions are omitted.

[0024] [Embodiment] (Embodiment 1) [Computing Device] In Embodiment 1, the case of calculating the correlation function from the structural model will be described. FIG. 1 is a block diagram showing an example of the configuration of a computing device 100 according to Embodiment 1. The computing device 100 may be connected to the X-ray diffractometer 200 via a control device 300 that controls the X-ray diffractometer 200 described later, or directly to the X-ray diffractometer 200.

[0025] The computing device 100 calculates a correlation function from a structural model. The computing device 100 is composed of a computer in which a CPU (Central Processing Unit), a ROM (Read Only Memory), a RAM (Random Access Memory), and a memory are connected to a bus. The computing device 100 may be a PC terminal or a server on the cloud. Also, not only the entire device but also some devices or some functions within the device may be provided on the cloud. The input device 510 and the display device 520 are connected to the CPU of the computing device 100 via appropriate interfaces. The input device 510 is, for example, a keyboard or a mouse and inputs to the computing device 100. The display device 520 is, for example, a display and displays a structural model, a specific atomic species, the atomic number ratio of a specific atomic species, a correlation function, a radial distribution function, a two-body distribution function, a specific plane in the structural model, an evaluation of the regularity of the atomic arrangement in the structural model, an index, a dispersion, etc.

[0026] The computing device 100 includes a structural model acquisition unit 110, an atomic species setting unit 120, and a correlation function calculation unit 130. Each unit can send and receive information via the control bus L.

[0027] The structural model acquisition unit 110 acquires a structural model. The structural model acquisition unit 110 may acquire information regarding the characteristics of the structural model together with the structural model. Information regarding the characteristics of the structural model is, for example, information such as that the structural model has a layered structure. The structural model acquisition unit 110 may directly acquire the structural model from a device or software that generates the structural model, or may acquire the structural model stored in a storage device or the like. Also, the computing device 100 itself may have a function of generating a structural model.

[0028] A structural model is a model showing the arrangement of particles (atoms, molecules) within a finite region. The structural model can be given as data showing the arrangement of a finite number of particles in, for example, a cube, a rectangular parallelepiped, or a parallelepiped according to the sample. In the present invention, the structural model is a model including a plurality of types of particles (atoms, molecules).

[0029] The structural model to which the present invention can be applied may be a structural model created by structural modeling using a crystal structure as an initial structure, regardless of the measurement data of any device. For example, it is not limited to a structural model created based on total scattering data measured by an X-ray diffractometer, and can be applied to a structural model created based on measurement data measured by a probe similar thereto. Specifically, for example, it can be applied to a structural model created based on measurement data by synchrotron radiation or measurement data by particle beams such as neutron beams and electron beams.

[0030] The structural model is preferably a model generated by the RMC method (Reverse Monte Carlo). The RMC method is a method of estimating a structural model that reproduces measured values by moving the atomic (molecular) arrangement of a given structural model using random numbers. Since the RMC method has a wide search space and can obtain a global minimum solution, it is effective as a solution method for complex optimization problems. When the RMC method is applied to the present invention, the possibility of obtaining a structural model that reproduces measurement data increases, and the correlation function calculated based thereon is likely to be a meaningful function for understanding the measurement data. Note that the method for generating the structural model is not limited to the RMC method. The structural model can also be generated, for example, by the MD method (molecular dynamics) or the MC method (Monte Carlo method).

[0031] The atomic species setting unit 120 sets a specific atomic species in the structural model. The specific atomic species is one of the types of atoms for which the correlation function in the structural model is to be calculated. The setting of the specific atomic species may be performed according to a user's instruction.

[0032] The correlation function calculation unit 130 calculates a correlation function that is the ratio of the first radial distribution function to the second radial distribution function. The first radial distribution function is the radial distribution function between atoms of a specific atomic species. The second radial distribution function is the radial distribution function between an atom of a specific atomic species and atoms of two or more atomic species including the specific atomic species in the structural model. The two or more atomic species including the specific atomic species in the structural model may be some of the atomic species in the structural model or all of the atomic species. It can be said that the correlation function including the ratio of the first radial distribution function to the second radial distribution function expresses the distance dependence of the density fluctuation of the atomic species.

[0033] The radial distribution function shows the distribution of atoms and is defined as a function of distance for the distribution of atoms located around a certain atom. That is, the first radial distribution function can be said to be the distribution of atoms of the specific atomic species located around the atom of the specific atomic species. Also, the second radial distribution function can be said to be the distribution of atoms of two or more selected atomic species including the specific atomic species located around the atom of the specific atomic species.

[0034] Examples will be given and explained for two or more selected atomic species including a specific atomic species. For example, when the atomic species included in the structural model are A, B, and C and the specific atomic species is A, the two or more selected atomic species including the specific atomic species are any of A and B, A and C, and A, B, and C.

