A method for computing simulation of two-dimensional small-angle x-ray scattering patterns of orientation systems

Abstract

The application relates to the field of substance structure detection and small-angle scattering simulation, and provides a two-dimensional small-angle X-ray scattering pattern calculation simulation method for an orientation system. The method controls the geometric shape of a scattering body through a super-ellipsoid model, combines a Log-normal distribution to describe a three-dimensional size distribution, and uses a Von Mises distribution and a uniform distribution to respectively represent zenith angle preferred orientation and azimuth angle distribution; two-dimensional Fourier transformation is performed on shape representation data, scattering intensity at each position of a detection plane is calculated in combination with a scattering intensity model, and a simulation pattern is generated through ensemble averaging. The method can reproduce typical scattering characteristics such as "butterfly shape" and "X shape", is suitable for a sparse system with a length-diameter ratio of 0.1-100, and provides simulation support for microstructure analysis of an orientation system such as a high-performance fiber and a polymer composite.

Description

Technical Field

[0001] This invention relates to the field of material structure detection and small-angle scattering simulation, and more specifically, to a method for calculating and simulating two-dimensional small-angle X-ray scattering patterns of oriented systems. Background Technology

[0002] Small-angle X-ray scattering (SAXS) is a commonly used technique for characterizing the nanoscale microstructure of materials, and is particularly suitable for defect detection, grain orientation analysis, and structural evolution studies of oriented systems such as fibers and thin films. By analyzing the azimuth distribution and intensity attenuation of the scattering pattern, microstructural information such as the size, shape, and orientation of the scatterer can be obtained.

[0003] However, existing two-dimensional small-angle X-ray scattering simulation methods have the following shortcomings.

[0004] First, there are limitations in adaptability to oriented systems. Traditional methods are mostly based on isotropic systems and do not fully consider the preferred orientation distribution characteristics of the scatterers. For systems with obvious preferred orientations, such as fibers, the scatterers exhibit a certain degree of concentrated distribution around the fiber axis, resulting in characteristic anisotropy in their scattering patterns. Existing methods struggle to reproduce typical orientation scattering features such as "butterfly" and "X" shapes, thus limiting their application in the microstructure analysis of oriented systems.

[0005] Second, the methods for representing the shape of scatterers are relatively limited. Existing methods mostly use regular geometric models such as ellipsoids or cylinders, which can only describe a limited range of geometric shapes. For scatterers with complex geometric features, such as pinhole-like pores, irregular grain boundary defects, nanorods, and nanosheets that actually exist within fibers, a single model cannot provide an accurate shape description, which means that the agreement between simulation results and experimental data needs to be improved.

[0006] Third, the accuracy of quantitative analysis results needs improvement. Due to simplifications in orientation description and shape characterization, there are significant discrepancies between the theoretical patterns generated by existing simulation methods and experimentally measured patterns, making it difficult to provide reliable simulation support for quantitative analyses such as orientation parameter calculation and size distribution statistics. Therefore, a two-dimensional small-angle X-ray scattering pattern calculation and simulation method for orientation systems is proposed to address the above problems. Summary of the Invention

[0007] To overcome the aforementioned deficiencies of the prior art, embodiments of the present invention provide a method for calculating and simulating two-dimensional small-angle X-ray scattering patterns in an orientation system. This method aims to address the limitations in adaptability to orientation systems and the relatively singular method for characterizing scatterer shapes in the prior art, while also addressing the need to improve the accuracy of quantitative analysis results.

[0008] To achieve the above objectives, this invention provides a method for calculating and simulating two-dimensional small-angle X-ray scattering patterns of an orientation system. By leveraging the synergistic effect of a super ellipsoid model, a Log-normal size distribution function, and a Von Mises orientation distribution function, multi-parameter modeling of the scatterer's shape, size distribution, and orientation characteristics is achieved. Combined with two-dimensional Fourier transform and scattering intensity calculation, a two-dimensional small-angle X-ray scattering simulation pattern of the orientation system is generated.

[0009] This method obtains a super ellipsoidal model of the scatterer and controls the geometry of the scatterer by adjusting the shape parameters.

