Computing device, method, and program

Abstract

This invention provides a computing device, method, and program for calculating correlation functions from structural models. [Solution] A computing device 100 for calculating a correlation function from a structural model, comprising: a structural model acquisition unit 110 for acquiring the structural model containing multiple types of atoms in space; an atom species setting unit 120 for setting specific atom species in the structural model; and a correlation function calculation unit 130 for calculating the correlation function which is the ratio of a first radial distribution function to a second radial distribution function, wherein the first radial distribution function is the radial distribution function between atoms of the specific atom species and atoms of the specific atom species, and the second radial distribution function is the radial distribution function between atoms of the specific atom species and atoms of two or more atom species including the specific atom species.

Description

[Technical Field]

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

[0002] In recent years, advancements in analytical techniques such as the RMC method have made it possible to analyze areas larger than the unit cell. This has allowed for the acquisition of information that could not be obtained with conventional unit cell-based analyses. One example of this information is the position of particles within the structural model.

[0003] However, conventionally, the only way to discuss structural models was to use the two-body distribution function g(r) of partial correlations, and there was no way to evaluate the mixing state of neighboring atoms in the structural model. Knowing the mixing state of neighboring atoms in the structural model is important because it advances our understanding of material properties.

[0004] Non-patent document 1 discloses a method for estimating the S(Q) of a two-element mixture state through experimental measurement. It also discloses thermodynamic equations that can be used to investigate the concentration and temperature dependence of various types of mixtures (regular, ordered-disordered, athermally volatile, etc.).

[0005] Non-Patent Document 2 discloses an analysis of the dipole correlation of water as a function of temperature and density, and in the case of a simple ionic solute, using molecular dynamics simulations and empirical potentials. Non-Patent Document 2 defines a dipole-dipole spatial correlation function and discusses its characteristics. [Prior art documents] [Non-patent literature]

[0006] [Non-Patent Document 1] AB Bhatia, DE Thornton, Phys. Rev. B 2 (1970) 3004-3012. https: / / doi.org / 10.1103 / PhysRevB.2.3004. [Non-Patent Document 2] C. Zhang, G. Galli, J. Chem. Phys. 141 (2014) 084504 (5 pp). https: / / doi.org / 10.1063 / 1.4893638. [Overview of the Initiative] [Problems that the invention aims to solve]

[0007] However, the methods described in Non-Patent Documents 1 and 2 do not take into account the representation of the mixed state of adjacent atoms in the structural model.

[0008] As a result of diligent research, the inventors discovered that the mixing state of neighboring atoms in a structural model can be represented by calculating a correlation function, which is the ratio of two types of radial distribution functions focusing on specific atomic species. Furthermore, they found that the mixing state of neighboring atoms in a structural model can be evaluated by analyzing the calculated correlation function, thus completing the present invention.

[0009] This invention has been made in view of these circumstances, and aims to provide a computing device, method, and program for calculating a correlation function from a structural model. [Means for solving the problem]

[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, 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; and a correlation function calculation unit that calculates the correlation function, which is the ratio of a first radial distribution function and a 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 comprises a display unit that displays the correlation function.

[0012] (3) 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) 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 comprises a plane determination unit that determines a specific plane in the structural model, and the correlation function calculation unit calculates the correlation function on the specific plane.

[0015] (6) Further, the computing device according to one aspect of the present invention further comprises 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 comprises 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) Further, 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) Further, 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) Further, 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) Further, one aspect of the method of the present invention is a method for calculating a correlation function from a structural model, including the steps of obtaining the structural model containing a plurality of types of atoms in space, setting a specific atomic species in the structural model, and calculating the correlation function which is the ratio of the first radial distribution function and the second radial distribution function, wherein 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.

[0021] (12) Further, one aspect of the program of the present invention is a program for calculating a correlation function from a structural model, causing a computer to execute the processes of obtaining the structural model containing a plurality of types of atoms in space, setting a specific atomic species in the structural model, and calculating the correlation function which is the ratio of the first radial distribution function and the second radial distribution function, wherein 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.

