Computing device, system, method, and program

Abstract

To provide a computing device, system, method, and program capable of simply estimating an orientation direction from a two-dimensional diffraction image and calculating a structural model of a polymer.SOLUTION: A computing device 400 for calculating a structural model of a polymer comprises: a data acquisition unit 410 that acquires a two-dimensional diffraction image and crystal structure data; an initial structural model creation unit 420 that creates an initial structural model including one crystallite; and a crystallite direction calculation unit 430 that calculates a direction of the crystallite. The direction of the crystallite is calculated on the basis of the two-dimensional diffraction image calculated from the initial structural model and the actually measured two-dimensional diffraction image.SELECTED DRAWING: Figure 3

Description

[Technical Field]

[0001] The present invention relates to a computer device, a system, a method and a program for calculating a structural model of a polymer. [Background technology]

[0002] The properties of polymeric materials are closely related to their orientation distribution. Wide-angle X-ray diffraction (WAXD) is a widely used method for measuring the orientation distribution of polymeric materials. However, because polymeric materials have a lower degree of crystallinity than low-molecular-weight materials, there are problems such as fewer diffraction points in the diffraction pattern and strong diffuse diffraction from non-crystals, making it difficult to analyze polymeric materials in the same way as low-molecular-weight materials. Therefore, a unique method for analyzing polymeric materials is required.

[0003] Non-Patent Document 1 describes a method for estimating the electron density distribution in real space from a diffraction pattern by the Reverse Monte Carlo (RMC) method.

[0004] Non-Patent Document 2 applies the method of Non-Patent Document 1 to polymer materials, and describes a method for determining the three-dimensional structure of polymers that reproduces the measured WAXD image by simulation using the RMC method.

[0005] Non-Patent Document 3 describes a method for determining the orientation direction and orientation distribution by creating a structural model of a uniaxially oriented sample and comparing a diffraction image calculated from the structural model with an actually measured diffraction image. [Prior art documents] [Non-patent literature]

[0006] [Non-Patent Document 1] RL McGreedy, L. Pusztai. "Reverse Monte Carlo Simulation: A New Technique for the Determination of Disordered Structures". Molecular Simulation, 1988, 1, 6, p. 359-367 [Non-patent document 2] Daisuke Tahara, Koji Tashiro. "Development of polymer 3D higher-order structure analysis based on computer simulation techniques of measured wide-angle and small-angle X-ray scattering data." Proceedings of the Society of Polymer Science, 2018, 67, 1, 1Pe027 [Non-patent document 3] Y. Zhang, et. al., “Uncovering three-dimensional gradients in fibrillar orientation in an impact-resistant biological armor”, Scientific Reports 6, 26249 (2016). Summary of the Invention [Problem to be solved by the invention]

[0007] The analysis in Non-Patent Document 2 has a problem in that it takes a long time to reach an equilibrium state due to the large number of degrees of freedom and the large amount of calculation required to change each degree of freedom.

[0008] In Non-Patent Document 3, the analysis target is limited to uniaxially oriented samples such as fibers. In other words, only two-dimensional orientation distribution is assumed. However, to analyze the structure of industrially important polymer films, it is necessary to clarify three-dimensional orientation distribution. Furthermore, because the analysis assumes fiber orientation due to uniaxial stretching, it is unable to express complex orientation distributions, unlike Non-Patent Document 2, which uses simulations using the RMC method.

[0009] As a result of extensive research, the inventors have discovered a method for easily estimating the orientation of a sample from a WAXD image, even for a sample with a three-dimensional orientation distribution. Furthermore, they have found that by performing a simulation using the RMC method with the estimated orientation as the initial value, the amount of calculation can be reduced and a globally optimal solution can be obtained, thereby completing the present invention.

[0010] The present invention has been made in consideration of the above circumstances, and aims to provide a computing device, system, method, and program for easily estimating the orientation direction from a two-dimensional diffraction image and calculating a structural model of a polymer. [Means for solving the problem]

[0011] (1) In order to achieve the above object, the computing device of the present invention is a computing device for calculating a structural model of a polymer, and is characterized in that it comprises a data acquisition unit that acquires two-dimensional diffraction images and crystal structure data, an initial structural model creation unit that creates an initial structural model including one crystallite, and a crystallite orientation calculation unit that calculates the orientation of the crystallite, and the orientation of the crystallite is calculated based on the two-dimensional diffraction image calculated from the initial structural model and the two-dimensional diffraction image that is actually measured.

[0012] (2) Furthermore, in the calculation device of the present invention, the crystallite orientation calculation unit calculates the degree of agreement between the two-dimensional diffraction image calculated from the multiple initial structure models corresponding to the multiple directions of the single crystallite and the measured two-dimensional diffraction image, and calculates the direction of the crystallite based on the calculated degree of agreement.

[0013] (3) The calculation device of the present invention further includes a pre-calculation structural model creation unit that creates a pre-calculation structural model for a structural model having a plurality of crystallites, with the orientation of the plurality of crystallites being in the same direction, and a calculation execution unit that changes the structural model based on the degree of agreement between a two-dimensional diffraction image calculated from the structural model and the measured two-dimensional diffraction image, and is characterized in that the calculation execution unit uses the pre-calculation structural model as an initial value and calculates a post-calculation structural model whose degree of agreement satisfies a convergence condition.

[0014] (4) Furthermore, the calculation device of the present invention is characterized in that it further includes a crystalline component extraction unit that extracts crystalline components from the measured two-dimensional diffraction image, and the crystallite orientation calculation unit calculates the orientation of the crystallite using the crystalline components from the measured two-dimensional diffraction image.

[0015] (5) In the calculation device of the present invention, the direction of the crystallite is a three-dimensional vector.

[0016] (6) In the calculation device of the present invention, the calculation execution unit calculates the post-calculation structural model using the RMC method.

