A method and system for measuring chemical short-range order based on pair distribution functions of atoms

Abstract

The application relates to a chemical short-range order measurement method and system based on an atomic pair distribution function, and the method comprises the following steps: performing a total scattering experiment on a polycrystalline powder sample to obtain total scattering data, a scattering function and an atomic pair distribution function; based on the total scattering data, an initial three-dimensional atomic structure model is constructed; further, the initial three-dimensional atomic structure model is fitted and reconstructed by taking minimization of a fitting goodness factor as a target, so that a three-dimensional atomic structure model after fitting and reconstruction is obtained; according to the three-dimensional atomic structure model after fitting and reconstruction, a radial distribution function and a bulk average distribution concentration are calculated, and a chemical short-range order parameter calculation cutoff is set according to a near-neighbor atomic cutoff distance; further, the probability of an atom finding other types of atoms under the calculation cutoff is calculated; and the chemical short-range order parameter is calculated based on the probability and the bulk average distribution concentration. Compared with the prior art, the application has the advantage of wide application scenarios.

Description

A chemical short-range ordered measurement method and system based on atom pair distribution function Technical Field

[0001] This invention relates to the field of materials characterization technology, and in particular to a chemical short-range order measurement method and system based on the atomic pair distribution function. Background Technology

[0002] With the continuous development of materials science research, researchers' demand for refined characterization of material structures is increasing. Atomic disorder-occupied materials, as a class of excellent functional materials with complex crystal structures, have wide applications in many fields such as thermoelectric conversion, energy storage, and high-temperature superconductivity. Traditional materials characterization assumes that the crystal structure of atomically disorder-occupied materials follows the assumption of proportionally divided lattice sites. However, atomically disorder-occupied materials often exhibit superior physicochemical properties far exceeding the average structure assumption, leading to the discovery that, under the assumption of an average crystal structure, atoms in the local structure of the material have a certain degree of ordered arrangement according to elemental rules; this is called chemical short-range order. Chemical short-range order, as a local structural feature widely present in disordered materials, makes significant contributions to the physicochemical properties of materials, such as mechanical, thermal, electrical conductivity, and ion mobility.

[0003] However, current researchers mainly use methods such as high-resolution transmission electron microscopy (HRTEM) real-space atomic image contrast differences, electron diffraction (EDS) additional diffraction spots, and energy-dispersive spectroscopy (EDS) intensity distribution differences to characterize chemical short-range order. These methods analyze the intensity distribution of two-dimensional images obtained from testing, which can qualitatively analyze the presence or absence of chemical short-range order, but it is difficult to obtain quantitative information such as the distribution size and distribution pattern of chemical short-range order in three-dimensional space. Furthermore, high-quality electron microscopy analysis requires difficult sample preparation, can only obtain limited information within the field of view, and relies on this to make global assumptions, making it difficult to obtain the true distribution information of the material's local structure.

[0004] The invention disclosed in CN120195199A presents a method for measuring local lattice distortion in multi-principal alloys based on synchrotron X-ray atomic pair distribution functions. The method includes the following steps: preparing experimental materials; acquiring two-dimensional diffraction data using synchrotron high-energy X-rays; separating local and average structural information using atomic pair distribution functions; and verifying the cause of local distortion by combining structural fitting and DFT supercell relaxation. This invention improves the accuracy of capturing local distortion at the atomic scale, fully supplements the completeness of statistical information for quantitatively characterizing the local structural distortion of materials, and systematically achieves high-precision measurement and quantitative analysis of dynamic distortion. However, this method does not further measure and analyze the phenomenon of short-range chemical ordering in materials where atomic disorder occupies the space.

[0005] Therefore, in order to comprehensively analyze the distribution characteristics of chemical short-range order in three-dimensional space and its impact on performance, this method provides an experimental measurement method for chemical short-range order in materials based on the atomic pair distribution function. Summary of the Invention

[0006] The purpose of this invention is to overcome the shortcomings of the prior art by providing a chemical short-range ordered measurement method based on the atomic pair distribution function.

[0007] The objective of this invention can be achieved through the following technical solutions:

[0008] A chemical short-range order measurement method based on the atomic pair distribution function, the method comprising the following steps:

[0009] A total scattering experiment was conducted on a pre-prepared polycrystalline powder sample to obtain total scattering data, and the scattering function and atom pair distribution function were obtained based on the total scattering data; an initial three-dimensional atomic structure model was constructed based on the total scattering data.

[0010] The fitting quality factor is calculated based on the scattering function and the atom pair distribution function. With the goal of minimizing the fitting quality factor, the initial three-dimensional atomic structure model is fitted and reconstructed using the inverse Monte Carlo method to obtain the fitted and reconstructed three-dimensional atomic structure model.