Brief Description of the Drawings

[0022] [Figure 1] It is a block diagram showing an example of the configuration of the computing device according to Embodiment 1. [Figure 2]This is a block diagram showing a modified configuration of the computing device according to Embodiment 1. [Figure 3] This flowchart shows an example of the operation of the computing device according to Embodiment 1. [Figure 4] This is a block diagram showing an example of the configuration of a computing device according to Embodiment 2. [Figure 5] This flowchart shows an example of the operation of the computing device according to Embodiment 2. [Figure 6] This is a block diagram showing an example of the configuration of a computing device according to Embodiment 3. [Figure 7] This is a block diagram showing a modified configuration of the computing device according to Embodiment 3. [Figure 8] This flowchart shows an example of the operation of the computing device according to Embodiment 3. [Figure 9] This is a block diagram showing an example of the configuration of a computing device according to the embodiment. [Figure 10] This is a conceptual diagram showing an example of a system configuration. [Figure 11] This is a cylinder representing an example of the configuration of a control device. [Figure 12] (a) and (b) are schematic diagrams showing examples of the states of structural model 1 and structural model 2, respectively. [Figure 13] (a) and (b) are graphs of the two-body distribution function and correlation function, respectively, when Ne in structural model 1 is a specific atomic species. [Figure 14] (a) and (b) are graphs of the two-body distribution function and correlation function, respectively, when Ar in structural model 1 is a specific atomic species. [Figure 15] (a) and (b) are graphs of the two-body distribution function and correlation function, respectively, when Ne in structural model 2 is a specific atomic species. [Figure 16] (a) and (b) are graphs of the two-body distribution function and correlation function, respectively, when Ar in structural model 2 is a specific atomic species. [Figure 17] This is a schematic diagram showing an example of the state of structural model 3. [Figure 18](a) and (b) are graphs of the two-body distribution function and correlation function, respectively, when Ne in structural model 3 is a specific atomic species. [Figure 19] (a) and (b) are graphs of the two-body distribution function and correlation function, respectively, when Ar in structural model 3 is a specific atomic species. [Figure 20] (a) and (b) are schematic diagrams showing the crystal structure model and unit cell of NCM333, respectively. [Figure 21] (a) and (b) are graphs of the first radial distribution function and correlation function, respectively, when Ni, Co, and Mn in structural model 4 are treated as specific atomic species. [Figure 22] (a) and (b) are graphs of the first radial distribution function and correlation function, respectively, when Ni, Co, and Mn in structural model 5 are treated as specific atomic species. [Modes for carrying out the invention]

[0023] Next, embodiments of the present invention will be described with reference to the drawings. To facilitate understanding of the description, the same reference numerals are used for identical components in each drawing, and redundant descriptions are omitted.

[0024] [Embodiment] (Embodiment 1) [Computing device] Embodiment 1 describes the case in which a correlation function is calculated from a structural model. Figure 1 is a block diagram showing an example of the configuration of the 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, which will be 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 with a CPU (Central Processing Unit), ROM (Read Only Memory), RAM (Random Access Memory), and memory connected to a bus. The computing device 100 may be a PC terminal or a server on the cloud. Furthermore, not only the entire device, but also some of the devices or some of the 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 and mouse, and provides input to the computing device 100. The display device 520 is, for example, a display, and displays the structural model, specific atomic species, atomic ratio of specific atomic species, correlation function, radial distribution function, two-body distribution function, specific plane in the structural model, evaluation of the regularity of atomic arrangement in the structural model, indices, variance, 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 a control bus L.

[0027] The structural model acquisition unit 110 acquires a structural model. The structural model acquisition unit 110 may also acquire information regarding the characteristics of the structural model. Information regarding the characteristics of the structural model may include, for example, information that the structural model has a layered structure. The structural model acquisition unit 110 may acquire the structural model directly from a device or software that generates structural models, or it may acquire a structural model stored in a storage device or the like. The computing device 100 itself may also have a function to generate structural models.

[0028] A structural model is a model that shows the arrangement of particles (atoms, molecules) within a finite region. Depending on the sample, the structural model can be provided as data showing the arrangement of a finite number of particles within, for example, a cube, a rectangular prism, or a parallelepiped. In this invention, the structural model is a model that includes multiple types of particles (atoms, molecules).

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

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

[0031] The atomic species setting unit 120 sets a specific atomic species within the structural model. A specific atomic species is one of the types of atoms for which the correlation function within the structural model is to be calculated. The setting of the specific atomic species may also be done according to user instructions.

