COMPUTING DEVICE, METHOD AND PROGRAM

Abstract

A computing device, a procedure, and a program for calculating a correlation function from a structural model are provided.The computing device 100 for calculating a correlation function from a structural model comprises a structural model acquisition unit 110, which is configured to acquire a structural model comprising several types of atoms in a space, an atom type specification unit 120, which is configured to specify a particular type of atom in the structural model, and a correlation function calculation unit 130, which is configured to calculate a correlation function that is the ratio of a first radial distribution function to a second radial distribution function, wherein the first radial distribution function is a radial distribution function between atoms of the particular type of atom and wherein the second radial distribution function is a radial distribution function between atoms of the particular type of atom and atoms of two or more types of atoms including the particular type of atom.

Description

TECHNICAL AREA The present invention relates to a computing device, a method and a program for calculating a correlation function from a structural model. TECHNICAL BACKGROUND Recently, advances in analytical methods, such as the RMC method, have made it possible to analyze regions larger than unit cells. This allows for the acquisition of information that was previously unobtainable with conventional unit cell analyses. One example of such information is the particle positions within the structural model. However, conventionally, discussions were limited to the partial pair distribution function g(r) calculated from the estimated structural model, and there was no method to evaluate the mixing state of neighboring atoms within the structural model. Since knowledge of the mixing state of neighboring atoms within the structural model improves the understanding of material properties, such information is of great importance. Non-patent document 1 discloses a method by which S(Q) in the mixing state of a two-element system can be estimated from measured data. It also discloses thermodynamic equations with which the concentration and temperature dependence of various types of mixtures (regular or ordered, with transitions between ordered and disordered, athermal, etc.) can be investigated. Non-patent document 2 discloses a method for analyzing the dipole correlation of water in the presence of a simple ionic solute using molecular dynamics simulations and empirical potentials. In this analytical method, the dipole correlation of water is defined as a function of temperature and density. Non-patent document 2 defines a spatial dipole-dipole correlation function and investigates its properties. Non-patent documents 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 INVENTION However, the methods described in Non-Patent Document 1 and Non-Patent Document 2 do not take into account how the mixing state of neighboring atoms can be described in the structural model. The inventors of the present invention discovered, through detailed investigations, that by focusing on a specific type of atom, two types of radial distribution functions can be calculated, and that by calculating a correlation function describing the ratio of these two radial distribution functions, the mixing state of neighboring atoms in the structural model can be represented. Furthermore, they found that by analyzing the calculated correlation function, the mixing state of the neighboring atoms in the structural model can be evaluated, thus leading to the present invention. The present invention was made taking these circumstances into account and aims to provide a computing device, a method and a program for calculating a correlation function from a structural model. MEANS OF SOLVING THE TASK (1) To solve the above-mentioned problem, a calculating device according to the present invention has the following features.A computing device according to one aspect of the present invention is a computing device for calculating a correlation function from a structural model, comprising: a structural model acquisition unit configured to acquire a structural model comprising several types of atoms in a space, an atom type determination unit configured to determine a specific type of atom in the structural model, and a correlation function calculation unit configured to calculate a correlation function that is the ratio of a first radial distribution function to a second radial distribution function, wherein the first radial distribution function is a radial distribution function between atoms of the specific type of atom, and the second radial distribution function is a radial distribution function between atoms of the specific type of atom and atoms of two or more types of atoms, including the specific type of atom.(2) A computing device according to one aspect of the present invention further comprises a display unit configured to display the correlation function. (3) In a computing device according to another aspect of the present invention, the display unit is configured to display the correlation function and the atomic number ratio of the specific type of atom within the structural model in superimposed form. (4) In a computing device according to another aspect of the present invention, the display unit is configured to display the correlation function of the specific type of atom and the correlation function of a different type of atom simultaneously.(5) A computing device according to a further aspect of the present invention further comprises a level determination unit configured to define a specific level within the structural model, wherein the correlation function calculation unit is configured to calculate the correlation function in the specified level. (6) A computing device according to a further aspect of the present invention further comprises an evaluation unit configured to evaluate the regularity of the atomic arrangement within the structural model based on the correlation function. (7) A computing device according to a further aspect of the present invention further comprises a characteristic value calculation unit configured to calculate a characteristic value based on the correlation function, wherein the evaluation unit is configured to evaluate the regularity of the atomic arrangement based on the characteristic value.(8) In a computing device according to a further aspect of the present invention, the characteristic value is the variance or the standard deviation of the correlation function. (9) A computing device according to a further aspect of the present invention is configured to calculate the characteristic value based on the correlation function and the atomic number ratio of the specific type of atom within the structural model. (10) In a computing device according to a further aspect of the present invention, the structural model is a model generated by a reverse Monte Carlo method.(11) A method according to one aspect of the present invention is a method for calculating a correlation function from a structural model, comprising: a step for obtaining a structural model comprising several types of atoms in a space, a step for specifying a particular type of atom in the structural model, and a step for calculating a 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 a radial distribution function between atoms of the particular type of atom, and the second radial distribution function is a radial distribution function between atoms of the particular type of atom and atoms of two or more locations including the particular type of atom.