[0017] (7) Furthermore, in the calculation device of the present invention, the pre-calculation structural model creation unit selectively creates either the pre-calculation structural model or a second pre-calculation structural model in which the crystallite orientation is randomly arranged relative to the structural model, and the calculation execution unit calculates the post-calculation structural model using either the pre-calculation structural model or the second pre-calculation structural model as an initial value.

[0018] (8) The system of the present invention is characterized by comprising an X-ray diffraction apparatus having an X-ray generating unit that generates X-rays, a detector that detects X-rays, and a sample stage that controls the rotation of the sample, and a calculation device described in any one of (1) to (7) above.

[0019] (9) Furthermore, the method of the present invention is a method for calculating a structural model of a polymer, comprising the steps of acquiring a two-dimensional diffraction image and crystal structure data, creating an initial structural model including one crystallite, and calculating the orientation of the crystallite, wherein in the step of calculating the orientation of the crystallite, the orientation of the crystallite is calculated based on the two-dimensional diffraction image calculated from the initial structural model and the two-dimensional diffraction image that is actually measured.

[0020] (10) Furthermore, the program of the present invention is a program for calculating a structural model of a polymer, and is characterized in that it causes a computer to execute a process of acquiring a two-dimensional diffraction image and crystal structure data, a process of creating an initial structural model including one crystallite, and a process of calculating the orientation of the crystallite, and in that in the process of calculating the orientation of the crystallite, the orientation of the crystallite is calculated based on the two-dimensional diffraction image calculated from the initial structural model and the two-dimensional diffraction image that is actually measured. [Brief explanation of the drawings]

[0021] [Figure 1] 1 is a conceptual diagram showing an example of the configuration of a computing system according to the present invention. [Figure 2] FIG. 2 is a block diagram showing an example of the configuration of a control device. [Figure 3] FIG. 1 is a block diagram illustrating an example of a configuration of a computing device. [Figure 4] This is a schematic diagram showing the state in which a polymer is replaced with the electron density of a cylinder and placed within a unit cell. [Figure 5] FIG. 2 is a schematic diagram showing an example of the direction of a crystallite. [Figure 6] FIG. 10 is a block diagram showing a modified example of the configuration of the computing device. [Figure 7] FIG. 10 is a block diagram showing a modified example of the configuration of the computing device. [Figure 8] 1(a) to 1(d) are schematic diagrams of two-dimensional diffraction images showing one stage of an example of extraction of crystalline components from measured two-dimensional diffraction images. [Figure 9] 10 is a flowchart illustrating an example of the operation of the computing device. [Figure 10] 10 is a flowchart illustrating a modified example of the operation of the computing device. [Figure 11] 10 is a flowchart illustrating a modified example of the operation of the computing device. [Figure 12] 1(a) to 1(c) are schematic diagrams showing the measured two-dimensional diffraction image of an HDPE sample, the two-dimensional diffraction image of a calculated structural model of an example, and the two-dimensional diffraction image of a comparative example, respectively. [Figure 13]1 is a graph showing changes in fitness in an example and a comparative example. [Figure 14] 1A and 1B are projections showing the distribution of alignment directions in the initial state of an example, and projections showing the distribution of alignment directions when the convergence condition is satisfied, respectively. [Figure 15] 10(a) and 10(b) are projections showing the distribution of alignment directions in the initial state of a comparative example, and projections showing the distribution of alignment directions when the convergence condition is satisfied, respectively. DETAILED DESCRIPTION OF THE INVENTION

[0022] Next, an embodiment of the present invention will be described with reference to the drawings. To facilitate understanding of the description, the same reference numerals are used to designate the same components in the drawings, and duplicated descriptions will be omitted.

[0023] [principle] In systems with many degrees of freedom, the RMC method can obtain approximate solutions more efficiently than a full search by appropriately sampling. However, when applying RMC calculations to estimate the crystal orientation distribution of polymeric materials, the Metropolis method takes a long time to reach equilibrium due to the large number of degrees of freedom and the large amount of calculation required to change each degree of freedom. As a result, it cannot be used in cases where analytical results for a large number of samples must be obtained quickly.

[0024] The inventors noticed that many of the samples used in the development of polymeric materials have a relatively high degree of orientation. They found that when estimating the orientation distribution of such samples using the RMC method, the initial value can be shortened by estimating the orientation direction in which as many crystallites as possible of the sample are likely to be oriented from a measured two-dimensional diffraction image, rather than using a random orientation distribution, and starting the calculation using this as the initial value.

[0025] That is, the method of the present invention is a method of detecting the crystallite orientation with the smallest potential in a structural model in which all crystallites are assumed to be oriented in the same direction, and then performing the RMC method using this as the initial value. The orientation distribution obtained from such initial values is more likely to avoid local minima for samples with a relatively high degree of orientation, increasing the likelihood that the crystal orientation distribution of the sample can be estimated with high accuracy. Furthermore, since the initial value estimation method of the present invention obtains results similar to those of the RMC method in which all crystallites are restricted to the same direction, it is considered to be a suitable initial value estimation method for estimating initial values before performing the RMC method. The method of calculating the initial crystallite orientation and the orientation distribution of the present invention will be described in detail in the embodiments.

[0026] [Embodiment] [Overall system] FIG. 1 is a conceptual diagram showing an example of the configuration of a computing system 100 of the present invention. The computing system 100 includes an X-ray diffraction apparatus 200, a control device 300, and a computing device 400. The X-ray diffraction apparatus 200 forms an optical system that irradiates X-rays onto a sample and detects diffracted X-rays generated from the sample, and the optical system includes a goniometer. Note that the configuration shown in FIG. 1 is just one example, and various other configurations can be adopted.