[0032] The correlation function calculation unit 130 calculates a correlation function which is the ratio of a first radial distribution function to a second radial distribution function. The first radial distribution function is the radial distribution function between atoms of a specific atomic species and atoms of a specific atomic species. The second radial distribution function is the radial distribution function between atoms of a specific atomic species and atoms of two or more atomic species, including a specific atomic species, within the structural model. The two or more atomic species, including a specific atomic species, within the structural model may be some of the atomic species in the structural model or all of the atomic species. The correlation function, which includes the ratio of the first radial distribution function to the second radial distribution function, can be said to represent the distance dependence of the density fluctuations of the atomic species.

[0033] A radial distribution function represents the distribution of atoms, and is defined as a function of distance to a particular atom, showing the distribution of atoms surrounding it. In other words, the first radial distribution function can be said to be the distribution of atoms of a specific atomic species surrounding it. 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, surrounding it, while focusing on an atom of a specific atomic species.

[0034] An example will be given to explain the selection of two or more atomic species that include a specific atomic species. For example, if the atomic species included in the structural model are A, B, and C, and the specific atomic species is A, then the selection of two or more atomic species that include the specific atomic species can be A and B, A and C, or A, B, and C.

[0035] Let A be a specific atomic species, and let N be the first radial distribution function. AA (r), the second radial distribution function is N AX Let (r) be the first radial distribution function N. AA (r) can be expressed, for example, by the following formula (1). Also, the second radial distribution function N AX (r) can be expressed, for example, by the following formula (2), where r is the distance and N A is the number of A elements, 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 is the number of selected atomic species that include a specific atomic species.

[0036]

Number

[0037]

Number

[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 an expression 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 so as to have such a property.

[0040]

Number

[0041] The above explanation showed an example where the correlation function is defined as the ratio of the first radial distribution function to the second radial distribution function. However, the correlation function does not necessarily have to be defined as the ratio of the first and second radial distribution functions. For example, it can also be defined as the ratio of the two-body distribution functions for a particular atomic species.

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

[0043]

number

[0044]

number

[0045] Therefore, even when the correlation function is defined as the ratio of the two-body distribution functions for a particular atomic species, the correlation function can be said to be the ratio of the first radial distribution function to the second radial distribution function. The correlation function may be calculated after calculating the radial distribution function or the two-body distribution function, or it may be calculated directly from the definition formula without calculating the radial distribution function or the two-body distribution function.

[0046] Figure 2 is a block diagram showing a modified configuration of the computing device 100 according to Embodiment 1. As shown in Figure 2, it is preferable that the computing device 100 further includes a display unit 150 in addition to the structural model acquisition unit 110, atomic species setting unit 120, and correlation function calculation unit 130. The display unit 150 displays the correlation function on the display device 520. The display unit 150 may also display the structural model, a specific atomic species, the 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 structural model, an evaluation of the regularity of the atomic arrangement within the structural model, an index, variance, etc.

[0047] The display unit 150 preferably displays the correlation function and the atomic ratio of a specific atomic species within the structural model overlaid. The atomic ratio of a specific atomic species within the structural model may be the atomic ratio of that specific atomic species to two or more atomic species, including the specific atomic species selected when calculating the second radial distribution function. Alternatively, the atomic ratio of a specific atomic species within the structural model may be the atomic ratio of that specific atomic species to any two or more atomic species, including the specific atomic species. By displaying the correlation function and the atomic ratio of a specific atomic species within the structural model overlaid in this way, the characteristics of the correlation function with respect to the average concentration of the specific atomic species can be grasped.

[0048] The display unit 150 preferably displays simultaneously the correlation function of a specific atomic species and the correlation function of an atomic species different from the specific atomic species (also called a second specific atomic species). This allows for a comparison of the characteristics of the correlation functions for each atomic species, and enables the understanding of the similarities and differences.

[0049] Figure 3 is a flowchart illustrating an example of the operation of the computing device 100 according to Embodiment 1. Figure 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 using the structural model acquisition unit 110 (step S1). Next, the atomic species setting unit 120 sets specific atomic species within the structural model acquired by the structural model acquisition unit 110 (step S2). Then, the correlation function calculation unit 130 calculates the correlation function (step S3). The correlation function may be output as needed. Alternatively, the radial distribution function or the two-body distribution function may be output. In this way, a correlation function can be calculated from a structural model.