(12) A program according to one aspect of the present invention is a program for calculating a correlation function from a structural model, which, when executed on a computer, causes the computer to perform the following: a processing step to obtain a structural model comprising several types of atoms in a space; a processing step to specify a particular type of atom in the structural model; and a processing step to calculate a correlation function, a processing step which is the ratio of a first radial distribution function to a second radial distribution function, wherein the first radial distribution function is a radial distribution function between atoms of the particular type of atom, and the second radial distribution function is a radial distribution function between atoms of the particular type of atom and atoms of two or more types of atoms, including the particular type of atom. Fig. 1 is a block diagram showing an example of the construction of a computing device according to embodiment 1. Fig. 2 is a block diagram showing a modified example of the construction of the computing device according to embodiment 1. Fig. 3 is a flowchart showing an example of the operating sequence of the computing device according to embodiment 1. Fig. 4 is a block diagram showing an example of the construction of a computing device according to embodiment 2. Fig. 5 is a flowchart showing an example of the operating sequence of the computing device according to embodiment 2. Fig. 6 is a block diagram showing an example of the construction of a computing device according to embodiment 3. Fig. 7 is a block diagram showing a modified example of the construction of the computing device according to embodiment 3. Fig. 8 is a flowchart showing an example of the operating sequence of the computing device according to embodiment 3.Figure 9 is a block diagram showing an example of the construction of a computing device according to a further embodiment of the invention. Figure 10 is a schematic diagram showing an example of the construction of a system. Figure 11 is a block diagram showing an example of the construction of a control device. Figures 12A and 12B are schematic representations, each showing by way of example the state of structural model 1 and structural model 2, respectively. Figures 13A and 13B are graphs of the pair distribution functions and the correlation function for the case where Ne is defined as a specific atom species in structural model 1. Figures 14A and 14B are graphs of the pair distribution functions and the correlation function for the case where Ar is defined as a specific atom species in structural model 1. Figures 15A and 16B are graphs of the pair distribution functions and the correlation function for the case where Ar is defined as a specific atom species in structural model 1.Figures 15B and 16B are graphs of the pair distribution functions and the correlation function for the case where Ne is defined as the specific atom species in structure model 2. Figures 16A and 16B are graphs of the pair distribution functions and the correlation function for the case where Ar is defined as the specific atom species in structure model 2. Figure 17 is a schematic representation showing an example of the state of structure model 3. Figures 18A and 18B are graphs of the pair distribution functions and the correlation function for the case where Ne is defined as the specific atom species in structure model 3. Figures 19A and 19B are graphs of the pair distribution functions and the correlation function for the case where Ar is defined as the specific atom species in structure model 3. Figures 20A and 20B are schematic representations showing the crystal structure model and the unit cell of NCM333, respectively. Figures 21A and 21B are schematic representations of the crystal structure model and the unit cell of NCM333, respectively.Figures 21B and 22B are graphs of the first radial distribution function and the correlation function for the case where Ni, Co, and Mn are each defined as specific atom types in structural model 4. Figures 22A and 22B are graphs of the first radial distribution function and the correlation function, respectively, for the case where Ni, Co, and Mn are each defined as specific atom types in structural model 5. DETAILED DESCRIPTION OF THE INVENTION The following section explains embodiments of the invention with reference to the figures. For ease of understanding, identical structural elements in the figures are designated with the same reference numerals, and repetitive explanations are omitted. EXECUTION FORMS Design 1 Computing device In embodiment 1, the calculation of a correlation function from a structural model is described. Fig. 1 is a block diagram showing an example of the construction of a computing device 100 according to embodiment 1. The computing device 100 can be connected via a control device 300 to an X-ray diffraction device (or X-ray diffractometer) 200, which will be explained later, or directly to the X-ray diffraction device 200. The computing device 100 calculates a correlation function from a structural model. The computing device 100 is a computer in which a CPU (Central Processing Unit), a ROM (Read-Only Memory), a RAM (Random Access Memory), and a storage device are connected via a bus. The computing device 100 can be a PC terminal or a server in a cloud environment. Furthermore, not only the entire device, but also parts of the device or individual functions within the device can be provided in the cloud. An input device 510 and a display device 520 are connected to the CPU of the computing device 100 via suitable interfaces. The input device 510 is, for example, a keyboard or a mouse and serves to input data into the computing device 100.The display device 520, for example, is a display and serves to display structural models, specific types of atoms, the atomic ratio of specific types of atoms, correlation functions, radial distribution functions, pair distribution functions, specific levels in the structural model, the evaluation of the regularity of the atomic arrangement in the structural model, as well as characteristic values, variances and the like. The computing device 100 comprises a structure model acquisition unit 110, an atom type determination unit 120, and a correlation function calculation unit 130. The individual units can exchange information with each other via a control bus L. The structural model acquisition unit 110 acquires a structural model. Along with the structural model, the structural model acquisition unit 110 can also acquire information about the properties of this structural model. Information about the properties of the structural model includes, for example, details that the structural model has a layered structure. The structural model acquisition unit 110 can acquire the structural model directly from a device or software that generates the structural model, or it can acquire a structural model stored in a storage device or the like. Furthermore, the computing device 100 itself can have functionality for generating structural models. A structural model is a model that specifies the arrangement of particles (atoms or molecules) in a finite region. Depending on the sample, such a structural model can, for example, be given in the form of data that represent the arrangement of a finite number of particles within a cube, a cuboid, or a parallelepiped. In the present invention, the structural models are models that comprise several types of particles (atoms or molecules). The structural models to which the present invention can be applied can be any structural models created by structural modeling using a crystal structure as the initial structure, regardless of the device used to obtain the measurement data. For example, the present invention is not limited to structural models based on all scattering data measured with an X-ray diffraction device, but can also be applied to structural models created from measurement data obtained with similar measurement setups. More specifically, it can also be applied, for example, to structural models based on measurement data obtained using synchrotron radiation or particle beams such as neutron or electron beams. The structural model is preferably generated using a reverse Monte Carlo (RMC) method. The RMC method involves randomly modifying the arrangement of atoms (or molecules) in a given structural model to estimate or determine a model that reproduces