[0027] 1, the control device 300 and the calculation device 400 are shown as the same PC. However, as will be described below, the method of the present invention can acquire a two-dimensional diffraction image, calculate the crystallite orientation, and calculate a post-calculation structural model independently of the X-ray diffraction device 200 and the control device 300, and therefore the calculation device 400 may be configured as a device different from the control device 300. The following describes the case where the control device 300 and the calculation device 400 are configured as different devices.

[0028] [X-ray diffractometer] The X-ray diffraction instrument 200 includes at least an X-ray generation unit 210 that generates X-rays from an X-ray focus, i.e., an X-ray source, a sample stage 240 on which a sample is placed and that controls the rotation of the sample, and a detector 260 that detects the X-rays. The X-ray diffraction instrument 200 may also include an incident-side optical unit 220, a goniometer 230, or an exit-side optical unit 250. The X-ray generation unit 210, incident-side optical unit 220, goniometer 230, sample stage 240, exit-side optical unit 250, and detector 260 that configure the X-ray diffraction instrument 200 may be general components, and detailed description thereof will be omitted.

[0029] The wavelength of the X-ray source of the X-ray generating unit 210 may be one used in general diffraction measurements, such as CuKα rays or MoKα rays. The X-rays generated from the X-ray source are irradiated onto the sample in a point-like irradiation field, and the generated diffracted X-rays are detected by the detector 260 (two-dimensional detector). Methods for creating a point-like irradiation field include a slit, a collimator, a mirror, and a polycapillary.

[0030] [Control device] The control device 300 is connected to the X-ray diffraction device 200 and controls the X-ray diffraction device 200 and processes, stores, and displays acquired data. In the calculation system 100, if the calculation device 400 does not create a pre-calculation structural model or calculate a post-calculation structural model, the control device 300 or another device (e.g., a structural model creation device) may have the function of creating a pre-calculation structural model or calculating a post-calculation structural model.

[0031] The control device 300 is configured by a computer having a CPU (Central Processing Unit), ROM (Read Only Memory), RAM (Random Access Memory), 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 device, but also some of the devices or some functions within the devices may be provided on the cloud.

[0032] 2 is a block diagram showing an example of the configuration of the control device 300. The control device 300 includes a control unit 310, a device information storage unit 320, a measurement data storage unit 330, and a display unit 340. Each unit can send and receive information via a control bus L. An input device 510 and a display unit 520 are connected to the CPU of the control device 300 via an appropriate interface. The input device 510 is, for example, a keyboard or a mouse, and performs input to the control device 300. The display unit 520 is, for example, a display, and displays measurement data, a measured two-dimensional diffraction image, crystal structure data of the sample, a two-dimensional diffraction image calculated from an initial structure model, etc.

[0033] The control unit 310 controls the operation of the X-ray diffraction apparatus 200. The apparatus information storage unit 320 stores apparatus information acquired from the X-ray diffraction apparatus 200. The apparatus information may include information about the X-ray diffraction apparatus 200, such as the apparatus name, type of radiation source, wavelength, background, etc.

[0034] The measurement data storage unit 330 stores measurement data including two-dimensional diffraction images acquired from the X-ray diffraction instrument 200. Along with the measurement data, necessary information may be stored, including information about the X-ray diffraction instrument 200, such as the type of radiation source, wavelength, and background, as well as the crystal structure data, shape, arrangement, types of constituent elements, composition, and absorption coefficient of the sample. The display unit 340 displays the measurement data, the actually measured two-dimensional diffraction image, the crystal structure data of the sample, or the two-dimensional diffraction image calculated from the initial structure model on the display device 520. This allows the user to confirm the measurement data, etc. Furthermore, the user can issue instructions and specifications to the control device 300, the computing device 400, etc. based on the measurement data, etc.

[0035] [Computing device] The calculation device 400 calculates a structural model of a polymer. The calculation device 400 is configured by a computer having a CPU, ROM, RAM, and memory connected to a bus. The calculation device 400 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 functions within the device may be provided on the cloud. The calculation device 400 may be connected to the X-ray diffraction device 200 via the control device 300, for example.

[0036] 3 is a block diagram showing an example of the configuration of a computing device 400. The computing device 400 includes a data acquisition unit 410, an initial structure model creation unit 420, a crystallite orientation calculation unit 430, and a storage unit 440. Each unit can send and receive information via a control bus L.

[0037] The input device 510 and the display device 520 are connected to the CPU of the calculation device 400 via an appropriate interface. In this case, the input device 510 and the display device 520 may be different from those connected to the control device 300. The input device 510 is, for example, a keyboard or a mouse, and performs input to the calculation device 400. The display device 520 is, for example, a display, and displays measurement data, a measured two-dimensional diffraction image, an initial structure model or a two-dimensional diffraction image calculated from the structure model, crystal structure data, the initial structure model, the crystallite orientation, a pre-calculation structure model, or a post-calculation structure model, etc.

[0038] The data acquisition unit 410 acquires two-dimensional diffraction images and crystal structure data. The crystal structure data includes the types and atomic coordinates of atoms in the crystallite, the orientation of the crystallite, and crystal structure parameters (unit cell, temperature factor, etc.).

[0039] The two-dimensional diffraction image acquired by the data acquisition unit 410 from the X-ray diffraction instrument 200, the control device 300, or another device may be only a measured two-dimensional diffraction image. When the two-dimensional diffraction image acquired by the data acquisition unit 410 from the control device 300 or the X-ray diffraction instrument 200 is only a measured two-dimensional diffraction image, the initial structure model creation unit 420 calculates the two-dimensional diffraction image from the created initial structure model. In this case, the data acquisition unit 410 acquires the two-dimensional diffraction image calculated from the initial structure model (also referred to as the two-dimensional diffraction image corresponding to the initial structure model) from the initial structure model creation unit 420.