[0011] Based on the reconstructed three-dimensional atomic structure model, the radial distribution function and the bulk average distribution concentration of atoms of different elements are calculated; based on the radial distribution function, the nearest neighbor atom cutoff distance is calculated, and the chemical short-range order parameter is set according to the nearest neighbor atom cutoff distance to calculate the cutoff; further, the probability of each atom finding other types of atoms under the cutoff calculated by the chemical short-range order parameter is calculated; the chemical short-range order parameter is calculated based on the probability and the bulk average distribution concentration.

[0012] Furthermore, the fitting and reconstruction process specifically includes:

[0013] Each time, an atom is randomly selected and moved by a random amount. The corresponding new fit quality factor is calculated. If it is less than the current fit quality factor, the move is accepted and the current fit quality factor is replaced with the new fit quality factor. If the new fit quality factor after the move is greater than the current fit quality factor, the probability index determines whether to accept the move and replace the current fit quality factor with the new fit quality factor. The new fit quality factor is continuously calculated and compared with the current fit quality factor until the fit quality factor no longer decreases, at which point the fitting convergence is achieved.

[0014] The formula for calculating the fitting quality factor is as follows:

[0015]

[0016] Where K is the structure factor and L is the radial distribution function. and Let be the experimental error function. and The scattering functions are obtained from calculation and experiment, respectively. and These are the atomic pair distribution functions obtained through calculation and experiment, respectively. This represents the i-th reciprocal space sampling point. This represents the i-th real space distance sampling point.

[0017] Furthermore, during the fitting and reconstruction process, an atomic position exchange operation is employed to exchange atoms of different element types located at the same lattice sites in order to explore the chemical short-range ordered arrangement phenomenon in the polycrystalline powder sample.

[0018] Furthermore, the formula for calculating the short-range chemical order parameter is as follows:

[0019] , 𝑖=𝑗

[0020] i≠j

[0021] in, This represents the probability of finding a class i atom near a class j atom within the m-shell. This represents the average concentration of class j atoms within the system; A negative value indicates that there is an aggregation between type j atoms and type i atoms, while a positive value indicates that type j atoms and type i atoms tend to be separated; if it is 0, it indicates that type i atoms and type j atoms are completely randomly distributed.

[0022] Furthermore, based on the fitted three-dimensional atomic structure model and the chemical short-range order parameters, the chemical short-range order phenomenon existing in the polycrystalline powder sample is analyzed.

[0023] Furthermore, the total scattering data is refined using Ritwald to obtain the lattice constant and atomic positions of the unit cell in the polycrystalline powder sample, and then the initial three-dimensional atomic model is constructed based on the lattice constant and atomic positions.

[0024] Furthermore, during the conduct of the total scattering experiment:

[0025] Select an X-ray source with energy in the hard X-ray range to collect data in a reciprocal space range greater than a preset value, thereby obtaining total scattering data with the best resolution.

[0026] Extend the exposure time of a single acquisition of a two-dimensional diffraction image to achieve a signal-to-noise ratio greater than a preset value between the diffraction signal and the background signal acquired at a high inverted space position.

[0027] Furthermore, if the signal-to-noise ratio of the diffraction signal and the background signal acquired at the high inverted space position does not meet the requirements, multiple two-dimensional diffraction images are acquired, and the influence of the background and detector background count at the high inverted space position is reduced by averaging the multiple two-dimensional diffraction images to obtain better average count statistics.

[0028] Furthermore, during the total scattering experiment, the same experimental parameters and configuration were used to collect total scattering data from the standard powder sample and the empty sample container in order to calibrate the distance from the pre-prepared polycrystalline powder sample to the detector and to remove experimental errors caused by scattering from the air and the sample container itself.

[0029] The present invention also provides a chemical short-range ordered measurement system based on the atomic pair distribution function, including a memory and a processor, wherein the memory stores a computer program, and the processor calls the computer program to execute the steps of any of the methods described above.

[0030] Compared with the prior art, the present invention has the following advantages:

[0031] (1) The present invention obtains a three-dimensional atomic structure model by fitting and reconstructing the initial three-dimensional atomic structure model according to the scattering function and the atomic pair distribution function using the inverse Monte Carlo method; calculates the chemical short-range order parameters based on the three-dimensional atomic structure model; and uses the chemical short-range order parameters to analyze the chemical short-range order distribution characteristics in the material.

[0032] This study reveals the spatial distribution of short-range chemical order in a three-dimensional atomic structure model. By fitting the three-dimensional atomic structure model with a supercell containing tens of thousands of atoms and characterizing the local atomic distribution, it is beneficial to explore the local structure of atoms of different element types at the same lattice site. By performing position exchange operations on atoms of different types occupying the same lattice site during the fitting process, the chemical short-range order distribution associated with the element can be explored, and a three-dimensional atomic structure model containing chemical short-range order can be obtained for further analysis.