the measured values. RMC methods have a large search space and allow the determination of a global minimum, making them well-suited for solving complex optimization problems. When an RMC method is applied in the present invention, the probability of obtaining a structural model that reproduces the measurement data increases, and a correlation function calculated using this structural model can, with a high probability, serve as a meaningful function for understanding the measurement data.The method for generating the structural model is not limited to RMC methods. Rather, the structural model can also be generated, for example, by an MD method (Molecular Dynamics method) or an MC method (Monte Carlo method). The atom type specification unit 120 defines a specific atom type within the structural model. A specific atom type refers to one of the atom types for which a correlation function is to be calculated within the structural model. The specific atom type can be defined by the user. The correlation function calculation unit 130 calculates a correlation function that indicates the relationship between 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 specified atomic species. The second radial distribution function is the radial distribution function between atoms of the specified atomic species and atoms of two or more atomic species within the structural model, where these atomic species include the specified atomic species. The two or more atomic species within the structural model that include the specified atomic species can comprise some or all of the atomic species contained in the structural model.The correlation function is defined using the ratio of the first radial distribution function to the second radial distribution function, and with this correlation function the distance dependence of the density fluctuations of an atom type can be represented. A radial distribution function is a function that describes the distribution of atoms and is defined such that, considering a specific atom, it specifies the distribution of atoms in its vicinity as a function of distance. More precisely, the first radial distribution function is a function that considers an atom of a specific type and describes the distribution of atoms of the same type in the vicinity of that atom. The second radial distribution function is a function that considers an atom of a specific type and describes the distribution of atoms of two or more selected types, including that specific type, in the vicinity of that atom. The following examples illustrate the selected two or more types of atoms that include the specific type of atom. For instance, if the types of atoms in the structural model are A, B, and C, and the specific type of atom is A, then the selected two or more types of atoms that include the specific type of atom are the combinations A and B, A and C, or A, B, and C. Let the specific type of atom be A, the first radial distribution function be NAA(r), and the second radial distribution function be NAX(r). In this case, the first radial distribution function NAA(r) can be represented, for example, by equation (1) below. The second radial distribution function NAX(r) can be represented, for example, by equation (2) below. Here, r is the distance, NA is the number of A atoms, δ is the delta function, rij is the distance between the i-th A atom and the j-th A atom or an atom of the selected type of atom, and N is the number of selected two or more types of atoms that enclose the specific type of atom. Equation 1: Equation 2: The defining equations of the first radial distribution function and the second radial distribution function are not limited to equations (1) and (2). For example, the delta function can also be replaced by a function such as a Gaussian distribution, which gives the probability of presence of the specific type of atom or of the selected two or more types of atoms that include the specific type of atom. Let the first radial distribution function be NAA(r), the second radial distribution function be NAX(r), and the correlation function be CA(r). Then the correlation function CA(r) can be represented, for example, by equation (3) below. The defining equation of the correlation function is not limited to equation (3). The correlation function simply needs to be an equation that expresses the ratio of the first radial distribution function to the second radial distribution function. If, however, the correlation function CA(r) is defined as in equation (3), then the correlation function CA(r) has an upper limit of 1. If CA(r) takes the value 1, it is evident that only combinations of the specific type of atom are present at the relevant correlation interval r, so it is preferable to define the correlation function in such a way that it exhibits this property. [Equation 3] The description above explained 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 radial distribution function to the second radial distribution function. For example, it can also be defined as the ratio of paired distribution functions for the specific type of atom. More precisely, let A be the specific type of atom, gAA(r) be the pair distribution function that considers only atoms of type A and is based on a single atom A (first pair distribution function), while gAX(r) is the pair distribution function for selected two or more types of atoms that include type A and is based on a single atom A (second pair distribution function). In this case, the correlation function CA(r) can be defined by equation (4) below, as in equation (3). This is because the relationship shown in equation (5) below exists between the radial distribution function N(r) and the pair distribution function g(r), where ρ denotes the mean density of the structural model. [Equation 4] [Equation 5] Consequently, even when defined as the ratio of pair distribution functions for a given type of atom, the correlation function can be viewed as the ratio of the first radial distribution function to the second radial distribution function. The correlation function can be calculated after the radial and pair distribution functions have been calculated, but it can also be calculated directly from the defining equation itself, without first calculating the radial and pair distribution functions. Fig. 2 is a block diagram showing a modified example of the setup of the computing device 100 according to embodiment 1. As shown in Fig. 2, the computing device 100 preferably comprises, in addition to the structure model acquisition unit 110, the atom type determination unit 120, and the correlation function calculation unit 130, a display unit 150. The display unit 150 causes the display device 520 to display the correlation function. Furthermore, the display unit 150 can cause the display device 520 to display the structure model, the determined atom type, the atomic ratio of the determined atom type, radial distribution functions (the first radial distribution function or the second radial distribution function), pair distribution functions (the first pair distribution function or the second pair distribution function), specific levels in the structure model, evaluations of the regularity of the atomic arrangement in the structure model, characteristic values, variances, etc.to display. Preferably, the display unit 150 shows the correlation function and the atomic ratio of the specific atom species within the structural model in superimposed form. The atomic ratio of the specific atom species within the structural model can, for example, be the atomic ratio of the specific atom species relative to the two or more atom species selected for calculating the second radial distribution function that include the specific atom species. Furthermore, the atomic ratio of the specific atom species within the structural model can also be the atomic ratio of the specific atom species relative to any two or more atom species that include the specific atom species.By superimposing the correlation function and the atomic number ratio of the specific type of atom within