[0040] The two-dimensional diffraction image acquired by the data acquisition unit 410 may include a measured two-dimensional diffraction image and a two-dimensional diffraction image corresponding to an initial structure model. For example, if crystal structure data and two-dimensional diffraction images corresponding to an initial structure model are stored in a database or the like, a two-dimensional diffraction image corresponding to the initial structure model may be acquired.

[0041] The initial structure model creation unit 420 creates an initial structure model including one crystallite. When the three-dimensional orientation is fixed, the initial structure model is a structure model including one crystallite, but it may also be a structure model in which the orientation of multiple crystallites is the same. However, the initial structure model is used to calculate a two-dimensional diffraction image corresponding to the orientation of one crystallite for comparison with the measured two-dimensional diffraction image, and even if the orientation of multiple crystallites is the same, the diffraction intensity of the calculated two-dimensional diffraction image will only be increased, so it is simpler and preferable to include only one crystallite.

[0042] The crystallite orientation calculation unit 430 calculates the orientation of the crystallite. The crystallite orientation calculation unit 430 may calculate the size of the crystallite in addition to the orientation of the crystallite. The orientation or size of the crystallite is calculated based on a two-dimensional diffraction image calculated from the initial structure model and a measured two-dimensional diffraction image. By calculating the size of the crystallite based on the two-dimensional diffraction image calculated from the initial structure model and a measured two-dimensional diffraction image, the initial value of the size of the crystallite can be estimated.

[0043] The diffraction intensity of a two-dimensional diffraction image calculated from an initial structure model is calculated from the crystallite orientation and crystal structure data. This method involves, for example, calculating the diffraction intensity in reciprocal space from the crystal structure. Next, the intensity distribution in reciprocal space is rotated to correspond to the crystallite orientation, and the intensity on the Ewald sphere is calculated. In this way, the diffraction intensity of a two-dimensional diffraction image corresponding to the initial structure model can be calculated. A known crystal structure can be used as the crystal structure data. The crystallite size may also be obtained from the actually measured diffraction width.

[0044] To calculate the diffraction intensity of a two-dimensional diffraction image from an initial structure model or a structural model, it is generally necessary to know the specific atomic coordinates of the crystal. However, in reality, the crystal structure may be unknown. In such cases, determining the atomic coordinates is necessary, but adjusting individual atomic coordinates to find the optimal coordinates is difficult due to the large number of diffraction points in a two-dimensional diffraction image of a polymer. Therefore, as a preliminary step to determining the precise crystal structure, a method such as replacing the polymer with a cylindrical electron density and placing it within a unit lattice is considered. Figure 4 is a schematic diagram showing a polymer replaced with a cylindrical electron density and placed within a unit lattice. In the example of Figure 4, the cylindrical electron density distribution within the unit lattice is used as the initial structure model or structural model instead of the atomic coordinates of the polymer to calculate the diffraction intensity of the two-dimensional diffraction image. Note that the shape of the electron density replacement is not limited to a cylindrical shape; any method that allows for coarse graining is acceptable. For example, various shapes are possible, such as polygonal columns, cylinders, polygonal tubes, plates, wires, spheres, and ellipsoids. These shapes may also be used in combination.

[0045] Using this method, it is possible to calculate two-dimensional diffraction patterns using approximate electron density distributions. Furthermore, RMC analysis can be performed using the lattice constant of the unit cell as a parameter in addition to the crystallite orientation distribution, allowing for a rough estimation of the lattice constant. This is just the first step, and the structure can be refined by adding more parameters, for example, by applying a periodic density distribution along a cylinder to reproduce the fiber period.

[0046] The crystallite orientation is preferably a three-dimensional vector. The three-dimensional vector indicating the crystallite orientation includes the Euler angle representation. FIG. 5 is a schematic diagram showing an example of the crystallite orientation. FIG. 5 shows the orientation of one crystallite expressed as Euler angles (θ1, θ2, θ3) in coordinates fixed to the sample. Note that 0°≦θ1<360°, 0°≦θ2<180°, and 0°≦θ3<360°. The three-dimensional vector indicating the crystallite orientation may be expressed in a manner other than Euler angles. When the crystallite orientation is a three-dimensional vector, the orientation distribution of the structural model described below is expressed as a set of three-dimensional vectors equal to the number of crystallites. The correlation between the positions of the crystallites need not be considered. When uniaxial symmetry of the sample is assumed, the orientation may be expressed as a two-dimensional vector by taking a rotational average around the axis.

[0047] The crystallite orientation calculation unit 430 preferably calculates the degree of agreement between two-dimensional diffraction images calculated from multiple initial structure models corresponding to multiple directions of a single crystallite and the measured two-dimensional diffraction image, and calculates the crystallite orientation based on the calculated degree of agreement. The calculated crystallite orientation may be the direction with the best degree of agreement among the respective degrees of agreement, or may be two directions: the direction with the best degree of agreement and the direction with the second best degree of agreement. When two crystallite orientations are calculated, the crystallite orientations in the pre-calculation structure model described below may be arranged, for example, half in the best direction and half in the second best direction, but it is preferable to arrange them in a ratio based on the intensity ratio of each two-dimensional diffraction image and the degree of agreement value.

[0048] When a sample has uniaxial orientation, there may be little difference in the degree of coincidence between multiple crystallites with the same axis direction and different axes direction, making it impossible to determine one or two directions with the best degree of coincidence. In such cases, the direction of the identical axis may be determined as the crystallite direction, and the directions of the remaining axes may be random. That is, the crystallite direction calculated based on the degree of coincidence may include cases where one or two axes are fixed and the remaining axes are random. Note that the above-mentioned axes are not limited to the actual axes of the crystallite. Furthermore, when the crystallite direction is expressed as a three-dimensional vector, the crystallite direction calculated based on the degree of coincidence may include cases where one or two values of the three-dimensional vector are restricted and the remaining value is random, as well as cases where the ratio of the two values is restricted and the remaining value is random. When the crystallite direction is expressed as an Euler angle, the crystallite direction calculated based on the degree of coincidence may include cases where the values of certain Euler angles are restricted and the values of the remaining Euler angles are random.