[0035] Let the specific atomic species be A, the first radial distribution function be N AA (r), and the second radial distribution function be N AX (r). At this time, the first radial distribution function N AA (r) is represented by, for example, the following mathematical formula (1). The second radial distribution function N AX (r) is represented by, for example, the following mathematical formula (2). However, r is the distance, N[[ID=2i]] A is the number of A, δ is the delta function, r ij is the distance between the i-th A and the j-th A or the selected atomic species, and N indicates the number of two or more selected atomic species including the specific atomic species.

[0036] [Numerals]

[0037] [Numerals]

[0038] Note that the defining formulas for the first radial distribution function and the second radial distribution function are not limited to Mathematical Formulas (1) and (2). For example, the delta function may be replaced with a function such as a Gaussian distribution indicating the probability of existence of a specific atomic species or two or more selected atomic species including a specific atomic species.

[0039] Let the first radial distribution function be N AA (r), the second radial distribution function be N AX (r), and the correlation function be C A (r). At this time, the correlation function C A (r) can be expressed, for example, by the following Mathematical Formula (3). Note that the defining formula for the correlation function is not limited to Mathematical Formula (3). The correlation function may be any formula including the ratio of the first radial distribution function and the second radial distribution function. On the other hand, by defining the correlation function C A (r) as in Mathematical Formula (3), the upper limit of the correlation function C A (r) becomes 1. When C A (r) is 1, it can be seen that only a specific atomic species pair exists at the correlation distance r. Therefore, it is preferable to define the correlation function to have such a property.

[0040] [Numerals]

[0041] In the above description, an example of defining a correlation function as the ratio of the first radial distribution function and the second radial distribution function was shown. However, the correlation function does not necessarily have to be defined as the ratio of the first radial distribution function and the second radial distribution function. For example, it can also be defined as the ratio of pair distribution functions for a specific atomic species.

[0042] Specifically, let a specific atomic species be A, and let g AA (r) be the pair distribution function of only A centered on A (the first pair distribution function), and g AX (r) be the pair distribution function of two or more selected atomic species including A centered on A (the second pair distribution function). At this time, the correlation function C A (r) identical to Equation (3) can also be defined by the following Equation (4). This is because the radial distribution function N(r) and the pair distribution function g(r) have the relationship shown in the following Equation (5). Here, ρ is the average density of the structural model.

[0043]

Equation

[0044]

Equation

[0045] Therefore, even when the correlation function is defined as the ratio of pair distribution functions for a specific atomic species, it can be said that the correlation function is the ratio of the first radial distribution function and the second radial distribution function. The calculation of the correlation function may be performed after calculating the radial distribution function or the pair distribution function, or it may be directly calculated from the definition formula itself without calculating the radial distribution function or the pair distribution function.

[0046] FIG. 2 is a block diagram showing a modified example of the configuration of the computing device 100 according to Embodiment 1. As shown in FIG. 2, the computing device 100 preferably further includes a display unit 150 in addition to a structure model acquisition unit 110, an atomic species setting unit 120, and a correlation function calculation unit 130. The display unit 150 causes the display device 520 to display the correlation function. Further, the display unit 150 may display a structure model, a specific atomic species, an atomic number ratio of a specific atomic species, a radial distribution function (first radial distribution function or second radial distribution function), a two-body distribution function (first two-body distribution function or second two-body distribution function), a specific plane in the structure model, an evaluation of the regularity of the atomic arrangement in the structure model, an index, a dispersion, and the like.

[0047] The display unit 150 preferably superimposes and displays the correlation function and the atomic number ratio of a specific atomic species in the structure model. The atomic number ratio of a specific atomic species in the structure model may be the atomic number ratio of a specific atomic species with respect to two or more atomic species including the specific atomic species selected when calculating the second radial distribution function. Further, the atomic number ratio of a specific atomic species in the structure model may be the atomic number ratio of a specific atomic species with respect to any two or more atomic species including the specific atomic species. Thus, by superimposing and displaying the correlation function and the atomic number ratio of a specific atomic species in the structure model, the characteristics of the correlation function with respect to the average concentration of a specific atomic species can be grasped.

[0048] The display unit 150 preferably simultaneously displays the correlation function of a specific atomic species and the correlation function of an atomic species different from the specific atomic species (also referred to as a second specific atomic species). Thereby, the characteristics of the correlation function for each atomic species can be compared, and the characteristics of the points of agreement and differences can be grasped.

[0049] FIG. 3 is a flowchart showing an example of the operation of the computing device 100 according to Embodiment 1. FIG. 3 shows an example of the operation when calculating a correlation function from a structural model. First, the computing device 100 acquires a structural model by the structural model acquisition unit 110 (step S1). Next, the atomic species setting unit 120 sets a specific atomic species in the structural model acquired by the structural model acquisition unit 110 (step S2). Then, the correlation function calculation unit 130 calculates a correlation function (step S3). If necessary, the correlation function may be output. Also, a radial distribution function or a pair distribution function may be output. In this way, the correlation function can be calculated from the structural model.