[0050] If the computing device 100 is equipped with a display unit 150, it may display the correlation function, radial distribution function, or two-body distribution function as needed. In this way, the characteristics of the correlation function calculated from the structural model can be captured. Since the correlation function can be said to be a function that represents the mixing state of adjacent particles in the structural model, the mixing state of adjacent particles in the structural model can be explained by analyzing it.

[0051] (Embodiment 2) [Computing device] Embodiment 2 describes the case in which a correlation function is calculated for a specific plane within a structural model. Figure 4 is a block diagram showing an example of the configuration of the computing device 100 according to Embodiment 2. As shown in Figure 4, it is preferable that the computing device 100 further includes a plane determination unit 125 in addition to the structural model acquisition unit 110, atomic species setting unit 120, and correlation function calculation unit 130.

[0052] The plane determination unit 125 determines a specific plane within the structural model. This specific plane is the plane from which the correlation function within the structural model is to be calculated. By determining this specific plane, the mixing state of adjacent particles within that plane can be analyzed. The determination of the specific plane may be performed according to user instructions. Furthermore, if the structural model is accompanied by information regarding its characteristics, the system may be configured to provide the user with an option to determine whether or not to determine a specific plane based on this information.

[0053] If the plane determination unit 125 determines a specific plane, the correlation function calculation unit 130 calculates the correlation function for that specific plane. The correlation function for a specific plane is the correlation function that is the ratio of the first radial distribution function to the second radial distribution function for that specific plane. If 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] Figure 5 is a flowchart illustrating an example of the operation of the computing device 100 according to Embodiment 2. Figure 5 shows an example of the operation when determining whether or not to determine a specific plane. First, the computing device 100 acquires a structural model using the structural model acquisition unit 110 (step T1). Next, the atomic species setting unit 120 sets specific atomic species within the structural model acquired by the structural model acquisition unit 110 (step T2).

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

[0056] (Embodiment 3) [Computing device] Embodiment 3 describes a case in which the regularity of atomic arrangement is evaluated based on a correlation function. Figure 6 is a block diagram showing an example of the configuration of the computing device 100 according to Embodiment 3. As shown in Figure 6, it is preferable that the computing device 100 further includes an evaluation unit 140 in addition to the structure model acquisition unit 110, atomic species setting unit 120, and correlation function calculation unit 130.

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

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

[0059] The index calculation unit 135 calculates an index based on a correlation function. If 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. Preferably, the index is a numerical value that can be used to evaluate the regularity of the atomic arrangement in the structural model. The evaluation unit 140 may determine that there is regularity when the index satisfies predetermined conditions. The predetermined conditions vary depending on the type of index.

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

[0061] Furthermore, it is preferable that the index is calculated based on the correlation function and the atomic ratio of a specific atomic species within the structural model. When the atomic arrangement within the structural model is random, the correlation function approaches the atomic ratio of a specific atomic species within the structural model (hereinafter referred to as the abundance of the specific atomic species). That is, if the abundance of the specific atomic species and the value of the correlation function deviate from each other, it can be determined that there is regularity in the atomic arrangement. When a specific plane is determined and the correlation function is calculated, the atomic ratio of a specific atomic species within the structural model may be the atomic ratio of a specific atomic species on that specific plane. When it is determined 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 atomic ratio of the specific atomic species and the value of the correlation function is greater than or equal to a certain value.

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

[0063] Next, the correlation function calculation unit 130 calculates the correlation function (step U3). Then, the evaluation unit 140 evaluates the regularity of the atomic arrangement in the structural model (step U4). If the computing device 100 is equipped with an index calculation unit 135, the index is calculated by the index calculation unit 135 before evaluating the regularity of the atomic arrangement in the structural model. After that, the evaluation unit 140 evaluates the regularity of the atomic arrangement based on the index. The correlation function, radial distribution function, two-body distribution function, evaluation, or index may be output as needed. Also, if the computing device 100 is equipped with a display unit 160, these may be displayed as needed. In this way, the regularity of the atomic arrangement in the structural model can be evaluated based on the correlation function.