[0010] The superellipsoid model defines the spatially occupied region of the scatterer using the following equation: when the spatial coordinates satisfy the following inequality, the point is located inside the scatterer: ; in, , , The scatterer is in axis, axis, The characteristic dimension along the axis determines the size of the scatterer in three dimensions; and The shape adjustment parameters are controlled separately. - Planar cross-sectional shape and The axial profile enables a continuous transformation from an ellipsoid to a cube.

[0011] By adjusting and With a single model, various geometric shapes of scatterers can be uniformly described, adapting to the description needs of complex shapes such as pinhole-like pores within fibers, irregular grain boundary defects, and nanoparticles. Specifically: when and When the equation degenerates into a standard ellipsoid, it is suitable for simulating near-spherical or ellipsoidal scatterers; when and When the equation approaches a cuboid, it is suitable for simulating a square scatterer with obvious edges; when and When the equation approaches a cylinder, it is suitable for simulating pinhole-like holes extending along the axial direction.

[0012] In terms of size distribution description, this method determines the characteristic size distribution of the scatterer in three orthogonal directions based on the Log-normal size distribution function.

[0013] The Log-normal size distribution function is: ; in, For the characteristic size variable, corresponding sequentially , , ; The logarithmic mean represents the central location of the size distribution; The standard deviation is the logarithm, which characterizes the width and asymmetry of the size distribution.

[0014] , , Each scatterer independently follows its own defined log-normal distribution, with different logarithmic mean and logarithmic standard deviations set for each direction. The size distribution of the scatterer along the major axis, minor axis, and third dimension can be described separately, thus fitting the case where the scatterer in the actual system has different size polydispersities in different directions.

[0015] In terms of orientation feature description, this method determines the preferred orientation features of the scatterer zenith angle based on the Von Mises orientation distribution function.

[0016] The Von Mises orientation distribution function is: ; in, The zenith angle between the principal axis of the scatterer and the macroscopic preferred principal axis; This represents the orientation average, corresponding to the orientation direction in which the scatterer is most concentrated. The orientation concentration factor determines the degree of concentration of the scatterer around the orientation mean direction; For a first-order zero-order modified Bessel function, the probability density is guaranteed to be within... Interval normalization.

[0017] This distribution is determined by its value. The adjustment achieves a continuous transition from random orientation to highly oriented orientation: when When the distribution degenerates into a uniform distribution, it indicates that the scatterer is completely randomly oriented; when When the distribution approaches the Dirac delta function, it indicates that the scatterer is perfectly oriented.

[0018] Meanwhile, the azimuth distribution of the scatterers is uniform, with the scatterers distributed with equal probability along each azimuth direction in a plane perpendicular to the preferred orientation direction. This setting is compatible with the rotational invariance of the fiber system, meaning that the scattering pattern in the cross-section perpendicular to the fiber axis is rotationally symmetric.

[0019] After completing the multi-parameter modeling, a two-dimensional Fourier transform is performed on the shape characterization data of the scatterer to obtain a two-dimensional complex matrix, thereby converting the geometric information of the scatterer in real space to the reciprocal space.

[0020] The scattering amplitude is calculated based on the two-dimensional complex matrix, and the scattering intensity at each location within the detection plane is obtained by combining this with the scattering intensity calculation model. The scattering intensity calculation model uses: ; in, For scattering intensity, The scattering amplitude is represented by a two-dimensional complex matrix.

[0021] The scatterers are suitable for sparse systems with aspect ratios ranging from 0.1 to 100. In these systems, the distance between the scatterers is greater than their own size, the interference effect between the scatterers is negligible, and the structure factor is low. When the value is 1, the total scattering intensity of the system is approximately the incoherent superposition of the scattering intensities of each scatterer.

[0022] After obtaining the scattering intensity of each scatterer, the contributions of all scatterers are ensemble averaged to generate a two-dimensional small-angle X-ray scattering simulation pattern of the orientation system.

[0023] Thanks to the synergy of the aforementioned multi-parameter models, this method can reproduce the scattering characteristics of typical orientation systems such as "butterfly-shaped," "X-shaped," and "double-spotted" patterns. These characteristic patterns are generated by the combined effect of the preferred orientation distribution and anisotropic shape of the scatterer.