[0050] When the computing device 100 includes the display unit 150, if necessary, the correlation function, the radial distribution function, or the pair distribution function may be displayed. In this way, the characteristics of the correlation function calculated from the structural model can be grasped. Since the correlation function can be said to be a function representing the mixing state of neighboring particles in the structural model, the mixing state of neighboring particles in the structural model can be explained by analyzing this.

[0051] (Embodiment 2) [Computing Device] In Embodiment 2, the case of calculating a correlation function for a specific plane in the structural model will be described. FIG. 4 is a block diagram showing an example of the configuration of the computing device 100 according to Embodiment 2. As shown in FIG. 4, in addition to the structural model acquisition unit 110, the atomic species setting unit 120, and the correlation function calculation unit 130, the computing device 100 preferably further includes a plane determination unit 125.

[0052] The plane determination unit 125 determines a specific plane in the structural model. The specific plane is the plane for which the correlation function in the structural model is to be calculated. By determining the specific plane, the mixing state of neighboring particles in the specific plane can be analyzed. The determination of the specific plane may be performed according to a user's instruction. Also, when information regarding the characteristics of the structural model is attached to the structural model, it may be configured to provide the user with an option to determine whether or not to determine a specific plane based on the information.

[0053] When the plane determination unit 125 determines a specific plane, the correlation function calculation unit 130 calculates the correlation function on the specific plane. The correlation function on the specific plane is a correlation function that is the ratio of the first radial distribution function and the second radial distribution function on the specific plane. Also, when the plane determination unit 125 does not determine a specific plane, the correlation function calculation unit 130 calculates the correlation function for the entire structural model.

[0054] FIG. 5 is a flowchart showing an example of the operation of the computing device 100 according to Embodiment 2. FIG. 5 shows an example of the operation when determining whether to determine a specific plane. First, the computing device 100 acquires a structural model by the structural model acquisition unit 110 (step T1). Next, the atomic species setting unit 120 sets a specific atomic species in the structural model acquired by the structural model acquisition unit 110 (step T2).

[0055] Next, it is determined whether to determine a specific plane (step T3). When determining a specific plane (step T3 - YES), the plane determination unit 125 determines a specific plane (step T4). Then, the correlation function calculation unit 130 calculates the correlation function (step T5). On the other hand, when not determining a specific plane (step T3 - NO), the correlation function calculation unit 130 calculates the correlation function (step T5). If necessary, the correlation function, the specific plane, the radial distribution function, or the pair distribution function may be output. Also, when the computing device 100 includes the display unit 150, these may be displayed as necessary. In this way, the correlation function on the specific plane can be calculated. Note that the determination of the specific plane may be performed before the setting of the specific atomic species.

[0056] (Embodiment 3) [Computing Device] In Embodiment 3, the case of evaluating the regularity of the atomic arrangement based on the correlation function will be described. FIG. 6 is a block diagram showing an example of the configuration of the computing device 100 according to Embodiment 3. As shown in FIG. 6, in addition to the structural model acquisition unit 110, the atomic species setting unit 120, and the correlation function calculation unit 130, the computing device 100 preferably further includes an evaluation unit 140.

[0057] The evaluation unit 140 evaluates the regularity of the atomic arrangement in the structural model based on the correlation function. The regularity of the atomic arrangement in the structural model includes the perspective of whether the atomic arrangement in the structural model can be said to be statistically random or whether it has some regularity and cannot be said to be statistically random. The evaluation of the regularity of the atomic arrangement in the structural model may include, for example, the evaluation of whether clusters are formed between adjacent particles in a specific atomic species of the structural model. When the correlation distance r is small and the correlation coefficient is greater than the atomic number ratio of a specific atomic species, it may be determined that clusters are formed. The evaluation of the regularity of the atomic arrangement in the structural model may be a numerical value calculated based on the correlation function or a descriptive content determined based on the characteristics of the correlation function.

[0058] FIG. 7 is a block diagram showing a modified example of the configuration of the computing device 100 according to Embodiment 3. As shown in FIG. 7, in addition to the structural model acquisition unit 110, the atomic species setting unit 120, the correlation function calculation unit 130, and the evaluation unit 140, the computing device 100 preferably further includes an index calculation unit 135.

[0059] The index calculation unit 135 calculates an index based on the correlation function. When the computing device 100 includes the index calculation unit 135, the evaluation unit 140 evaluates the regularity of the atomic arrangement in the structural model based on the index calculated by the index calculation unit 135. The index is preferably a numerical value that can be used for evaluating the regularity of the atomic arrangement in the structural model. The evaluation unit 140 may determine that there is regularity when the index satisfies a predetermined condition. The predetermined condition varies depending on the type of the index.