[0049] The multiple directions of a single crystallite refer to different directions of the crystallite. For example, when the direction of a crystallite is expressed by Euler angles (θ1, θ2, θ3), the multiple directions of a single crystallite are expressed by a combination of different Euler angles (θ1, θ2, θ3). The multiple directions of a single crystallite preferably include all possible combinations depending on the resolution of the X-ray diffraction device 200. For example, if the resolution of the X-ray diffraction device 200 is 0.5°, the possible combinations are θ1 = 0.5l (l = 0, 1, ... , 719), θ2 = 0.5m (m = 0, 1, ... , 359), and θ3 = 0.5n (n = 0, 1, ... , 719).

[0050] Various methods can be used to calculate the degree of coincidence between multiple two-dimensional diffraction images calculated from multiple initial structure models corresponding to multiple directions of one crystallite and a measured two-dimensional diffraction image, and to calculate the crystallite direction based on the calculated degree of coincidence. For example, if the sum of squares of the intensity difference between a two-dimensional diffraction image calculated from a certain initial structure model and a measured two-dimensional diffraction image is used as the degree of coincidence (deviation) of the initial structure model, the crystallite direction corresponding to the initial structure model with a smaller value can be calculated as the initial value. Generally, the degree of coincidence is a criterion that indicates that a larger value is better, and the degree of deviation is a criterion that indicates that a smaller value is better. However, in this specification, the term "degree of coincidence" also includes the degree of deviation.

[0051] The fitness between the two-dimensional diffraction image calculated from the initial structural model and the measured two-dimensional diffraction image can be calculated using, for example, the following formula (1): x ,q y : Position on WAXD image, I obsd : Measured intensity, I calcd : calculated intensity, a: scaling coefficient calculated by the least squares method. Formula (1) is a criterion for determining that a smaller fitness is better. Note that the formula for calculating the degree of agreement between the two-dimensional diffraction image calculated from the initial structure model and the measured two-dimensional diffraction image is not limited to Formula (1).

[0052]

number

[0053] The storage unit 440 stores necessary items among the data acquired by the data acquisition unit 410, the initial structure model created by the initial structure model creation unit 420, the diffraction intensity of the two-dimensional diffraction image corresponding to the initial structure model, the multiple coincidence values calculated by the crystallite orientation calculation unit 430, the crystallite orientation, the pre-calculation structure model created by the pre-calculation structure model creation unit 450 described below, the structure model changed by the calculation execution unit 460, the created post-calculation structure model, etc. The storage unit 440 also stores necessary items among the initial structure model or a formula for calculating the diffraction intensity of the two-dimensional diffraction image from the structure model, a formula for calculating the coincidence between the initial structure model or the two-dimensional diffraction image calculated from the structure model and the actually measured two-dimensional diffraction image, and numerical values, conditions, etc. for calculating these.

[0054] To clarify the three-dimensional orientation, it is necessary to calculate the orientation direction from multiple two-dimensional diffraction images. Therefore, to estimate the initial value of the orientation direction to be set in the initial structure model, specialized knowledge of polymer materials and diffraction methods is usually required. However, by using the method of the present invention, the initial value can be estimated automatically, eliminating the need for specialized knowledge.

[0055] 6 is a block diagram showing a modified example of the configuration of the calculation device 400. As shown in FIG. 6, the calculation device 400 preferably includes a pre-calculation structural model creation unit 450 and a calculation execution unit 460.

[0056] The pre-calculation structural model creation unit 450 creates a pre-calculation structural model in which the orientations of the multiple crystallites are the same for a structural model having multiple crystallites. In this specification, "structural model" refers to a model having multiple crystallites. Furthermore, in a pre-calculation structural model, the orientations of multiple crystallites being the same refers to the orientations of the crystallites calculated by the crystallite orientation calculation unit 430 being the same. In other words, the orientations of the multiple crystallites in the pre-calculation structural model include cases in which one or two axes are fixed and the remaining axes are random. The pre-calculation structural model creation unit 450 sets the number of crystallites in the RMC method. Since the number of crystallites is in a trade-off relationship between the calculation accuracy of the orientation distribution that can be calculated from the post-calculation structural model and the calculation time, it is preferable to set an appropriate number of crystallites depending on the desired calculation accuracy. The pre-calculation structural model creation unit 450 may set the number of crystallites based on values such as the calculation time specified by the user.

[0057] When the crystallite orientation calculation unit 430 calculates the orientation of two crystallites as initial values, the pre-calculation structural model created by the pre-calculation structural model creation unit 450 may be a structural model in which the orientation of multiple crystallites is one of the two crystallite orientations. Such a pre-calculation structural model is also included in the pre-calculation structural model in which the orientation of multiple crystallites is the same direction. In this case, the orientation of one or two crystallites may include a case in which one or two axes are fixed and the remaining axes are random.

[0058] The calculation execution unit 460 changes the structural model based on the degree of agreement between the two-dimensional diffraction image calculated from the structural model and the measured two-dimensional diffraction image. Furthermore, the calculation execution unit 460 uses the pre-calculation structural model as an initial value and calculates a post-calculation structural model whose degree of agreement satisfies the convergence condition. This results in a post-calculation structural model that incorporates the orientation of crystallites likely to be contained in the sample, and the measured two-dimensional diffraction image can be explained using such a post-calculation structural model.