[0024] The pattern can be output as a two-dimensional distribution map of scattering intensity; it can also output one-dimensional scattering curves in the equatorial and meridional directions, as well as orientation parameter analysis results. The equatorial scattering curve reflects the size information perpendicular to the orientation direction, the meridional scattering curve reflects the size information along the orientation direction, and the orientation parameter analysis results are used to quantify the degree of orientation of the scatterer.

[0025] In terms of computational implementation, the two-dimensional Fourier transform utilizes its conjugate symmetry property to obtain the complete transformation result by calculating only half of the complex matrix elements, thus reducing the amount of computation.

[0026] Simultaneously, by combining the parallel acceleration technology of the graphics processing unit (GPU), the Fourier transform and intensity calculation tasks of multiple scatterers can be distributed to multiple computing units of the GPU for simultaneous processing, thereby achieving rapid calculation of large-size, high-precision simulations.

[0027] This application also provides an electronic device, including a memory and a processor. The memory stores a computer program, and the processor executes the computer program to sequentially perform superellipsoidal shape modeling of the scatterer, Log-normal size distribution modeling, Von Mises orientation distribution modeling, two-dimensional Fourier transform and scattering intensity calculation, and ensemble averaging and simulation pattern generation, thereby realizing the above-mentioned method for calculating and simulating two-dimensional small-angle X-ray scattering patterns of the orientation system.

[0028] This application also provides a computer-readable storage medium storing computer-executable instructions thereon. When executed by a processor, these computer-executable instructions cause the processor to perform multi-parameter modeling of the scatterer, Fourier transform and scattering intensity calculation, and simulation pattern generation, thereby realizing the above-mentioned method for calculating and simulating two-dimensional small-angle X-ray scattering patterns of the orientation system.

[0029] The technical effects and advantages of this invention are as follows: First, regarding improving the adaptability of the orientation system, this application introduces the Von Mises orientation distribution function to describe the preferred orientation characteristics of the zenith angle of the scatterer. By adjusting the orientation concentration coefficient κ, it can describe the continuous transition state from completely random orientation to perfect orientation. Simultaneously, a uniform distribution is used to describe the azimuth distribution, adapting to the rotational invariance characteristics of the fiber system. This orientation modeling method enables the reproduction of typical orientation scattering characteristics such as "butterfly-shaped," "X-shaped," and "double-spotted" patterns, showing good agreement with experimentally detected two-dimensional small-angle X-ray scattering spectra, and is adaptable to sparse orientation systems with aspect ratios ranging from 0.1 to 100.

[0030] Secondly, regarding the enrichment of scatterer shape characterization capabilities, this application employs a super ellipsoid model to define the spatially occupied region of the scatterer. By adjusting the shape adjustment parameters e and n, it can uniformly describe various geometric shapes such as cubes, cylinders, ellipsoids, and rhomboids. Compared to a single ellipsoid or cylinder model, it can adapt to scatterers with complex shapes, such as pinhole-like pores within fibers, irregular grain boundary defects, and nanoparticles. Simultaneously, the Log-normal size distribution function independently describes the characteristic dimensions of the scatterer in three orthogonal directions, allowing the scatterer to have different size distribution characteristics in the major axis, minor axis, and third dimension, which helps improve the accuracy of describing the polydispersity of scatterer dimensions in real-world systems.

[0031] Third, regarding improving the accuracy of quantitative analysis, based on the collaborative modeling of the aforementioned multi-parameter model, the deviation between the simulated patterns generated by this method and the experimentally measured spectra is improved. It can output a two-dimensional distribution spectrum of scattering intensity, one-dimensional scattering curves along the equatorial and meridional directions, and orientation parameter analysis results, providing simulation support for the quantitative analysis of the microstructure of orientation systems. In terms of computation, this method does not require atomic coordinates, directly performing geometric modeling and two-dimensional Fourier transforms at the mesoscopic scale. It utilizes the conjugate symmetry property of the Fourier transform to reduce computational load and can be combined with parallel acceleration technology of graphics processing units to achieve rapid computation. Attached Figure Description

[0032] Figure 1 This is a flowchart illustrating the steps of the 2D SAXS simulation method in Embodiment 1 of this application; Figure 2 Schematic diagrams of different shapes (and parameter variations) of the superellipsoid model in Embodiment 1 of this application. Figure 3 This is a comparative analysis of the simulated scattering characteristics of the carbon fiber system in Example 1 of this application and the experimentally measured scattering characteristics. Detailed Implementation

[0033] To make the objectives, technical solutions, and advantages of this application clearer, the application will be further described in detail below with reference to the accompanying drawings and specific embodiments. It should be understood that the specific embodiments described herein are only for explaining this application and are not intended to limit this application.