the structural model in this way, the properties of the correlation function in relation to the average concentration of the specific type of atom can be captured. Preferably, the display unit 150 simultaneously displays the correlation function for the specified atom species and the correlation function for a different atom species (hereinafter also referred to as the "second specified atom species"). This allows the properties of the correlation functions for the individual atom species to be compared and for similar as well as different properties to be identified. Fig. 3 is a flowchart illustrating an example of the operating sequence of the computing device 100 according to embodiment 1. Fig. 3 shows an example of the process for calculating a correlation function from a structural model. First, the computing device 100 obtains a structural model using the structural model acquisition unit 110 (step S1). Then, the atom type determination unit 120 determines a specific atom type within the structural model obtained by the structural model acquisition unit 110 (step S2). Next, the correlation function calculation unit 130 calculates the correlation function (step S3). The correlation function can also be output if required. Furthermore, the radial distribution functions or pair distribution functions can also be output. Thus, the correlation function can be calculated from the structural model. If the computing device 100 includes a display unit 150, the correlation function, radial distribution functions, or pair distribution functions can also be displayed if required. In this way, the properties of the correlation function calculated from the structural model can be determined. Since the correlation function can be viewed as a function that describes the mixing state of neighboring particles in the structural model, the mixing state of neighboring particles in the structural model can be described by analyzing the correlation function. Design 2 Computing device In embodiment 2, the case is explained in which the correlation function is calculated for a specific level within the structural model. Fig. 4 is a block diagram showing an example of the setup of the computing device 100 according to embodiment 2. As shown in Fig. 4, the computing device 100 preferably comprises, in addition to the structural model acquisition unit 110, the atom type determination unit 120, and the correlation function calculation unit 130, a level determination unit 125. The level determination unit 125 determines a specific level within the structural model. The determined level is the level within the structural model for which a correlation function is to be calculated. By determining the specific level, the mixing state of the neighboring particles present at that level can be analyzed. The determination of the specific level can be performed at the user's instruction. If information about the properties of the structural model is associated with it, an arrangement can also be provided in which the user is offered the option, based on this information, to choose whether or not a specific level should be determined. If the level determination unit 125 has determined a specific level, the correlation function calculation unit 130 calculates the correlation function at that specific level. The correlation function at that specific level is a correlation function that indicates the ratio of the first radial distribution function to the second radial distribution function at that specific level. If, however, the level determination unit 125 does not determine a specific level, the correlation function calculation unit 130 calculates the correlation function for the entire structural model. Fig. 5 is a flowchart showing an example of the operating sequence of the computing device 100 according to embodiment 2. Fig. 5 shows an example of the sequence in a case where a decision is made as to whether or not a specific level is determined. First, the computing device 100 obtains a structural model by means of the structural model acquisition unit 110 (step T1). Subsequently, the atom type determination unit 120 determines a specific atom type within the structural model obtained by the structural model acquisition unit 110 (step T2). Next, a decision is made as to whether or not a specific level should be determined (step T3). If a specific level is to be determined (Yes in step T3), then the level determination unit 125 determines the specific level (step T4). Then, the correlation function calculation unit 130 calculates the correlation function (step T5). If, however, no specific level is to be determined (No in step T3), then the correlation function calculation unit 130 calculates the correlation function (step T5). If required, the correlation function, the specific level, radial distribution functions, or pair distribution functions can be output. If the computing device 100 includes a display unit 150, then these can also be displayed, if necessary. In this way, the correlation function for a specific level can be calculated. The determination of the specific level can also be performed before the determination of the specific atom type. embodiment 3 Computing device In embodiment 3, a case is described in which the regularity of the atomic arrangement is evaluated using the correlation function. Fig. 6 is a block diagram showing an example of the setup of the computing device 100 according to embodiment 3. As shown in Fig. 6, the computing device 100 preferably comprises, in addition to the structure model acquisition unit 110, the atom type determination unit 120, and the correlation function calculation unit 130, an evaluation unit 140. The assessment 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 refers, among other things, to whether the arrangement can be considered statistically random or whether it exhibits a certain regularity. The evaluation of the regularity of the atomic arrangement within the structural model can, for example, also include assessing whether neighboring particles of a particular atom type form clusters. If the correlation distance r is small and the value of the correlation function is greater than the atomic ratio of the particular atom type, then it can be determined that clusters are formed.The assessment of the regularity of the atomic arrangement within the structural model can be a numerical value calculated using the correlation function or a descriptive statement determined based on the properties of the correlation function. Fig. 7 is a block diagram showing a modified example of the structure of the computing device 100 according to embodiment 3. As shown in Fig. 7, the computing device 100 preferably comprises, in addition to the structural model acquisition unit 110, the atom type determination unit 120, the correlation function calculation unit 130, and the evaluation unit 140, a characteristic value calculation unit 135. The characteristic value calculation unit 135 calculates a characteristic value using the correlation function. If the computing device 100 includes the characteristic value calculation unit 135, then the evaluation unit 140 assesses the regularity of the atomic arrangement within the structural model based on the characteristic value calculated by the characteristic value calculation unit 135. Preferably, the characteristic value is a numerical value that can be used to assess the regularity of the atomic arrangement within the structural model. The evaluation unit 140 can determine that regularity exists if the characteristic value fulfills a predefined condition. The predefined condition can vary depending on the type of characteristic value. Preferably, the characteristic value is the variance or the standard deviation of the correlation function. In the case of a random atomic arrangement, the correlation function approaches a constant value regardless of the spacing. That is, if the deviation from a constant value is large, the atomic arrangement can be assumed to exhibit some regularity. Therefore, for example, it can be assessed