[0059] Various conditions can be set as the convergence condition. For example, the formula for determining the convergence condition may directly use the formula for calculating the degree of match, or another formula using a series of values of the degree of match calculated from the formula may be used. For example, the convergence condition may be determined to be met and the process may end when the absolute value of the degree of match becomes equal to or less than a threshold. Alternatively, the convergence condition may be determined to be met and the process may end when the standard deviation of the degree of match over a predetermined number of recent runs is obtained, and the convergence condition is determined to be met and the process may end when the standard deviation becomes equal to or less than a predetermined threshold. Alternatively, the convergence condition may be determined to be met and the process may end when (a) the change in the average degree of match and (b) the standard deviation of the degree of match over a predetermined number of recent runs are obtained, and the ratio of (a) to (b) becomes equal to or less than a predetermined threshold.

[0060] The Geweke method is shown as a specific example of determining convergence by comparing the change in the mean value and the standard deviation. The Geweke method is a method in which convergence is determined when |Z| in the following formula (2) is sufficiently smaller than 1, where G1 is the mean value of the first 10% of the sample, G2 is the mean value of the last 50% of the sample, V1 is the variance of the first 10% of the sample, and V2 is the variance of the last 50% of the sample. In this case, the sample can be, for example, a series of values of the degree of similarity calculated using a formula for calculating the degree of similarity.

[0061]

number

[0062] The calculation execution unit 460 preferably calculates the post-calculation structural model using the RMC method. The RMC method is a method of estimating a structural model that reproduces actual measured values by changing the atomic positions and crystallite orientations of a given structural model using random numbers. The RMC method generally has a wide search space and can obtain a global minimum solution, making it effective as a method for solving complex optimization problems. When the RMC method is applied to the present invention, the post-calculation structural model is calculated using a pre-calculation structural model with consistent crystallite orientations as the initial value, thereby reducing the risk of the post-calculation structural model becoming a local minimum. An evolutionary algorithm may also be used as the optimization method.

[0063] Various methods can be used to calculate a two-dimensional diffraction pattern from a structural model. For example, the intensity of a two-dimensional diffraction pattern can be calculated from the orientation of one crystallite in the structural model and the crystal structure data, and then the two-dimensional diffraction patterns can be calculated from the structural model by superimposing the two-dimensional diffraction patterns for all crystallites.

[0064] The pre-calculation structural model creation unit 450 preferably selectively creates either the pre-calculation structural model or a second pre-calculation structural model in which the orientations of multiple crystallites are randomly arranged relative to the structural model. The second pre-calculation structural model is a structural model in which all values of the orientations of multiple crystallites are randomly arranged. In this case, the calculation execution unit 460 calculates the post-calculation structural model using either the pre-calculation structural model or the second pre-calculation structural model as an initial value.

[0065] As a result, for samples considered to have a high degree of orientation, a pre-calculation structural model in which the orientation of multiple crystallites is in the same direction can be used as the initial value to calculate the post-calculation structural model. For samples considered to have a low degree of orientation, a second pre-calculation structural model in which the orientation of multiple crystallites is randomly arranged can be used as the initial value to calculate the post-calculation structural model. As a result, the time required to calculate the post-calculation structural model can be reduced for both samples considered to have a high degree of orientation and samples considered to have a low degree of orientation.

[0066] The selection of the pre-calculation structure model or the second pre-calculation structure model may be performed by a user instruction. Alternatively, the selection of the pre-calculation structure model or the second pre-calculation structure model may be determined by the calculation device 400 based on the numerical value of the degree of agreement between the two-dimensional diffraction image calculated from the initial structure model and the measured two-dimensional diffraction image. For example, the degree of agreement between the two-dimensional diffraction image calculated from multiple initial structure models corresponding to multiple directions of a single crystallite and the measured two-dimensional diffraction image may be calculated, and if there is no crystallite direction determined to have a sufficiently high degree of agreement, the second pre-calculation structure model may be selected.

[0067] Fig. 7 is a block diagram showing a modified example of the configuration of the calculation device 400. As shown in Fig. 7, the calculation device 400 preferably includes a crystalline component extraction unit 415. In Fig. 7, the calculation device 400 further includes a pre-calculation structural model creation unit 450 and a calculation execution unit 460, but the configuration of Fig. 3 may also include the crystalline component extraction unit 415.

[0068] The crystalline component extraction unit 415 extracts the crystalline components from the measured two-dimensional diffraction image. When the calculation device 400 includes the crystalline component extraction unit 415, the crystallite orientation calculation unit 430 calculates the crystallite orientation using the extracted crystalline components from the measured two-dimensional diffraction image. This makes the calculated crystallite orientation less susceptible to the influence of the amorphous components from the measured two-dimensional diffraction image.

[0069] Extraction of crystalline components from measured 2D diffraction patterns can be performed in various ways. For example, crystalline peaks are extracted from a known crystal structure to estimate the crystalline regions. Next, the amorphous components at the positions of the crystalline regions are determined by interpolation, and the crystalline components can be extracted by subtracting them from the measured 2D diffraction pattern. Figures 8(a) to 8(d) are schematic diagrams of 2D diffraction patterns showing one step in an example of extracting crystalline components from measured 2D diffraction patterns. Figures 8(a) to 8(d) respectively show the measured 2D diffraction pattern, the estimated crystalline regions, the extracted crystalline components, and the remaining amorphous components. Figure 8(b) shows the estimated crystalline regions overlaid in a gray annular shape on the measured 2D diffraction image (Figure 8(a)).

[0070] The computational device 400 of the present invention can calculate a two-dimensional diffraction pattern for a specified orientation distribution. Using this function, two-dimensional diffraction patterns for various orientation distributions can be prepared. By performing supervised learning using two-dimensional diffraction patterns as input data and corresponding orientation distributions as output, it is believed that orientation distributions can be obtained from two-dimensional diffraction patterns without using time-consuming analyses such as RMC analysis.