[0060] The index is preferably the variance or standard deviation of the correlation function. In the case of a random atomic arrangement, the correlation function approaches a constant value regardless of the distance. That is, when the deviation from the constant value is large, it is considered that the atomic arrangement has some regularity. Therefore, for example, when the variance of the correlation function is greater than a certain value, it may be evaluated that the atomic arrangement has regularity, and when the variance of the correlation function is less than a certain value, the atomic arrangement is random. Also, for example, when the variance of the correlation function is larger compared to the variance of the correlation function of the comparison target, the atomic arrangement has regularity compared to the atomic arrangement of the comparison target, and when the variance of the correlation function is smaller compared to the variance of the correlation function of the comparison target, the atomic arrangement may be evaluated as random compared to the atomic arrangement of the comparison target. The same applies to the standard deviation. When determining that there is regularity when the index satisfies a predetermined condition, the predetermined condition may be that the variance or standard deviation is equal to or greater than a certain value. Specific examples in the case of using the variance as the index will be described in detail in the examples.

[0061] Also, the index is preferably calculated based on the ratio of the number of atoms of a specific atomic species in the correlation function and the structural model. When the atomic arrangement in the structural model is random, the correlation function approaches the ratio of the number of atoms of a specific atomic species in the structural model (hereinafter, the abundance of the specific atomic species). That is, when the value of the correlation function deviates from the abundance of the specific atomic species, it can be determined that the atomic arrangement has regularity. When calculating the correlation function by determining a specific plane, the ratio of the number of atoms of a specific atomic species in the structural model may be the ratio of the number of atoms of a specific atomic species in the specific plane. When determining that there is regularity when the index satisfies a predetermined condition, the predetermined condition may be that the value of the index calculated from the ratio of the number of atoms of the specific atomic species and the value of the correlation function is equal to or greater than a certain value.

[0062] FIG. 8 is a flowchart showing an example of the operation of the computing device 100 according to Embodiment 3. FIG. 8 shows an example of the operation when evaluating the regularity of an atomic arrangement based on a correlation function. First, the computing device 100 acquires a structural model by the structural model acquisition unit 110 (step U1). Next, the atomic species setting unit 120 sets a specific atomic species in the structural model acquired by the structural model acquisition unit 110 (step U2).

[0063] Next, the correlation function calculation unit 130 calculates a correlation function (step U3). Then, the evaluation unit 140 evaluates the regularity of the atomic arrangement in the structural model (step U4). When the computing device 100 includes the index calculation unit 135, before evaluating the regularity of the atomic arrangement in the structural model, the index calculation unit 135 calculates an index. Thereafter, the evaluation unit 140 evaluates the regularity of the atomic arrangement based on the index. If necessary, the correlation function, radial distribution function, pair distribution function, evaluation, or index may be output. Also, when the computing device 100 includes the display unit 160, these may be displayed as necessary. In this way, the regularity of the atomic arrangement in the structural model can be evaluated based on the correlation function.

[0064] Note that Embodiment 1 to Embodiment 3 may each be configured to include a part or all of the configurations of other embodiments. FIG. 9 is a block diagram showing an example of the configuration of the computing device 100 according to an embodiment of the present invention. As shown in FIG. 9, the computing device 100 includes a structural model acquisition unit 110, an atomic species setting unit 120, a plane determination unit 125, a correlation function calculation unit 130, an index calculation unit 135, an evaluation unit 140, and a display unit 150. Among these, the plane determination unit 125, the index calculation unit 135, the evaluation unit 140, or the display unit 150 is an optional component.

[0065] [Overall System] The computing device 100 or the computing method of the present invention can obtain a structural model and calculate or evaluate a correlation function independently of the X-ray diffractometer 200 and the control device 300. Therefore, the computing device 100 does not need to be used simultaneously with the X-ray diffractometer 200 or the control device 300. On the other hand, it can also be integrated with the X-ray diffractometer 200 and the control device 300 into a system. FIG. 10 is a conceptual diagram showing an example of the configuration of a system 400 including the computing device 100 and the X-ray diffractometer 200. The system 400 includes a computing device 100, an X-ray diffractometer 200, and a control device 300.

[0066] In addition, in FIG. 10, the computing device 100 and the control device 300 are described as the same PC. However, the computing device 100 may be configured as a device different from the control device 300. Hereinafter, the case where the computing device 100 and the control device 300 are configured as different devices will be described.