[0064] Embodiments 1 to 3 may each include some or all of the configurations of the other embodiments. Figure 9 is a block diagram showing an example of the configuration of a computing device 100 according to an embodiment of the present invention. As shown in Figure 9, the computing device 100 comprises a structure 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. Of these, the plane determination unit 125, the index calculation unit 135, the evaluation unit 140, or the display unit 150 are arbitrary components.

[0065] [Overall System] The computing device 100 or computing method of the present invention can acquire 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 and the control device 300. On the other hand, it can also be integrated into a system with the X-ray diffractometer 200 and the control device 300. Figure 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 has the computing device 100, the X-ray diffractometer 200, and the control device 300.

[0066] Note that in Figure 10, the computing device 100 and the control device 300 are depicted as the same PC. However, the computing device 100 may be configured as a different device from the control device 300. The following section will explain the case where the computing device 100 and the control device 300 are configured as different devices.

[0067] [X-ray diffractometer] The X-ray diffractometer 200 comprises an optical system that incidents X-rays onto a sample and detects the reflected X-rays generated from the sample. The X-ray diffractometer 200 includes at least an X-ray generator 210 that generates X-rays from an X-ray focal point, i.e., an X-ray source; a sample stage 240 on which the sample is placed and which controls the rotation of the sample; and a detector 260 that detects the X-rays. The X-ray diffractometer 200 may also include an incident optical unit 220, a goniometer 230, or an exit optical unit 250. The X-ray generator 210, incident optical unit 220, goniometer 230, sample stage 240, exit optical unit 250, and detector 260 that constitute the X-ray diffractometer 200 can be general-purpose components, so a detailed explanation is omitted. Note that the configuration shown in Figure 10 is just one 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, as well as processing, storing, and displaying the acquired data.

[0069] Figure 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 with a CPU, ROM, RAM, and memory connected to a bus. The control device 300 may be a PC terminal or a server on the cloud. Furthermore, not only the entire system, but also some of the system or some of the functions within the system may be located on the cloud. The control device 300 is connected to the X-ray diffractometer 200 to receive information.

[0070] The control device 300 comprises a control unit 310, a device information storage unit 320, a measurement data storage unit 330, and a display unit 340. Each unit can send 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 an appropriate interface. 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 device information acquired from the X-ray diffractometer 200. The device information may include information about the X-ray diffractometer 200 such as the device name, type of radiation source, wavelength, and background.

[0072] The measurement data storage unit 330 stores measurement data acquired from the X-ray diffractometer 200. Along with the measurement data, it may also store necessary information such as the type of radiation source, wavelength, background, and other information related to the X-ray diffractometer 200, as well as the shape, arrangement, types and composition of constituent elements of the sample, and absorption coefficient. The display unit 340 displays the measurement data on the display device 520. This allows the user to confirm the measurement data. The user can also give instructions and specifications to the control device 300, the calculation device 100, etc., based on the measurement data.

[0073] The computing device 100 may be configured as a part of the control device 300. Alternatively, the computing device 100 and the control device 300 may be configured as an integrated device.

[0074] [Measurement method] A sample is placed in the X-ray diffractometer 200, and based on the control of the control device 300, X-rays are incident on the sample, and the diffracted X-rays and other radiation generated from the sample are detected. If necessary, the sample stage or goniometer is driven under predetermined conditions. This allows for the acquisition of measurement data such as total scattering data. The X-ray diffractometer 200 transmits the acquired measurement data and necessary device information to the control device 300.

[0075] [Method for generating structural models] A structural model that reproduces the measurement data is generated by the control device 300, the computing device 100, or an external device. Any method can be used to generate the structural model. Depending on the sample, the structural model can be provided as data showing a finite number of atomic (molecule) arrangements within a cube, cuboid, or parallelepiped. A structural model showing such an atomic arrangement within a finite region is obtained, and the total scattering intensity of the structural model is calculated. The structural model is then modified until the degree of agreement or deviation between the total scattering intensity of the structural model and the measurement data is better than a set value. Once the degree of agreement or deviation between the total scattering intensity of the structural model and the measurement data is better than a set value, the generation of the structural model is terminated.