[0034] This application provides a method for calculating and simulating two-dimensional small-angle X-ray scattering patterns in oriented systems, an electronic device, and a computer-readable storage medium. This method is mainly applied to the microstructure analysis of sparse systems with preferred orientations, such as high-performance fibers, polymer composites, and nano-hybrid materials. It should be noted that the scatterers mentioned in this application refer to micro-defects or particles within the system that have an electron density difference with the matrix, such as pores within fibers, grain boundary defects, interfaces between amorphous and crystalline regions, or nanoparticles dispersed in the matrix. The sparse system refers to a system where the interference effect between scatterers is negligible.

[0035] Example 1

[0036] This embodiment provides a method for calculating and simulating two-dimensional small-angle X-ray scattering patterns in an orientation system. Figure 1 The diagram shown is a flowchart of the steps of the method in this embodiment. (See attached diagram.) Figure 1 The method includes the following steps S100 to S300.

[0037] Step S100: Perform multi-parameter modeling of the scatterer, and characterize the shape, three-dimensional size distribution and preferred orientation features of the scatterer by using the super ellipsoid model, Log-normal size distribution function and Von Mises orientation distribution function, respectively.

[0038] To simulate scattering patterns, it is first necessary to fully describe the geometric and distribution characteristics of the scatterer population in a statistical sense. Therefore, this step uses three sub-models to collaboratively complete the multi-parameter modeling of the scatterers.

[0039] Sub-step S110: Define the three-dimensional shape of a single scatterer using a superellipsoid model.

[0040] The shape of the scatterer directly determines its scattering characteristics. To flexibly describe complex-shaped micro-defects or nanoparticles within fibers, this application employs the superellipsoid equation to define the spatially occupied region of the scatterer. When the spatial coordinates of a point... The point is located inside the scatterer if the following inequality is satisfied: ; in, , , The scatterer is in axis, axis, The characteristic dimension along the axis determines the size of the scatterer in three dimensions. and The shape adjustment parameter controls the continuous change of the scatterer from an ellipsoid to a cube.

[0041] Figure 2 Showing different and Typical shapes corresponding to parameter combinations: when and When the above equations degenerate into the standard ellipsoid equations, they are applicable to simulating near-spherical or ellipsoidal scatterers.

[0042] when and When the equation approaches the cuboid equation, it is suitable for simulating square scatterers with obvious edges.

[0043] when and When the equation approaches that of a cylinder, it is particularly suitable for simulating pinhole-like pores extending axially within fibers. By adjusting... and The values ​​between 1 and infinity can also simulate transitional forms such as cubes and prisms, enabling accurate description of complex scattering body shapes.

[0044] The electron density difference distribution of the scatterer is determined based on the actual system. If the scatterer is a micro-defect within the fiber, the micro-defect includes pores, grain boundary defects, and interfaces between amorphous and crystalline regions, and its electron density difference is determined by... , or Characterization, in which , and These represent the electron density in the crystalline region, the electron density in the amorphous region, and the electron density in the micropores, respectively. If the scatterer is an actual particle, the electron density difference is the difference between the particle's electron density and the matrix's electron density.

[0045] Sub-step S120: Use the Log-normal distribution function to describe the size distribution of the scatterer in three directions.