[0067] [X-ray diffractometer] The X-ray diffractometer 200 constitutes an optical system that irradiates a sample with X-rays and detects the reflected X-rays generated from the sample. The X-ray diffractometer 200 includes at least an X-ray generation unit 210 that generates X-rays from an X-ray focus, i.e., an X-ray source, a sample stage 240 where a sample is placed and controls the rotation of the sample, and a detector 260 that detects X-rays. The X-ray diffractometer 200 may include an incident-side optical unit 220, a goniometer 230, or an exit-side optical unit 250. Since the X-ray generation unit 210, the incident-side optical unit 220, the goniometer 230, the sample stage 240, the exit-side optical unit 250, and the detector 260 that constitute the X-ray diffractometer 200 may be general ones, detailed descriptions are omitted. Note that the configuration shown in FIG. 10 is only an example, and various other configurations can be adopted.

[0068] [Control device] The control device 300 is connected to the X-ray diffractometer 200 and controls the X-ray diffractometer 200, and processes, stores, and displays the acquired data.

[0069] FIG. 11 is a block diagram showing an example of the configuration of the control device 300. The control device 300 is composed of a computer in which a CPU, a ROM, a RAM, and a memory are connected to a bus. The control device 300 may be a PC terminal or a server on the cloud. Also, not only the entire device but also some devices or some functions within the device may be provided on the cloud. The control device 300 is connected to the X-ray diffractometer 200 and receives information.

[0070] The control device 300 includes a control unit 310, a device information storage unit 320, a measurement data storage unit 330, and a display unit 340. Each unit can transmit and receive information via the control bus L. When the computing device 100 and the control device 300 have different configurations, the input device 510 and the display device 520 are connected to the CPU of the control device 300 via appropriate interfaces. In this case, the input device 510 and the display device 520 may be different from those connected to the computing device 100.

[0071] The control unit 310 controls the operation of the X-ray diffractometer 200. The device information storage unit 320 stores the device information acquired from the X-ray diffractometer 200. The device information may include information regarding the X-ray diffractometer 200 such as the device name, the type of radiation source, the wavelength, and the background.

[0072] The measurement data storage unit 330 stores the measurement data acquired from the X-ray diffractometer 200. Along with the measurement data, necessary information among information regarding the X-ray diffractometer 200 such as the type of radiation source, the wavelength, and the background, the shape, arrangement, type of constituent elements, composition, and absorption coefficient of the sample may be stored. The display unit 340 causes the measurement data and the like to be displayed on the display device 520. Thereby, the user can confirm the measurement data and the like. Also, the user can give instructions and specifications to the control device 300, the computing device 100, etc. based on the measurement data and the like.

[0073] Note that the computing device 100 may be configured as a part of the functions included in the control device 300. Also, the computing device 100 and the control device 300 may be configured as an integrated device.

[0074] [Measurement method] Place the sample on the X-ray diffractometer 200, and based on the control of the control device 300, irradiate the sample with X-rays and detect the diffracted X-rays and the like generated from the sample. Also, if necessary, drive the sample stage or the goniometer under predetermined conditions. Thereby, measurement data such as total scattering data is acquired. The X-ray diffractometer 200 transmits the acquired measurement data and necessary device information and the like to the control device 300.

[0075] [Method for generating a structural model] The control device 300, the calculation device 100, or an external device generates a structural model that reproduces the measurement data. The method for generating the structural model may be any method. The structural model can be given as data indicating an arrangement of a finite number of atoms (molecules) in, for example, a cube, a rectangular parallelepiped, or a parallelepiped according to the sample. Obtain a structural model showing the atomic arrangement within such a finite region, and calculate the total scattering intensity of the structural model. Then, the structural model is corrected until the degree of agreement or divergence between the total scattering intensity of the structural model and the measurement data becomes better than a set value. When the degree of agreement or divergence between the total scattering intensity of the structural model and the measurement data becomes better than the set value, the generation of the structural model is terminated.

[0076] For example, when generating a structural model by the RMC method, randomly move the atomic arrangement of the structural model. If the degree of agreement or divergence after the operation is better (the degree of closeness is greater) than the degree of agreement or divergence before the operation, further random movement is performed based on the atomic arrangement. On the other hand, if the degree of agreement or divergence after the operation is not better (the degree of closeness is not greater) than the degree of agreement or divergence before the operation, cancel the operation and perform random movement again from the atomic arrangement before the operation. Such an operation is performed until the degree of agreement or divergence satisfies a predetermined condition. Note that the method for creating the structural model may also be the MD method (Molecular Dynamics method) or the MC method (Monte Carlo method).

[0077] By using the above-described system 400, measurement data can be acquired from the X-ray diffractometer 200, and a structural model can be generated. Then, a correlation function can be calculated from the generated structural model.