[0076] For example, when generating a structural model using the RMC method, the atomic arrangement of the structural model is randomly moved. If the degree of agreement or deviation after the operation is better than the degree of agreement or deviation before the operation (the degree of closeness is greater), further random movements are performed based on that atomic arrangement. On the other hand, if the degree of agreement or deviation after the operation is not better than the degree of agreement or deviation before the operation (the degree of closeness is not greater), the operation is canceled, and random movements are performed again from the atomic arrangement before the operation. This operation is repeated until the degree of agreement or deviation satisfies the predetermined conditions. 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 system 400 described above, 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, we investigated whether the characteristics of the atomic arrangements appeared in the correlation function by assuming two different atomic arrangements. Specifically, we performed the following: We set up lattice points in a three-dimensional space where the distance between adjacent points was 3.0 Å on the edges, faces, and interior of a cube with sides of 24 Å. Next, we created a structural model in which Ne and Ar were randomly arranged in a 1:1 ratio on the lattice points. We also created another structural model in which Ne and Ar were alternately arranged at the same lattice points. We randomly assigned displacements of Δr ≤ 0.2 Å to the particles (Ne or Ar) of each structural model, designating the randomly arranged structural model as structural model 1 and the alternately arranged structural model as structural model 2. Figures 12(a) and (b) are schematic diagrams showing examples 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 two-body distribution function, the second two-body distribution function, and the correlation function were calculated. Figures 13(a) and (b) are graphs of the two-body distribution function and correlation function when Ne is the specific atomic species in structural model 1, respectively. Figures 14(a) and (b) are graphs of the two-body distribution function and correlation function when Ar is the specific atomic species in structural model 1, respectively. Also, Figures 15(a) and (b) are graphs of the two-body distribution function and correlation function when Ne is the specific atomic species in structural model 2, respectively. Figures 16(a) and (b) are graphs of the two-body distribution function and correlation function when Ar is the specific atomic species in structural model 2, respectively.

[0080] In Figures 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. Similarly, in Figures 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. All of these figures are displayed shifted along the vertical axis.

[0081] From the correlation function C(r) in Figures 13(b) and 14(b), it was found that in the case of structural model 1, in which two types of atoms are randomly arranged, the baseline of the correlation function C(r) coincides with the atomic ratio of a specific atomic species in the structural model (the proportion of a specific atomic species in the structural model, the average concentration). The straight line drawn at C(r) = 0.5 in Figures 13(b) and 14(b) represents the atomic ratio of a specific atomic species. The correlation function C(r) represents the probability of a specific atomic species being present at a correlation distance r from that specific atomic species. That is, a peak in the correlation function C(r) indicates that there are many pairs of a specific atomic species at that correlation distance. By displaying the atomic 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. Alternatively, the regularity of the atomic arrangement can be determined based on the correlation function C(r) and the atomic ratio of a specific atomic species. For example, a pattern may be determined to be regular if the deviation between the correlation function C(r) and the ratio of atoms of a particular atomic species is greater than or equal to a certain value.

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

[0083] Furthermore, variance was used to express the amplitude of the correlation function C(r) as an indicator. The variances of the correlation function C(r) for structural model 1 were 0.007 and 0.012, respectively, when Ne and Ar were specific atomic species. On the other hand, the variances of the correlation function C(r) for structural model 2 were 0.045 and 0.126, respectively, when Ne and Ar were specific atomic species. The larger variance for structural model 2 indicates that the atoms in structural model 2 are arranged regularly. In other words, the regularity of the atomic arrangement can be judged by using variance as an indicator. Here, in order to improve the calculation accuracy, the calculation range of variance was excluded from the range C(r)=0. Note that the same effect can be obtained by using the standard deviation instead of variance.

[0084] The results of Example 1 confirmed that, in the case of structural models where the presence or absence of regularity in the structural model is clear, the regularity of the atomic arrangement within the structural model is reflected in the correlation function.

[0085] [Example 2] Using the computing device 100 configured as described above, we investigated whether the characteristics of the atomic arrangement appear in the correlation function, assuming an atomic arrangement where the positions of atoms are not limited to lattice points. Specifically, we performed the following: We created a structural model in which Ne and Ar atoms were randomly arranged in a 1:1 ratio inside a cube with sides of 20 Å in three-dimensional space. Then, we performed collision detection on the particles of the structural model for 10 5 The structural model moved using MCSteps (Monte Carlo Steps) was designated as structural model 3. Figure 17 is a schematic diagram showing an example of the state of structural model 3.