[0046] In real-world systems, scatterers are not of a single size but exhibit a degree of size polydispersity. To accurately describe this distribution characteristic, this application uses the Log-normal distribution function to analyze the scatterer under different sizes. , , Feature dimensions in three orthogonal directions , , Describe independently. The Log-normal distribution function is: ; in, For the characteristic size variable, respectively corresponding to , , ; The logarithmic mean determines the central location of the size distribution; The logarithmic standard deviation determines the width and degree of asymmetry of the size distribution. , , Each has its own independent and The parameters mean that the scatterer can have completely different size distribution characteristics in the major axis, minor axis, and third dimension. For systems with broad distribution characteristics, such as micro-defects within fibers, The typical value range is 0.3 to 0.8.

[0047] Sub-step S130: Use the Von Mises distribution function to describe the preferred orientation of the scatterer.

[0048] Orientation characteristics are the key difference between this method and simulations of isotropic systems. For oriented systems such as fibers, the principal axes of the scatterer are not randomly pointed, but rather exhibit a certain degree of preferred distribution around the fiber axes. To describe this orientation characteristic, this application uses the Von Mises distribution function to define the zenith angle of the scatterer. probability density: ; in, The zenith angle is the angle between the principal axis of the scatterer and the macroscopic preferred principal axis (such as the fiber axis). The orientation mean corresponds to the orientation direction in which the scatterer is most concentrated, and is usually set as the fiber axis direction; This is the orientation concentration coefficient; the larger the value, the more concentrated the orientation. For a first-order zero-order modified Bessel function, the probability density is guaranteed to be within... Interval normalization.

[0049] The physical meaning of this orientation distribution function is clear and unambiguous: when At this time, the distribution degenerates into a uniform distribution, corresponding to a completely random orientation state; when At that time, the distribution approached that of Dirac. The function corresponds to all scatterers strictly along the path. The perfect orientation of the directional alignment. This can be achieved through adjustment. The values ​​between 0 and infinity can simulate a continuous transition from random orientation to highly oriented orientation.

[0050] For azimuth angle This application uses a uniform distribution for description. The physical basis for this setting is that a uniaxially oriented system such as fibers has rotational symmetry in a cross section perpendicular to the fiber axis, and the scatterer has an equal probability of appearing in each azimuth direction.

[0051] Through sub-steps S110 to S130, this step fully defines the shape, three-dimensional size distribution, and spatial orientation distribution of the scattering population, providing an accurate real-space model for subsequent scattering calculations.

[0052] Step S200: Perform a two-dimensional Fourier transform on the shape characterization data of the scatterer and calculate the scattering intensity.

[0053] After completing the real space modeling, the geometric information of the scatterer needs to be converted to reciprocal space to obtain the distribution of scattering intensity.

[0054] Sub-step S210: Generate two-dimensional projection lattice data of the scatterer.

[0055] First, each scatterer is placed in three-dimensional space according to its superellipsoidal shape, three-dimensional dimensions, and spatial orientation. Then, a two-dimensional projection is performed on the scatterer along the detection direction to generate an equally spaced two-dimensional lattice that completely contains the projection of the scatterer. The spacing of the lattice determines the spatial resolution of the simulation; the smaller the spacing, the higher the accuracy.

[0056] Sub-step S220: Obtain the scattering amplitude and calculate the scattering intensity through two-dimensional Fourier transform.

[0057] Performing a two-dimensional Fourier transform on the above two-dimensional lattice data yields a two-dimensional complex matrix, which represents the scattering amplitude. Scattering vector The modulus corresponds to the position of the pixel on the detection plane, and their relationship is as follows: ,in The wavelength of the incident X-ray is 1.

[0058] After obtaining the scattering amplitude, the scattering intensity at each position on the detection plane is calculated according to the scattering intensity formula: ; in, For scattering intensity, The structure factor is used in the sparse system to which this application applies. The distance between scatterers is much larger than their own size, and the interference effect between scatterers can be ignored. In this case, the structure factor is... Approximately 1, the scattering intensity is the square of the scattering amplitude mode.

[0059] To improve computational efficiency, the two-dimensional Fourier transform in this step can utilize its conjugate symmetry property to compute only half of the complex matrix elements, thereby reducing the computational load. Furthermore, the computational task can be deployed on a graphics processing unit (GPU), leveraging its massively parallel computing capabilities to simultaneously process the Fourier transforms and intensity calculations of multiple scatterers, significantly improving the computational speed of large-scale, high-precision simulations.