[0078] [Example 1] Using the computing device 100 configured as described above, it was verified whether the characteristics of the atomic arrangement appear in the correlation function by assuming two different atomic arrangements. Specifically, the following was done. Lattice points with a distance of 3.0 Å between adjacent points on the edges, faces, and inside of a cube with a side length of 24 Å in three-dimensional space were set. Next, a structural model in which Ne and Ar were randomly arranged at a ratio of 1:1 on the lattice points was created. Also, another structural model in which Ne and Ar were alternately arranged at the same lattice points was created. A displacement of Δr ≦ 0.2 Å was randomly given to the particles (Ne or Ar) of each structural model, and the randomly arranged structural model was designated as structural model 1, and the alternately arranged structural model was designated as structural model 2. FIGS. 12(a) and (b) are schematic diagrams showing an example of the states of structural model 1 and structural model 2, respectively.

[0079] Next, using the computing device 100, specific atomic species were set for structural model 1 and structural model 2, and the first pair distribution function, the second pair distribution function, and the correlation function were calculated. FIGS. 13(a) and (b) are graphs of the pair distribution function and the correlation function when Ne in structural model 1 is the specific atomic species, respectively. FIGS. 14(a) and (b) are graphs of the pair distribution function and the correlation function when Ar in structural model 1 is the specific atomic species, respectively. Also, FIGS. 15(a) and (b) are graphs of the pair distribution function and the correlation function when Ne in structural model 2 is the specific atomic species, respectively. FIGS. 16(a) and (b) are graphs of the pair distribution function and the correlation function when Ar in structural model 2 is the specific atomic species, respectively.

[0080] In Figs. 13(a) and 15(a), Ne-Ne represents the first two-body distribution function when Ne is a specific atomic species, and Ne-Ar represents the second two-body distribution function when Ne is a specific atomic species. Also, in Figs. 14(a) and 16(a), Ar-Ar represents the first two-body distribution function when Ar is a specific atomic species, and Ar-Ne represents the second two-body distribution function when Ar is a specific atomic species. In all cases, they are shown with a shift in the vertical axis direction.

[0081] From the correlation functions C(r) in Figs. 13(b) and 14(b), in the case of structural model 1 where two types of atoms are randomly arranged, it was found that the baseline of the correlation function C(r) coincides with the atomic number ratio of a specific atomic species in the structural model (the proportion of a specific atomic species in the structural model, the average concentration). Note that the straight line drawn at C(r) = 0.5 in Figs. 13(b) and 14(b) indicates the atomic number ratio of a specific atomic species. The correlation function C(r) represents the probability of existence of a specific atomic species at the correlation distance r from a specific atomic species. That is, the fact that a peak is observed in the correlation function C(r) indicates that there are many pairs of a specific atomic species and a specific atomic species at that correlation distance. By displaying the atomic number ratio of a specific atomic species and the correlation function C(r) on the same graph, it is possible to determine at which correlation distance r a regular arrangement occurs. Also, the regularity of the atomic arrangement may be judged based on the correlation function C(r) and the atomic number ratio of a specific atomic species. For example, it may be determined that it is regular when the deviation between the correlation function C(r) and the atomic number ratio of a specific atomic species is equal to or greater than a certain value.

[0082] In the case of structural model 1 where two types of atoms are randomly arranged, it can be seen from Figs. 13(b) and 14(b) that the amplitude of the correlation function C(r) is small and converges in the region where the correlation distance r is about 10 Å or more. On the other hand, in the case of structural model 2 where two types of atoms are alternately and regularly arranged, the amplitude of the correlation function C(r) in Figs. 15(b) and 16(b) is large and does not converge even in the region where the correlation distance r is 20 Å or more. From this, it can be seen that the atoms in the structural model are regularly arranged even at a correlation distance of 20 Å or more.

[0083] In addition, variance was used as an index to express the amplitude of the correlation function C(r). The variances of the correlation function C(r) of Structure Model 1 were 0.007 and 0.012 when Ne and Ar were used as specific atomic species, respectively. On the other hand, the variances of the correlation function C(r) of Structure Model 2 were 0.045 and 0.126 when Ne and Ar were used as specific atomic species, respectively. Since the variance of Structure Model 2 is large, it can be seen that the atoms in Structure Model 2 are regularly arranged. That is, the regularity of the atomic arrangement can be determined by using the variance as an index. Here, in order to improve the calculation accuracy, the calculation range of the variance was calculated excluding the range where C(r) = 0. Note that a similar effect can be obtained by using the standard deviation instead of the variance.

[0084] As a result of Example 1, in the case of a structure model in which the presence or absence of the regularity of the structure model is clear, it was confirmed that the regularity of the atomic arrangement in the structure model appears in the correlation function.

[0085] [Example 2] Using the computing device 100 configured as described above, it was verified whether the characteristics of the atomic arrangement appear in the correlation function assuming an atomic arrangement where the positions of the atoms are not limited to lattice points. Specifically, it was performed as follows. A structure model in which Ne and Ar were randomly arranged at a ratio of 1:1 was created inside a cube with a side length of 20 Å in three-dimensional space. Then, the structure model in which the particles of the structure model were moved by 10 5 MCSteps (Monte Carlo Steps) only for collision determination was defined as Structure Model 3. FIG. 17 is a schematic diagram showing an example of the state of Structure Model 3.