that the atomic arrangement exhibits regularity if the variance of the correlation function is greater than a certain value, and that the atomic arrangement is random if the variance of the correlation function is less than a certain value.Furthermore, it can be assessed, for example, that the atomic arrangement exhibits higher regularity compared to a reference atomic arrangement if the variance of the correlation function is greater than the variance of the correlation function of the reference atomic arrangement, and that the atomic arrangement is more random compared to the reference atomic arrangement if the variance of the correlation function is less than the variance of the correlation function of the reference atomic arrangement. The same applies to the standard deviation. If it is determined that regularity exists if the characteristic value fulfills predefined conditions, these predefined conditions can, for example, consist of the variance or the standard deviation corresponding to at least a predefined value. A specific example of the case where the variance is used as a characteristic value is described in more detail in the exemplary embodiments. Preferably, the characteristic value is calculated using the correlation function and the atomic ratio of the specific atom types within the structural model. In the case of a random atom arrangement within the structural model, the correlation function approximates the atomic ratio of the specific atom type within the structural model (hereinafter also referred to as the occupancy level of the specific atom type). That is, if the occupancy level of the specific atom type and the value of the correlation function differ, it can be determined that the atoms are arranged regularly. If a specific plane is defined and the correlation function is calculated, the atomic ratio of the specific atom type within the structural model can also be used as the atomic ratio of the specific atom type at that specific plane.If it is to be decided that a regularity exists when the characteristic value fulfills a predetermined condition, then this predetermined condition can be, for example, that the characteristic value calculated on the basis of the atomic number ratio of the specific type of atom and the value of the correlation function is greater than or equal to a predetermined value. Fig. 8 is a flowchart showing an example of the operating sequence of the computing device 100 according to embodiment 3. Fig. 8 shows an example of the sequence in a case where the regularity of the atomic arrangement is evaluated using the correlation function. First, the computing device 100 obtains a structural model using the structure model acquisition unit 110 (step U1). Subsequently, the atom type determination unit 120 determines a specific atom type within the structural model obtained by the structure model acquisition unit 110 (step U2). Next, the correlation function calculation unit 130 calculates the correlation function (step U3). Then, the evaluation unit 140 assesses the regularity of the atomic arrangement within the structural model (step U4). If the computing device 100 includes a characteristic value calculation unit 135, the characteristic value is first calculated by the characteristic value calculation unit 135 before the assessment of the regularity of the atomic arrangement within the structural model. The evaluation unit 140 then assesses the regularity of the atomic arrangement based on this characteristic value. If required, the correlation function, radial distribution functions, pair distribution functions, the assessment, or the characteristic value can also be output. If the computing device 100 includes a display unit 160, these can be displayed if required. In this way, the regularity of the atomic arrangement within the structural model can be assessed based on the correlation function. In this context, embodiments 1 to 3 can also be configured such that they each include some or all of the features of the other embodiments. Fig. 9 is a block diagram showing an example of the structure of the computing device 100 according to a further embodiment of the present invention. As shown in Fig. 9, the computing device 100 comprises a structural model acquisition unit 110, an atom type determination unit 120, a level determination unit 125, a correlation function calculation unit 130, a characteristic value calculation unit 135, an evaluation unit 140, and a display unit 150. Of these, the level determination unit 125, the characteristic value calculation unit 135, the evaluation unit 140, and the display unit 150 are optional components. Overall system The computing device 100, or the calculation method of the present invention, can obtain a structural model and calculate or evaluate the correlation function independently of the X-ray diffraction device 200 and the control device 300. Therefore, the computing device 100 does not need to be used simultaneously with the X-ray diffraction device 200 or the control device 300. On the other hand, it can also be provided as an integrated system with the X-ray diffraction device 200 and the control device 300. Fig. 10 is a schematic diagram of an exemplary arrangement of a system 400 comprising a computing device 100 and an X-ray diffraction device 200. The system 400 includes the computing device 100, the X-ray diffraction device 200, and the control device 300. In Fig. 10, the computing device 100 and the control device 300 are shown as the same PC. However, the computing device 100 can also be configured as a separate device from the control device 300. A case in which the computing device 100 and the control device 300 are configured as separate devices is explained below. X-ray diffraction device The X-ray diffraction device 200 forms an optical system that directs X-rays onto a sample and detects the reflected X-rays produced by the sample. The X-ray diffraction device 200 comprises at least one X-ray generation unit 210, which generates X-rays from an X-ray focus, 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 for detecting the X-rays. The X-ray diffraction device 200 may further comprise an incident-side optical unit 220, a goniometer 230, and an outgoing-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, from which the X-ray diffraction device 200 is constructed, can be of conventional design, their detailed description is omitted. The arrangement shown in Fig. 10 is merely an example, and various other configurations can also be chosen. Control device The control device 300 is connected to the X-ray diffraction device 200 and performs the control of the X-ray diffraction device 200 as well as the processing, storage and display of the data obtained. Figure 11 is a block diagram showing an example of the setup of the control device 300. The control device 300 comprises a computer in which a CPU, ROM, RAM, and memory are connected via a bus. The control device 300 can be a PC terminal or a server in a cloud environment. Furthermore, not only the entire device, but also parts of the device or individual functions within the device can be provided in the cloud. The control device 300 is connected to the X-ray diffraction device 200 and receives information from it. 