[0086] Next, using the computing device 100, specific atomic species were set for structural model 3, and the first two-body distribution function, the second two-body distribution function, and the correlation function were calculated. Figures 18(a) and (b) are graphs of the two-body distribution function and correlation function when Ne is the specific atomic species in structural model 3, respectively. Figures 19(a) and (b) are graphs of the two-body distribution function and correlation function when Ar is the specific atomic species in structural model 3, respectively. In Figure 18(a), Ne-Ne represents the first two-body distribution function when Ne is the specific atomic species, and Ne-Ar represents the second two-body distribution function when Ne is the specific atomic species. Similarly, in Figure 19(a), Ar-Ar represents the first two-body distribution function when Ar is the specific atomic species, and Ar-Ne represents the second two-body distribution function when Ar is the specific atomic species. All graphs are displayed shifted along the vertical axis.

[0087] From the correlation function C(r) in Figures 18(b) and 19(b), it was found that in structural model 3, where two types of atoms are randomly arranged including their positions, the far-range side of the correlation function C(r) converges to the atomic ratio of a specific atomic species. The straight line drawn at C(r) = 0.5 in Figures 18(b) and 19(b) represents the atomic ratio of a specific atomic species.

[0088] The results from Examples 1 and 2 confirmed that information related to the mixing state can be obtained from the spatial correlation function of specific atomic species.

[0089] [Example 3] We used a crystal structure model that explains the measured X-ray diffraction profile to verify whether information about the mixing state of neighboring particles can be obtained from the correlation function. Specifically, we examined NCM333(Li(Ni)), which is used as a cathode material for Li-ion batteries. 0.33 Co 0.33 ,Mn 0.33 )O2) and NCM523(Li(Ni 0.5 Co 0.2 ,Mn 0.3A crystal structure model (structural model) was created to explain the measured X-ray diffraction profile of )O2). Figures 20(a) and (b) show the crystal structure model and unit cell of NCM333, respectively. As shown in Figure 20(a), NCM is composed of three types of sheet structures: Li ions only, oxygen atoms only, and transition metal elements only. Also, as shown in Figure 20(b), in NCM333, occupancy rates are assigned to transition metal sites, and they basically exist randomly according to the set occupancy rates. The same applies to NCM523.

[0090] For the structural models, the initial configurations for NCM333 and NCM523 were randomly arranged so that Ni:Co:Mn = 1:1:1 or 5:2:3 at the transition metal sites. Next, the arrangement of Ni, Co, and Mn was randomly changed using the RMC method, and some of the Ni, Co, and Mn were substituted with other elements (Ni, Co, Mn). The RMC step was repeated until a profile approximating the experimentally measured X-ray diffraction and neutron diffraction profiles was obtained. The structural model for NCM333 that yielded a profile sufficiently approximating the experimentally measured X-ray diffraction profile was designated as structural model 4, and the structural model for NCM523 was designated as structural model 5.

[0091] Next, the computing device 100 was used to determine specific planes for structural models 4 and 5. Then, specific atomic species were set for structural models 4 and 5, and the first radial distribution function, the second radial distribution function, and the correlation function were calculated. The specific plane was one of the planes in the sheet structure consisting only of transition metal elements. Figures 21(a) and (b) are graphs of the first radial distribution function and correlation function for structural model 4 when Ni, Co, and Mn are specified atomic species, respectively. Figures 22(a) and (b) are graphs of the first radial distribution function and correlation function for structural model 5 when Ni, Co, and Mn are specified atomic species, respectively. Both are displayed shifted along the vertical axis. 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] The atomic ratios (average concentrations) of Ni, Co, and Mn in specific planes in structural model 4 were 0.33, 0.33, and 0.3, respectively. The straight lines drawn on each correlation function in Figure 21(b) represent the atomic ratios of each specific atomic species. From Figure 21(b), it was found that in NCM333, Co and Mn are likely to be randomly distributed at any distance. On the other hand, Ni is likely to form clusters at its nearest neighbors.