[0086] Next, using the computing device 100, specific atomic species were set for the structural model 3, and the first pair distribution function, the second pair distribution function, and the correlation function were calculated. FIGS. 18(a) and (b) are graphs of the pair distribution function and the correlation function, respectively, when Ne of the structural model 3 is set as the specific atomic species. FIGS. 19(a) and (b) are graphs of the pair distribution function and the correlation function, respectively, when Ar of the structural model 3 is set as the specific atomic species. Ne-Ne in FIG. 18(a) represents the first pair distribution function when Ne is the specific atomic species, and Ne-Ar represents the second pair distribution function when Ne is the specific atomic species. Also, Ar-Ar in FIG. 19(a) represents the first pair distribution function when Ar is the specific atomic species, and Ar-Ne represents the second pair distribution function when Ar is the specific atomic species. In both cases, they are displayed with a shift in the vertical axis direction.

[0087] From the correlation functions C(r) in FIGS. 18(b) and 19(b), it was found that in the case of the structural model 3 in which two types of atoms are randomly arranged including their positions, the far-distance side of the correlation function C(r) converges to the atomic number ratio of the specific atomic species. Note that the straight line drawn at C(r)=0.5 in FIGS. 18(b) and 19(b) indicates the atomic number ratio of the specific atomic species.

[0088] As a result of Example 1 and Example 2, it was confirmed that information regarding the mixed state can be obtained from the spatial correlation function of the specific atomic species.

[0089] [Example 3] Using a crystal structure model that explains the measured X-ray diffraction profile, it was verified whether information regarding the mixed state of neighboring particles can be obtained from the correlation function. Specifically, NCM333 (Li(Ni 0.33 ,Co 0.33 ,Mn 0.33 )O2) and NCM523 (Li(Ni 0.5 ,Co 0.2 ,Mn 0.3)A crystal structure model (structural model) was created to explain the measured X-ray diffraction profile of O2). Figures 20(a) and (b) are schematic diagrams showing the crystal structure model of NCM333 and the unit cell, respectively. As shown in Figure 20(a), NCM is composed of three types of sheet structures: only Li ions, only oxygen atoms, and only transition metal elements. Also, as shown in Figure 20(b), in NCM333, an occupancy rate is assigned to the transition metal sites, and basically, they are randomly present with the set occupancy rate. The same applies to NCM523.

[0090] As the initial arrangement of NCM333 or NCM523, the structural model was randomly arranged so that Ni:Co:Mn = 1:1:1 or 5:2:3 at the transition metal sites. Next, while randomly changing the arrangements of Ni, Co, and Mn by the RMC method, some of Ni, Co, and Mn were replaced with other elements (Ni, Co, Mn), and the RMC steps were repeated until a profile approximated to the measured X-ray diffraction and neutron diffraction profiles was obtained. Then, the structural model of NCM333 with a profile sufficiently approximated to the measured X-ray diffraction profile was designated as structural model 4, and the structural model of NCM523 was designated as structural model 5.

[0091] Next, using the computing device 100, specific planes of structural model 4 and structural model 5 were determined. Then, specific atomic species were set for structural model 4 and structural model 5, and the first radial distribution function, the second radial distribution function, and the correlation function were calculated. The specific plane was taken as one of the sheet structures composed only of transition metal elements. Figures 21(a) and (b) are graphs of the first radial distribution function and the correlation function when Ni, Co, and Mn of structural model 4 are taken as specific atomic species, respectively. Figures 22(a) and (b) are graphs of the first radial distribution function and the correlation function when Ni, Co, and Mn of structural model 5 are taken as specific atomic species, respectively. In both cases, they are shown with a shift in the vertical axis direction. Note that the two or more atomic species including the specific atomic species in the second radial distribution function when calculating the correlation function were Ni, Co, and Mn.

[0092] In the structural model 4, the atomic ratios (average concentrations) of Ni, Co, and Mn in a specific plane were 0.33, 0.33, and 0.3, respectively. The straight lines drawn on each correlation function in Fig. 21(b) indicate the atomic ratios of the respective specific atomic species. From Fig. 21(b), it was found that in NCM333, Co and Mn are likely to be randomly present at any distance. On the other hand, it was found that Ni is likely to form clusters in the nearest neighbor.

[0093] In the structural model 5, the atomic ratios (average concentrations) of Ni, Co, and Mn in a specific plane were 0.3, 0.2, and 0.43, respectively. The straight lines drawn on each correlation function in Fig. 22(b) indicate the atomic ratios of the respective specific atomic species. From Fig. 22(b), it was found that in NCM523, Co is likely to be randomly present at any distance. On the other hand, it was found that Ni and Mn are likely to form clusters in the nearest neighbor.