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. The individual units can exchange information with each other via a control bus L. If the computing device 100 and the control device 300 are designed as separate devices, the input device 510 and the display device 520 are connected to the CPU of the control device 300 via suitable interfaces. In this case, the input device 510 and the display device 520 may also differ from those connected to the computing device 100. The control unit 310 controls the operation of the X-ray diffraction device 200. The device information storage unit 320 stores device information obtained from the X-ray diffraction device 200. This device information can include, for example, information about the X-ray diffraction device 200, such as the device name, the type of X-ray source, the wavelength, the background, and the like. The measurement data storage unit 330 stores the measurement data acquired by the X-ray diffraction device 200. Along with the measurement data, necessary information relating to the X-ray diffraction device 200, such as the type of radiation source, wavelength, and background, as well as information like the shape and structure of the sample, its constituent elements, composition, and absorption coefficient, can be stored. The display unit 340 displays the measurement data, etc., on the display device 520. This allows the user to verify the measurement data, etc. Furthermore, the user can use the measurement data, etc., to issue instructions or specifications to the control device 300, the computing device 100, and similar components. The computing device 100 can also be provided as part of the functionality within the control device 300. Furthermore, the computing device 100 and the control device 300 can also be designed as an integrated device. Measurement methods A sample is placed in the X-ray diffraction device 200, and X-rays are directed onto the sample by means of the control device 300. The diffracted X-rays produced by the sample are then measured. If necessary, the sample stage or the goniometer is moved under predefined conditions. In this way, measurement data, such as the complete scattering data, are obtained. The X-ray diffraction device 200 transmits the obtained measurement data, as well as the necessary device information, to the control device 300. Method for generating the structural model A structural model that reproduces the measurement data is generated using the control device 300, the computing device 100, or an external device. The method for generating the structural model is not limited to a specific procedure. Depending on the sample, the structural model can, for example, be specified in the form of data indicating the arrangement of a finite number of atoms (molecules) within a cube, a cuboid, or a parallelepiped. Such a structural model, which specifies the atomic arrangement in a finite region, is obtained, and the total scattering intensity is calculated from the structural model. The structural model is then modified until the degree of agreement or deviation between the total scattering intensity calculated from the structural model and the measurement data is better than a specified value. Once the degree of agreement or deviation is lower, the structural model is further refined.If the deviation between the total scattering intensity of the structural model and the measurement data is better than the specified value, the generation of the structural model is terminated. For example, when generating the structural model using a reverse Monte Carlo (RMC) method, the atomic positions in the model are randomly shifted. If, after such a step, the degree of agreement or deviation is better than before (i.e., the measure of proximity is greater), then further random shifts are made based on the resulting atomic arrangement. If, however, the degree of agreement or deviation after the step is not better than before (i.e., the measure of proximity is not greater), then the step is discarded, and another random shift is performed based on the atomic arrangement before the step. Such steps are repeated until the degree of agreement or deviation meets a predefined condition.However, the method for generating the structural model can also be an MD method (Molecular Dynamics method) or an MC method (Monte Carlo method). Using the system 400 described above, measurement data can be obtained from the X-ray diffraction device 200 and a structural model can be generated. The correlation function can then be calculated from the generated structural model. Example 1 Using the computing device 100 described above, two structural models with different states of atomic arrangement were generated, and it was verified whether the properties of the atomic arrangement were recognizable in the correlation function calculated from these structural models. More precisely, the following procedure was performed: In a three-dimensional space, lattice points were defined such that, in a cube with an edge length of 24 Å, the distance between adjacent points on edges, faces, and inside the cube was 3.0 Å. Next, a structural model was generated in which Ne and Ar were randomly arranged in a 1:1 ratio at these lattice points. Furthermore, another structural model was generated in which Ne and Ar were arranged alternately at the same lattice points. A displacement of Δr ≤ 0.2 Å was randomly applied to each of these particles (i.e., Ne or Ar) of the respective structural models.The structural model with the random arrangement is referred to below as structural model 1, and the structural model with the alternating arrangement as structural model 2. Figures 12A and 12B are schematic representations, each showing an example of the state of structural model 1 and structural model 2, respectively. Next, using the computer 100, a specific atom species was defined for both structural model 1 and structural model 2, and the first pair distribution function, the second pair distribution function, and the correlation function were calculated. Figures 13A and 13B are graphs of the pair distribution functions and the correlation function for the case where Ne is defined as the specific atom species in structural model 1. Figures 14A and 14B are graphs of the pair distribution functions and the correlation function for the case where Ar is defined as the specific atom species in structural model 1. Figures 15A and 15B are graphs of the pair distribution functions and the correlation function for the case where Ne is defined as the specific atom species in structural model 2. And Figures 16A and 16B are graphs of the pair distribution functions and the correlation function for the case where Ar is defined as the specific atom species in structural model 2. In Figures 13A and 15A, Ne-Ne represents the first pair distribution function for the case where Ne is assumed to be the specific atomic species, while Ne-Ar represents the second pair distribution function for the same case. Similarly, in Figures 14A and 16A, Ar-Ar represents the first pair distribution function for the case where Ar is assumed to be the specific atomic species, while Ar-Ne represents the second pair distribution function for the same case. In all these cases, the graphs are shown offset from each other in the vertical direction. From the correlation functions C(r) in Fig. 13B and Fig. 14B, it can be seen that in the case of structural model 1, where the two types of atoms are randomly arranged, the baseline of the correlation function C(r) coincides with the atomic ratio of the specific type of atom in the structural model (the proportion of the specific type of atom in the structural model or its average concentration). The straight line drawn in Fig. 13B and Fig. 14B at C(r) = 0.5 indicates the atomic ratio of the specific type of atom. The correlation function C(r) gives the probability of the specific type of atom being present at a correlation distance r from the specific type of atom. In other words, the occurrence of a peak in the correlation function C(r) means that many pairs of the specific type of atom are present at this correlation distance.By plotting the atomic ratio of a specific type of atom and the correlation function C(r) together in the same diagram, it is possible to determine the correlation values ​​r at which a regular arrangement occurs. Furthermore, the regularity of the atomic arrangement can also be assessed based on the correlation function C(r) and the atomic ratio of the specific type of atom. For example, it can be determined that a regular arrangement exists if the deviation between the correlation function C(r) and the atomic ratio of the specific type of atom is greater than or equal to a predetermined value. In the case of structural model 1, where the two types of atoms are randomly arranged, the correlation functions C(r) in Figs. 13B