[0093] The atomic ratios (average concentrations) of Ni, Co, and Mn in specific planes in structural model 5 were 0.3, 0.2, and 0.43, respectively. The straight lines drawn on each correlation function in Figure 22(b) represent the atomic ratios of each specific atomic species. From Figure 22(b), it was found that in NCM523, Co is likely to be present randomly at all distances. On the other hand, Ni and Mn are likely to form clusters at their nearest neighbors.

[0094] The results of Example 3 confirmed that in a structural model where the occupancy rate is set by the average structure, it is possible to investigate whether site replacement is random or regular.

[0095] Based on the above results, it has been confirmed that the computing device, method, and program of the present invention can calculate a correlation function from a structural model. Furthermore, it has been confirmed that the correlation function can be evaluated.

[0096] It goes without saying that the present invention is not limited to the embodiments described above. The scope of the present invention extends to various variations and equivalents included in the technical concept of the present invention. Furthermore, the names, structures, shapes, numbers, positions, sizes, etc., of the components shown in each drawing are for illustrative purposes only and may be changed as appropriate.

[0097] The functions of the elements disclosed herein may be implemented using circuits or processing circuits that include general-purpose processors, special-purpose processors, integrated circuits, ASICs (Application Specific Integrated Circuits), FPGAs (Field Programmable Gate Arrays), conventional circuits, 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. A processor is considered a circuit or processing circuit because it includes transistors and other circuits. A processor may be a programmed processor that executes programs stored in memory. In this disclosure, a circuit, unit, or means is hardware that performs the enumerated functions, or hardware programmed to perform the enumerated functions. Hardware may be any hardware disclosed herein that is programmed or configured to perform the enumerated functions. [Explanation of Symbols]

[0098] 100 Computing equipment 110 Structural Model Acquisition Section 120 Atomic species setting section 125 Plane determination section 130 Correlation Function Calculation Section 135 Indicator calculation section 140 Evaluation Department 150 Display section 200 X-ray diffractometer 210 X-ray generation unit 220 Incident Optical Unit 230 Goniometer 240 Sample stage 250 Output-side optical unit 260 detectors 300 Control device 310 Control Unit 320 Device information storage unit 330 Measurement data storage unit 340 Display section 400 System 510 Input device 520 Display device

Claims

1. A computing device for calculating correlation functions from structural models, A structural model acquisition unit that acquires the structural model containing multiple types of atoms in space, Atomic species setting unit for setting specific atomic species within the aforementioned structural model, The system includes a correlation function calculation unit that calculates the correlation function, which is the ratio of a first radial distribution function to a second radial distribution function, The first radial distribution function is the radial distribution function between atoms of the specified atomic species and atoms of the specified atomic species, The computing device is characterized in that the second radial distribution function is the radial distribution function of an atom of the specific atomic species and an atom of two or more atomic species including the specific atomic species.

2. The calculation device according to claim 1, further comprising a display unit for displaying the correlation function.

3. The calculation device according to claim 2, characterized in that the display unit displays the correlation function and the atomic ratio of the specific atomic species in the structural model in superimposed.

4. The calculation device according to claim 2, characterized in that 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. The structural model further comprises a plane determination unit that determines a specific plane within the structural model, The calculation device according to any one of claims 1 to 4, characterized in that 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. The system further includes an index calculation unit that calculates an index based on the aforementioned correlation function, The calculation device according to claim 6, characterized in that the evaluation unit evaluates the regularity of the atomic arrangement based on the index.

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

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

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

11. A method for calculating a correlation function from a structural model, A step of obtaining the structural model containing multiple types of atoms in space, The steps include: setting specific atomic species within the aforementioned structural model; The method includes the step of calculating the correlation function, which is the ratio of a first radial distribution function to a second radial distribution function, The first radial distribution function is the radial distribution function between atoms of the specified atomic species and atoms of the specified atomic species, The method is characterized in that the second radial distribution function is the radial distribution function of an atom of the specific atomic species and an atom of two or more atomic species including the specific atomic species.

12. This is a program that calculates a correlation function from a structural model. A process for obtaining the structural model containing multiple types of atoms in space, A process of setting specific atomic species within the aforementioned structural model, The computer is made to perform the process of calculating the correlation function, which 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 the specified atomic species and atoms of the specified atomic species, The program is characterized in that the second radial distribution function is the radial distribution function of an atom of the specific atomic species and an atom of two or more atomic species including the specific atomic species.

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