[0060] Step S300: Perform ensemble averaging to generate a two-dimensional small-angle X-ray scattering simulation pattern for the orientation system.

[0061] The scattering pattern of a single scatterer is only statistically significant; macroscopic measurements yield the superposition result of contributions from a large number of scatterers. Therefore, this step performs an ensemble averaging of the scattering intensities calculated from all scatterers to obtain the average scattering intensity distribution representing the macroscopic system.

[0062] Specifically, the average scattering intensity value of each pixel on the detection plane is converted into a grayscale value or a pseudo-color value according to a preset mapping relationship. The higher the intensity, the higher the brightness, thus generating a visualized two-dimensional small-angle X-ray scattering simulation pattern. This simulation pattern can be output in a standard image format, such as TIFF or EDF.

[0063] Thanks to the synergistic effect of the aforementioned multi-parameter models, this method can accurately reproduce the scattering characteristics of various typical orientation systems, such as "butterfly-shaped", "X-shaped" and "double-spotted". Figure 3 A comparison is presented between the simulated spectrum generated by this method and the measured spectrum from synchrotron radiation experiments in the carbon fiber system. The two spectra are highly consistent in terms of the shape, orientation, and intensity distribution of the scattering characteristics.

[0064] In addition to the two-dimensional scattering spectrum, this step can also simultaneously output the following analysis results: one-dimensional scattering curves extracted along the equatorial and meridional directions for quantitative analysis of the size and shape of the scatterer; orientation parameter analysis results, such as Hermans orientation parameters calculated based on the azimuth distribution of scattering intensity; and statistical histograms of the scatterer size distribution, etc.

[0065] It should be noted that this method is suitable for sparsely oriented systems with an aspect ratio of 0.1 to 100 and can be widely used for microstructure analysis of different types of oriented samples such as fibers, thin films and nano-hybrid materials.

[0066] Example 2

[0067] This embodiment provides an electronic device for performing the two-dimensional small-angle X-ray scattering pattern calculation and simulation method for the orientation system described in Embodiment 1 above. This electronic device can be a personal computer, workstation, or server.

[0068] This electronic device includes memory, a processor, input / output interfaces, a communication interface, and a bus. The processor employs a heterogeneous architecture of CPU and GPU. The CPU is responsible for overall process logic control, parameter optimization, and data read / write management; the GPU performs highly parallel numerical computation tasks such as Fourier transforms and scattering intensity calculations to improve overall simulation speed. The memory uses a combination of RAM and SSD. RAM is used to cache intermediate data generated during the simulation, while the SSD is used for long-term storage of model parameters, experimental spectra, and simulation results. The input / output interfaces receive user-defined simulation parameters, such as lattice spacing, X-ray wavelength, and shape adjustment parameters. and Logarithmic mean Logarithmic standard deviation Orientation Concentration Coefficient It supports importing scatterer model files and outputting generated simulation patterns and analysis reports. The communication interface is used for data exchange with other devices or networks.

[0069] When the processor executes the computer program stored in the memory, it sequentially performs the steps of scatterer modeling, Fourier transform and scattering intensity calculation, and simulated pattern generation as described in Example 1.

[0070] Example 3

[0071] This embodiment provides a computer-readable storage medium storing computer-executable instructions. When executed by a processor, these computer-executable instructions implement the two-dimensional small-angle X-ray scattering pattern calculation and simulation method for the orientation system as described in Embodiment 1.

[0072] The computer-readable storage medium can be any medium capable of storing program code, such as a read-only memory, random access memory, disk, optical disk, solid-state drive, etc.

[0073] The above description is merely a specific embodiment of this application. Those skilled in the art can make various changes, modifications, substitutions, and variations to these embodiments without departing from the principles and spirit of this application. The scope of this application is defined by the claims and their equivalents.