and 14B show that the range of variation of the correlation function C(r) is small and that it has largely settled in the region with correlation distances r of at least approximately 10 Å. On the other hand, in the case of structural model 2, where the two types of atoms are arranged regularly, i.e., alternately, the range of variation of the correlation function C(r) in Figs. 15B and 16B is large, and even in the region with correlation distances r of 20 Å and more, no convergence is yet apparent. This shows that the atoms within the structural model are arranged regularly even at correlation distances of 20 Å and greater. Furthermore, the variance was used to express the range of variation of the correlation function C(r) as a characteristic value. The variance of the correlation function C(r) for structural model 1, with Ne and Ar as the specific atom type, was 0.007 and 0.012, respectively. Conversely, the variance of the correlation function C(r) for structural model 2, with Ne and Ar as the specific atom type, was 0.045 and 0.126, respectively. The fact that the variance is larger in structural model 2 indicates that the atoms are arranged regularly in this model. Thus, the variance can be used as a characteristic value to assess whether the atoms are arranged regularly. To improve the accuracy of the calculation, regions where C(r) = 0 were excluded from the variance calculation. The standard deviation can also be used as a characteristic value instead of the variance, resulting in a similar effect. The results of embodiment 1 confirmed that with structural models in which a regularity is clearly either present or absent, the regularity of the atomic arrangement within the structural model can be recognized in the correlation function. Example 2 Using the computing device 100 described above, and assuming an atomic arrangement where the positions of the atoms are not restricted to lattice points, it was verified whether the properties of the atomic arrangement are recognizable in the correlation function. More precisely, the following procedure was performed: A structural model was created in which Ne and Ar were randomly arranged in a 1:1 ratio in three-dimensional space inside a cube with an edge length of 20 Å. The structural model, in which the particles of the structural model were moved exclusively under collision detection over 105 MCSteps (Monte Carlo Steps), is designated as structural model 3. Fig. 17 is a schematic diagram that exemplifies the state of structural model 3. Subsequently, a specific atom species was defined for structural model 3 using the computing device 100, and the first pair distribution function, the second pair distribution function, and the correlation function were calculated. Figures 18A and 18B are graphs of the pair distribution functions and the correlation function for the case where Ne is defined as the specific atom species in structural model 3. Figures 19A and 19B are graphs of the pair distribution functions and the correlation function for the case where Ar is defined as the specific atom species in structural model 3. In Figure 18A, Ne-Ne represents the first pair distribution function for the case where Ne is defined as the specific atom species, while Ne-Ar represents the second pair distribution function for the case where Ne is defined as the specific atom species. Similarly, in Figure 18B, the first pair distribution function is defined as the second pair distribution function for the case where Ne is defined as the specific atom species.19A Ar-Ar represents the first pair distribution function for the case where Ar is specified as the particular atomic species, while Ar-Ne represents the second pair distribution function for the same case. In all cases, the graphs are shown offset from each other in the vertical direction. From the correlation functions C(r) in Fig. 18B and Fig. 19B, it can be seen that in the case of structural model 3, in which two types of atoms, including their positions, are randomly arranged, the more distant part of the correlation function C(r) converges to the atomic ratio of the specific type of atom. The straight line shown in Fig. 18B and Fig. 19B at C(r) = 0.5 indicates the atomic ratio of the specific type of atom. The results of embodiments 1 and 2 confirmed that information about the state of the mixture can be obtained from the spatial correlation function of the specific type of atom. Example 3 Using a crystal structure model that describes the measured X-ray diffraction profile, it was investigated whether information about the mixing state of neighboring particles could be derived from the correlation function. More specifically, crystal structure models (structural models) were created that describe the measured X-ray diffraction profiles of NCM333 (Li(Ni0.33, Co0.33, Mn0.33)O2) and NCM523 (Li(Ni0.5, Co0.2,Mn0.3)O2), which are used as cathode materials in lithium-ion batteries. Figures 20A and 20B are schematic representations showing the crystal structure model of NCM333 and a unit cell thereof, respectively. As shown in Figure 20A, NCM is composed of three types of layered structures: layers containing only Li ions, layers containing only oxygen atoms, and layers containing only transition metal atoms. As shown in Figure 20A, the crystal structure of NCM333 is composed of three types of layered structures: layers containing only Li ions, layers containing only oxygen atoms, and layers containing only transition metal atoms.As shown in Figure 20B, the transition metal sites in NCM333 are assigned occupancy probabilities, and the transition metal atoms with these defined occupancy probabilities are, in principle, randomly distributed. The same applies to NCM523. The initial structure for NCM333 and NCM523 was generated such that the transition metal sites were randomly occupied by Ni, Co, and Mn in the ratios Ni : Co : Mn = 1 : 1 : 1 and 5 : 2 : 3, respectively. Subsequently, using a reverse Monte Carlo (RMC) process, the arrangements of Ni, Co, and Mn were randomly modified, with some of the Ni, Co, and Mn atoms being replaced by other elements (Ni, Co, and Mn, respectively). The RMC steps were repeated until a profile was obtained that closely approximated the measured X-ray and neutron diffraction profiles. The structure of NCM333 for which a profile was obtained that sufficiently approximates the measured X-ray diffraction profile is designated as structure model 4, and the corresponding structure of NCM523 is designated as structure model 5. Next, a specific layer was defined for structural models 4 and 5 using the computer 100. Then, a specific atom species was defined for each of structural models 4 and 5, and the first radial distribution function, the second radial distribution function, and the correlation function were calculated. One of the layers consisting exclusively of transition metal elements was chosen as the specific layer. Figures 21A and 21B are graphs of the first radial distribution functions and the correlation functions, respectively, for the case where Ni, Co, and Mn are defined as the specific atom species in structural model 4. Figures 22A and 22B are graphs of the first radial distribution functions and the correlation functions, respectively, for the case where Ni, Co, and Mn are defined as the specific atom species in structural model 5. In all cases, the graphs are shown offset from each other in the vertical direction.In calculating the correlation function, the second radial distribution function used the two or more types of atoms Ni, Co and Mn that comprise the specific type of atom. The atomic ratio (the average concentration) of Ni, Co, and Mn in the specified plane of structural model 4 is 0.33, 0.33, and 0.3, respectively. The straight lines plotted on the respective correlation functions in Fig. 21B indicate the atomic ratio of each specified atom type. Fig. 21B shows that in NCM333, Co and Mn are highly likely to be randomly distributed at all distances. In contrast, for Ni, it is likely that clusters are formed in the immediate vicinity. The