[0094] As a result of Example 3, it was confirmed that in the case of a structural model in which the occupancy is set in the average structure, it is possible to examine whether the site substitution is random or regular.

[0095] From the above results, it was confirmed that the computing device, method, and program of the present invention can calculate the correlation function from the structural model. It was also confirmed that the correlation function can be evaluated.

[0096] Needless to say, the present invention is not limited to the above-described embodiments. The scope of the present invention extends to various modifications and equivalents included in the technical idea of the present invention. Also, the names, structures, shapes, numbers, positions, sizes, etc. of the components shown in each drawing are for convenience of explanation and can be changed as appropriate.

[0097] The functions of the elements disclosed in this specification can be implemented using circuitry or processing circuitry including a general-purpose processor, a special-purpose processor, an integrated circuit, ASICs (Application Specific Integrated Circuits), FPGAs (Field Programmable Gate Arrays), conventional circuitry, and / or combinations thereof that are programmed using one or more programs stored in one or more memories or otherwise configured to perform the disclosed functions. Since a processor includes transistors and other circuitry, it is considered circuitry or processing circuitry. The processor may be a programmed processor that executes a program stored in a memory. In the present disclosure, a circuit, unit, or means is hardware that performs the recited functions or hardware that is programmed to perform the recited functions. The hardware may be any hardware disclosed herein that is programmed or configured to perform the recited functions.

Explanation of Signs

[0098] 100 Computing device 110 Structure model acquisition unit 120 Atomic species setting unit 125 Plane determination unit 130 Correlation function calculation unit 135 Index calculation unit 140 Evaluation unit 150 Display unit 200 X-ray diffractometer 210 X-ray generation unit 220 Incident-side optical unit 230 Goniometer 240 Sample stage 250 Exit-side optical unit 260 Detector 300 Control device 310 Control Unit 320 Device Information Storage Unit 330 Measurement Data Storage Unit 340 Display Unit 400 System 510 Input Device 520 Display Device

Claims

1. A computing device that calculates a correlation function from a structural model, comprising: a structural model acquisition unit that acquires the structural model including a plurality of types of atoms in space; an atomic species setting unit that sets a specific atomic species in the structural model; a correlation function calculation unit that calculates the correlation function, which is a ratio of a first radial distribution function and a second radial distribution function; wherein the first radial distribution function is a radial distribution function between atoms of the specific atomic species; and the second radial distribution function is a radial distribution function between atoms of the specific atomic species and atoms of two or more atomic species including the specific atomic species. A computing device characterized by this.

2. The computing device according to claim 1, further comprising a display unit that displays the correlation function.

3. The computing device according to claim 2, wherein the display unit superimposes and displays the correlation function and the atomic number ratio of the specific atomic species in the structural model.

4. The computing device according to claim 2, wherein the display unit simultaneously displays the correlation function of the specific atomic species and the correlation function of an atomic species different from the specific atomic species.

5. further comprising a plane determination unit that determines a specific plane in the structural model; The computing device according to any one of claims 1 to 4, wherein the correlation function calculation unit calculates the correlation function in the specific plane.

6. The computing device according to any one of claims 1 to 4, further comprising an evaluation unit that evaluates the regularity of the atomic arrangement in the structural model based on the correlation function.

7. further comprising an index calculation unit that calculates an index based on the correlation function; The computing device according to claim 6, wherein the evaluation unit evaluates the regularity of the atomic arrangement based on the index.

8. The computing device according to claim 7, wherein the index is the variance or standard deviation of the correlation function.

9. The computing device according to claim 7, wherein the index is calculated based on the correlation function and the atomic number ratio of the specific atomic species in the structural model.

10. The computing device according to any one of claims 1 to 4, wherein the structural model is a model generated by the RMC method.

11. A method for calculating a correlation function from a structural model, comprising: a step of acquiring the structural model including a plurality of types of atoms in space; A step of setting a specific atomic species in the structure model; A step of calculating the correlation function which is the ratio of the first radial distribution function and the second radial distribution function, The first radial distribution function is the radial distribution function between atoms of the specific atomic species and atoms of the specific atomic species, The second radial distribution function is the radial distribution function between atoms of the specific atomic species and atoms of two or more atomic species including the specific atomic species. A method characterized by this.

12. A program for calculating a correlation function from a structure model, A process of obtaining the structure model including a plurality of types of atoms in space; A process of setting a specific atomic species in the structure model; A process of causing a computer to execute a process of calculating the correlation function which is the ratio of the first radial distribution function and the second radial distribution function, The first radial distribution function is the radial distribution function between atoms of the specific atomic species and atoms of the specific atomic species, The second radial distribution function is the radial distribution function between atoms of the specific atomic species and atoms of two or more atomic species including the specific atomic species. A program characterized by this.

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