Claims

1. A method for calculating and simulating two-dimensional small-angle X-ray scattering patterns in an orientation system, characterized in that, include: Obtain a super ellipsoidal model of the scatterer, which is used to control the geometry of the scatterer through shape adjustment parameters; Based on the Log-normal size distribution function, the characteristic size distribution of the scatterer in the three orthogonal directions is determined respectively; The preferred orientation characteristics of the zenith angle of the scatterer are determined based on the Von Mises orientation distribution function, and the distribution of the azimuth angle of the scatterer is determined based on the uniform distribution. A two-dimensional Fourier transform is performed on the shape characterization data of the scatterer to obtain a two-dimensional complex matrix; The scattering amplitude is calculated based on the two-dimensional complex matrix, and the scattering intensity at each position in the detection plane is calculated in conjunction with the scattering intensity calculation model. An ensemble average is performed based on the scattering intensity to generate a two-dimensional small-angle X-ray scattering simulation pattern for the orientation system. The scatterer is adapted to sparse systems with aspect ratios ranging from 0.1 to 100.

2. The method for calculating and simulating two-dimensional small-angle X-ray scattering patterns in an orientation system according to claim 1, characterized in that, The superellipsoid model for obtaining the scatterer includes defining the spatially occupied region of the scatterer using the following superellipsoid equation: ； in, , , Let these be the coordinates of the scatterer in three-dimensional space; , , The scatterer is respectively in axis, axis, Feature dimensions in the axial direction; and The shape adjustment parameters; By adjusting and The value of is used to simulate a scatterer of at least one shape among a cube, cylinder, ellipsoid, and rhombus.

3. The method for calculating and simulating two-dimensional small-angle X-ray scattering patterns in an orientation system according to claim 2, characterized in that, The correspondence between the values ​​of the shape adjustment parameters and the geometry of the scatterer includes: when and At that time, the scatterer is a standard ellipsoid; when and At that time, the scatterer is a cuboid; when and At that time, the scatterer is a cylinder.

4. The method for calculating and simulating two-dimensional small-angle X-ray scattering patterns in an orientation system according to claim 1, characterized in that, The Log-normal size distribution function is: ； in, The characteristic size variable of the scatterer corresponds sequentially to , , ; The mean is logarithmic. The standard deviation is the logarithm. The , , Each scatterer independently follows its own defined log-normal distribution to describe the size distribution of the major axis, minor axis, and third dimension of the scatterer.

5. The method for calculating and simulating two-dimensional small-angle X-ray scattering patterns in an orientation system according to claim 1, characterized in that, The Von Mises orientation distribution function is: ； in, The zenith angle of the scatterer; The mean of orientation; This is the orientation concentration factor; It is a zeroth-order modified Bessel function of the first kind; when When the Von Mises orientation distribution function is used, the scatterer is characterized as having a completely random orientation; when When the Von Mises orientation distribution function is used, the scatterer is characterized as having a perfect orientation; The azimuth angle of the scatterer is uniformly distributed to adapt to the rotational invariance of the fiber system.

6. The method for calculating and simulating two-dimensional small-angle X-ray scattering patterns in an orientation system according to claim 1, characterized in that, The generation of the two-dimensional small-angle X-ray scattering simulation pattern for the orientation system includes: Reproduce at least one of the following orientation system characteristic scattering patterns: "butterfly-shaped", "X-shaped" and "double-spotted"; At least one of the following: a two-dimensional distribution spectrum of output scattering intensity, one-dimensional scattering curves in the equatorial and meridional directions, and the results of orientation parameter analysis.

7. The method for calculating and simulating two-dimensional small-angle X-ray scattering patterns in an orientation system according to claim 1, characterized in that, The scattering intensity calculation model adopts ,in For scattering intensity, The scattering amplitude is represented by the two-dimensional complex matrix, for the sparse architecture factor. The value is 1.

8. The method for calculating and simulating two-dimensional small-angle X-ray scattering patterns in an orientation system according to any one of claims 1 to 7, characterized in that, The two-dimensional Fourier transform utilizes its conjugate symmetry to reduce computational load and combines it with the parallel acceleration technology of the graphics processor to achieve computation.

9. An electronic device, characterized in that, It includes a memory and a processor, the memory storing a computer program, and the processor executing the computer program to implement the method as described in any one of claims 1 to 8.

10. A computer-readable storage medium having computer-executable instructions stored thereon, characterized in that, When the computer-executable instructions are executed by a processor, they implement the method as described in any one of claims 1 to 8.

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