[0071] [Measurement method] A sample is placed in the X-ray diffraction instrument 200, and under the control of the control device 300, X-rays are incident on the sample and diffracted X-rays generated from the sample are detected. If necessary, the sample stage or goniometer is driven under specified conditions. This allows a measured two-dimensional diffraction image to be acquired. The X-ray diffraction instrument 200 transmits the instrument information and the acquired two-dimensional diffraction image to the control device 300 as measurement data. Using this measurement data, the calculation device 400 or calculation method of the present invention can be used to calculate the crystallite orientation or to calculate a post-calculation structural model that explains the measured two-dimensional diffraction image.

[0072] [Calculation method for crystallite orientation] (Explanation of the flow to calculate the crystallite orientation) FIG. 9 is a flowchart showing an example of the operation of the calculation device 400. FIG. 9 shows an example of the operation up to calculating the crystallite orientation based on a measured two-dimensional diffraction image. First, the calculation device 400 acquires two-dimensional diffraction image and crystal structure data (step S1). Next, an initial structure model including one crystallite is created (step S2). Next, a two-dimensional diffraction image is calculated from the initial structure model (step S3). Then, the crystallite orientation is calculated (step S4), and the process ends. The crystallite orientation is calculated based on the two-dimensional diffraction image calculated from the initial structure model and the measured two-dimensional diffraction image. The crystallite orientation is preferably calculated by calculating the degree of agreement between two-dimensional diffraction images calculated from multiple initial structure models corresponding to multiple orientations of one crystallite and the measured two-dimensional diffraction image, and then calculating the crystallite orientation based on the calculated degree of agreement. If necessary, the calculated crystallite orientation or a two-dimensional diffraction image corresponding to the crystallite orientation may be output. In this way, the crystallite orientation can be easily and automatically calculated from the measured two-dimensional diffraction image and crystal structure data.

[0073] In this flow, a two-dimensional diffraction image is calculated from an initial structure model. However, it is not necessary to calculate a two-dimensional diffraction image from an initial structure model; multiple types of initial structure models and their corresponding two-dimensional diffraction images may be obtained in advance. In this case, the step of calculating a two-dimensional diffraction image from an initial structure model does not need to be performed. The same applies to the subsequent flowcharts.

[0074] (Explanation of the flow up to calculating the post-calculation structural model 1) Fig. 10 is a flowchart showing a modified example of the operation of the calculation device 400. Fig. 10 shows an example of the operation up to the calculation of the post-calculation structural model. In the following explanation of the flowchart, characteristic operations will be explained in detail, and explanation of operations that have already been explained may be omitted. The process from obtaining the two-dimensional diffraction image and crystal structure data (step T1) to calculating the crystallite orientation (step T4) is the same as steps S1 to S4 above.

[0075] Next, the calculation device 400 creates a pre-calculation structure model (step T5). The pre-calculation structure model is a structure model having multiple crystallites, all of which are oriented in the calculated direction of one or two crystallites. Next, the direction of each crystallite in the pre-calculation structure model is changed using a predetermined method (step T6). Next, a two-dimensional diffraction image is calculated from the changed pre-calculation structure model (step T7). Next, the degree of agreement between the measured two-dimensional diffraction image and the two-dimensional diffraction image calculated from the changed pre-calculation structure model is calculated (step T8). If the calculated degree of agreement does not satisfy the convergence condition (step T9-NO), the process returns to step T6 and repeats the process up to step T9.

[0076] On the other hand, if the calculated degree of coincidence satisfies the convergence condition (step T9-YES), a calculated structural model is determined (step T10) and the process ends. If necessary, the determined calculated structural model or a two-dimensional diffraction image corresponding to the calculated structural model may be output. In this way, the calculated structural model can be calculated using the measured two-dimensional diffraction image and the crystallite orientation calculated from the crystal structure data.

[0077] (Explanation of the flow up to calculating the post-calculation structural model 2) FIG. 11 is a flowchart showing a modified example of the operation of the calculation device 400. FIG. 11 shows a modified example of the operation up to the calculation of the post-calculation structural model. Except for the step of extracting crystalline components from the measured two-dimensional diffraction image (step U2), the steps are the same as steps T1 to T10 described above. In this case, the measured two-dimensional diffraction image used as the reference for calculating the degree of coincidence is the two-dimensional diffraction image from which the crystalline components have been extracted. This prevents the direction of the crystallites from being affected by the amorphous components of the measured two-dimensional diffraction image.

[0078] [Example] Using the calculation system 100 configured as described above, a WAXD image of a high-density polyethylene (HDPE) sample was measured. Next, using this, the orientation of one crystallite was estimated using the method of the present invention, and the orientation distribution of the HDPE sample was calculated using this as the initial value (Example). Because the HDPE sample has a uniaxial orientation, in the Example, the direction of one crystallite was estimated as the Euler angle θ = 15°. Therefore, θ = 15° was limited, and the remaining values were randomized to use the initial value. On the other hand, without using the method of the present invention, the orientation distribution of the HDPE sample was calculated using a general RMC method from an initial value in which the orientation of each crystallite was random (Comparative Example). Figures 12(a) to 12(c) are schematic diagrams showing the measured 2D diffraction image of the HDPE sample, the 2D diffraction image of the calculated structural model of the Example, and the 2D diffraction image of the structural model of the Comparative Example, respectively. Note that Figure 12(a) shows the measured WAXD image with the amorphous component removed.