atomic ratio (the average concentration) of Ni, Co, and Mn in the specified plane of structure model 5 is 0.3, 0.2, and 0.43, respectively. The straight lines plotted in the respective correlation functions in Fig. 22B indicate the atomic ratio of each specified atom type. Fig. 22B shows that in NCM523, Co is highly likely to be randomly distributed at all distances. In contrast, for Ni and Mn, it is likely that clusters are formed in the immediate vicinity. Based on the results of embodiment 3, it could be confirmed that for structural models in which occupancy probabilities are defined for the average structure, it is possible to check whether substitutions on the grid positions occur randomly or regularly. The above results confirm that the computing device, method, and program according to the present invention are capable of calculating a correlation function from a structural model. Furthermore, it confirms that the correlation function can be evaluated. The present invention is not limited to the embodiments described above. Rather, the scope of protection of the present invention also extends to various modifications and equivalents encompassed by the technical concept of the present invention. Furthermore, the designations, structures, shapes, numbers, positions, dimensions, etc., of the components shown in the figures are given for illustrative purposes only and may be modified accordingly if necessary. The functionalities of the elements disclosed in this description can be implemented by means of circuits or processing circuits, including general-purpose processors, application-specific processors, integrated circuits, ASICs (Application-Specific Integrated Circuits), FPGAs (Field-Programmable Gate Arrays), conventional circuits, or circuits and combinations thereof that are programmed using one or more programs stored in one or more memories or are otherwise configured to perform the disclosed functionalities. Since a processor comprises transistors and other circuits, it can be considered a circuit or processing circuit. Such a processor can also be a programmed processor that executes a program stored in memory.In this disclosure, "circuit," "unit," or "means" refer either to hardware components that perform the listed functions or to hardware components that are programmed to perform the listed functions. The hardware can be any hardware disclosed in this description, provided it is programmed or configured to perform the listed functions. There is no restriction regarding the type of hardware. The present application claims priority from Japanese patent application No. 2024-226055, which was filed on December 23, 2024. The complete content of Japanese patent application No. 2024-226055 is to be incorporated into the present application by reference. REFERENCE MARK LIST 100 Computing device 110 Structural model acquisition unit 120 Atom type determination unit 125 Level determination unit 130 Correlation function calculation unit 135 Characteristic value calculation unit 140 Evaluation unit 150 Display unit 200 X-ray diffraction device 210 X-ray beam generation unit 220 Incidence-side optical unit 230 Goniometer 240 Sample stage 250 Emission-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 QUOTES INCLUDED IN THE DESCRIPTION This list of documents cited by the applicant was automatically generated and is included solely for the reader's convenience. The list is not part of the German patent or utility model application. The DPMA accepts no liability for any errors or omissions. Cited patent literature JP 2024-226055

[0079] Cited non-patent literature AB Bhatia, DE Thornton, Phys. Rev. B 2 (1970) 3004-3012. https: / / doi.org / 10.1103 / PhysRevB.2.3004

[0005] C. Zhang, G. Galli, J. Chem. Phys. 141 (2014) 084504 (5 pp). https: / / doi.org / 10.1063 / 1.4893638

[0005]

Claims

A computing device for calculating a correlation function from a structural model, comprising: a structural model acquisition unit configured to acquire a structural model comprising several types of atoms in a space, an atom type specification unit configured to specify a particular type of atom in the structural model, and a correlation function calculation unit configured to calculate a correlation function that is the ratio of a first radial distribution function to a second radial distribution function, wherein the first radial distribution function is a radial distribution function between atoms of the particular type of atom, and the second radial distribution function is a radial distribution function between atoms of the particular type of atom and atoms of two or more types of atoms, including the particular type of atom. Computing device according to claim 1, further comprising a display unit configured to display the correlation function. Computing device according to claim 2, wherein the display unit is configured to represent the correlation function and the atomic number ratio of the specific type of atom within the structural model in superimposed form. Computing device according to claim 2 or 3, wherein the display unit is configured to simultaneously display the correlation function of the specified atom type and the correlation function of an atom type different from the specified atom type. Computing device according to one of claims 1 to 4, further comprising: a level determination unit configured to define a specific level within the structural model, wherein the correlation function calculation unit is configured to calculate the correlation function in the specified level. Computing device according to one of claims 1 to 5, further comprising: an evaluation unit which is configured to evaluate the regularity of the atomic arrangement within the structural model on the basis of the correlation function. Computing device according to claim 6, further comprising: a characteristic value calculation unit which is configured to calculate a characteristic value on the basis of the correlation function, wherein the evaluation unit is configured to evaluate the regularity of the atomic arrangement on the basis of the characteristic value. Computing device according to claim 7, wherein the characteristic value is the variance or the standard deviation of the correlation function. Computing device according to claim 7, configured to calculate the characteristic value based on the correlation function and the atomic number ratio of the specific type of atom within the structural model. Computing device according to one of claims 1 to 9, wherein the structural model is a model generated by means of a reverse Monte Carlo method. A method for calculating a correlation function from a structural model, comprising: a step to obtain a structural model comprising several types of atoms in a space, a step to specify a particular type of atom in the structural model, and a step to calculate a 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 a radial distribution function between atoms of the particular type of atom, and the second radial distribution function is a radial distribution function between atoms of the particular type of atom and atoms of two or more types of atoms including the particular type of atom. A program for calculating a correlation function from a structural model, which, when executed on a computer, causes the computer to perform the following: a processing step to obtain a structural model comprising several types of atoms in a space; a processing step to specify a particular type of atom in the structural model; and a processing step to calculate a correlation function; a processing step that is the ratio of a first radial distribution function to a second radial distribution function, wherein the first radial distribution function is a radial distribution function between atoms of the particular type of atom, and the second radial distribution function is a radial distribution function between atoms of the particular type of atom and atoms of two or more types of atoms, including the particular type of atom.

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