[0079] Figure 13 is a graph showing the changes in Fitness for the Example and Comparative Example. Fitness (degree of coincidence) was calculated using Equation (1), and the convergence condition was determined when Fitness reached 0.05 or less. In other words, in this Example and Comparative Example, the convergence condition was determined directly using the equation for calculating degree of coincidence. The graph in Figure 13 shows that it took approximately 2.5 seconds per step. In the Comparative Example, it took 5,000 steps and 12,500 seconds to satisfy the convergence condition. In contrast, in the Example, it only took 50 steps and 125 seconds to satisfy the convergence condition. The initial Fitness value for the Example was 0.633, and the final value was 0.026. On the other hand, the initial Fitness value for the Comparative Example was 0.866, and the final value was 0.041. This indicates that for samples with a high degree of orientation, the method of the present invention converges approximately two orders of magnitude faster than the conventional method.

[0080] Figures 14(a) and 14(b) are projections showing the initial orientation distribution of the Example and the orientation distribution when the convergence conditions are met, respectively. Figures 15(a) and 15(b) are projections showing the initial orientation distribution of the Comparative Example and the orientation distribution when the convergence conditions are met, respectively. In both cases, the orientation direction (c-axis direction) is represented by a point on a sphere, and the orientation distribution is displayed as a projection in the stretching direction. Figures 14 and 15 show examples of analysis of a uniaxially oriented sample. As mentioned above, the initial value of the crystallite orientation in Figure 14(a) is θ2 = 15°, and θ1 and θ3 are not restricted. Since there is no restriction on θ1, a circular projection is obtained. In the Comparative Example, because the sample starts from a random state, when the convergence conditions are met, a distribution of orientations that varies off the center occurs, resulting in an orientation that reaches a local minimum.

[0081] From the above results, it was confirmed that the calculation device, method, and program of the present invention can easily estimate the orientation from a two-dimensional diffraction image. Furthermore, it was confirmed that by performing a simulation using the RMC method with the estimated orientation as the initial state, the amount of calculation can be reduced and a global optimal solution can be obtained.

[0082] It goes without saying that the present invention is not limited to the above-described embodiments. The scope of the present invention extends to various modifications and equivalents that fall within the technical spirit of the present invention. Furthermore, the names, structures, shapes, numbers, positions, sizes, etc. of the components shown in each drawing are for the convenience of explanation and may be changed as appropriate. [Explanation of symbols]

[0083] 100 Computing Systems 200 X-ray Diffractometer 210 X-ray generator 220 Incident optical unit 230 Goniometer 240 Sample stage 250 Output optical unit 260 detector 300 control device 310 Control Unit 320 Device information storage unit 330 Measurement data storage unit 340 Display section 400 Computing equipment 410 Data Acquisition Unit 415 Crystalline component extraction section 420 Initial structural model creation section 430 Crystallite Orientation Calculation Unit 440 Storage section 450 Pre-calculation structural model creation section 460 Calculation Execution Unit 510 Input Device 520 Display device

Claims

1. A computing device for calculating a structural model of a polymer, a data acquisition unit for acquiring two-dimensional diffraction images and crystal structure data; an initial structure model creation unit that creates an initial structure model including one crystallite; a crystallite orientation calculation unit for calculating the orientation of the crystallite, The calculation device is characterized in that the crystallite orientation is calculated based on the two-dimensional diffraction image calculated from the initial structure model and the two-dimensional diffraction image that is actually measured.

2. The calculation device according to claim 1, characterized in that the crystallite orientation calculation unit calculates a degree of agreement between a two-dimensional diffraction image calculated from a plurality of the initial structure models corresponding to a plurality of orientations of the one crystallite and the measured two-dimensional diffraction image, and calculates the orientation of the crystallite based on the calculated degree of agreement.

3. a pre-calculation structural model creation unit that creates a pre-calculation structural model for the structural model having a plurality of crystallites, in which the orientations of the plurality of crystallites are the same; a calculation execution unit that changes the structural model based on a degree of agreement between a two-dimensional diffraction image calculated from the structural model and the actually measured two-dimensional diffraction image, 3. The computing device according to claim 1, wherein the calculation execution unit calculates a post-calculation structural model whose degree of coincidence satisfies a convergence condition, using the pre-calculation structural model as an initial value.

4. further comprising a crystalline component extraction unit that extracts crystalline components from the measured two-dimensional diffraction image; 3. The calculation device according to claim 1, wherein the crystallite orientation calculation unit calculates the orientation of the crystallite using the crystalline component of the measured two-dimensional diffraction image.

5. 3. The calculation device according to claim 1, wherein the crystallite direction is a three-dimensional vector.

6. The computing device according to claim 3 , wherein the computation execution unit computes the post-computation structural model using an RMC method.

7. the pre-calculation structural model creation unit selectively creates either the pre-calculation structural model or a second pre-calculation structural model in which the orientations of the plurality of crystallites are randomly arranged relative to the structural model; 4. The computing device according to claim 3, wherein the calculation execution unit calculates the post-calculation structural model using either the pre-calculation structural model or the second pre-calculation structural model as an initial value.

8. an X-ray diffraction apparatus including an X-ray generating unit that generates X-rays, a detector that detects X-rays, and a sample stage that controls the rotation of a sample; A system comprising: a computing device according to claim 1 or claim 2.

9. 1. A method for calculating a structural model of a polymer, comprising: acquiring two-dimensional diffraction images and crystal structure data; creating an initial structural model including one crystallite; and calculating the orientation of the crystallites; a step of calculating the orientation of the crystallites, the orientation of the crystallites being calculated based on the two-dimensional diffraction image calculated from the initial structure model and the two-dimensional diffraction image measured.

10. A program for calculating a structural model of a polymer, obtaining two-dimensional diffraction images and crystal structure data; A process of creating an initial structure model including one crystallite; and calculating the orientation of the crystallites. a program for calculating the orientation of the crystallites based on the two-dimensional diffraction image calculated from the initial structure model and the two-dimensional diffraction image measured in real time, in the process of calculating the orientation of the crystallites.

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