[0033] (2) This invention can infer the average distribution size of chemical short-range ordering behavior in materials by calculating chemical short-range ordering parameters at different cutoff distances. By screening and calculating the chemical short-range ordering parameters of different elements or different lattice sites, different elements at anion and cation sites can be distinguished, and interference from elements that do not participate in the chemical short-range ordering distribution can be eliminated. Only the chemical short-range ordering distribution phenomenon at a certain lattice site is considered, and the element distribution in three-dimensional space is analyzed. Furthermore, this calculation method can be extended from traditional metallic materials to many material systems such as electrode materials and semiconductor materials where some lattice sites are occupied by atomic disorder. In addition, this method is not only applicable to crystalline materials, but also to amorphous materials. Based on this, this invention can also be used to calculate the chemical short-range ordering between element clusters. In addition to traditional crystalline materials, it can also characterize the chemical short-range ordering phenomenon in amorphous clusters without periodic boundaries, and has a wide range of applicable scenarios.

[0034] (3) This invention directly calculates the radial distribution function based on the optimized atomic model and adaptively determines a physically reasonable nearest neighbor truncation based on its first nearest neighbor feature. Under a unified spatial criterion, it statistically analyzes the local atomic pairing probability and the global concentration distribution, achieving physically self-consistent and high-precision calculation of chemical short-range order parameters. This calculation method eliminates the subjectivity of truncation selection in traditional analysis, ensures reliable detection of weak order signals, improves detection accuracy, and provides a reliable tool for standardized quantitative characterization of atomic-scale chemical order in multi-component materials.

[0035] (4) This invention, through the design of an experimental collection strategy for total scattering data, can ensure the acquisition of high-quality atom pair distribution functions under limited experimental conditions; through careful setting of experimental parameters and experimental setup, it achieves the acquisition of large-scale and high signal-to-noise ratio reciprocal total scattering data in a short time. By generating high-quality total scattering data, more information about the local structure of materials is revealed, and a good data foundation is laid for subsequent fitting of three-dimensional atomic structure models.

[0036] (5) This invention calculates the fitting quality factor and the residual between the fitting and the experiment, which can quantitatively measure the quality of the fitting model and further explore the chemical short-range ordering phenomenon. During the calculation process, the scattering function and the atom pair distribution function are optimized at the same time, and the signal-to-noise ratio between different data is unified, so as to obtain more reliable chemical short-range ordering parameters and explore the chemical short-range ordering phenomenon in materials. Attached Figure Description

[0037] Figure 1 is a flowchart of a chemical short-range ordered measurement method based on the atomic pair distribution function provided in an embodiment of the present invention;

[0038] Figure 2 is a simplified flowchart of a chemical short-range ordered measurement method based on the atomic pair distribution function provided in an embodiment of the present invention. Detailed Implementation

[0039] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. The components of the embodiments of the present invention described and shown in the accompanying drawings can generally be arranged and designed in various different configurations.

[0040] Therefore, the following detailed description of the embodiments of the invention provided in the accompanying drawings is not intended to limit the scope of the claimed invention, but merely to illustrate selected embodiments of the invention. All other embodiments obtained by those skilled in the art based on the embodiments of the invention without inventive effort are within the scope of protection of the invention.

[0041] It should be noted that similar labels and letters in the following figures indicate similar items. Therefore, once an item is defined in one figure, it does not need to be further defined and explained in subsequent figures.

[0042] Definitions:

[0043] Total scattering data refers to a complete diffraction dataset containing all scattering signals of a material, obtained through high-energy X-ray or neutron diffraction experiments. It includes not only Bragg diffraction peaks reflecting long-range periodic order, but also continuous diffuse scattering signals originating from short-range ordered and disordered structures, lattice strain, defects, and atomic-scale correlations within the material. This data is typically obtained through measurements over a wide angular range with high momentum transfer (high q-values), simultaneously capturing structural information from the atomic to the nanoscale. The core value of total scattering data lies in its completeness; through Fourier transform, the pairwise distribution function (PDF) in real space can be obtained, enabling a comprehensive analysis of the fine structure of the material, including local structural environments, short-range chemical order, and atomic pairing correlations. It is particularly suitable for studying systems that are difficult to characterize using traditional Bragg diffraction, such as amorphous materials, nanomaterials, disordered alloys, and complex solid solutions.

[0044] High reciprocal space: refers to the reciprocal lattice space (momentum space) corresponding to a larger wave vector q value (usually q > 10 Å). -1The region of high reciprocal space. In X-ray or neutron diffraction experiments, high reciprocal space positions correspond to large scattering angles (detector edge regions), and their signals mainly reflect short-range structural information of materials at the atomic scale, such as chemical bond lengths, coordination environments, atomic pair correlations, and diffuse scattering caused by disorder. Since high q values ​​correspond to high real space resolution (Δr ≈ π / q), obtaining high-quality high reciprocal space data is a key prerequisite for realizing atomic-scale structural analysis and studying the local structure of chemically short-range ordered and amorphous materials. Experimentally, high-energy light sources (short wavelengths), large-size detectors, and optimized geometric configurations are typically required to acquire high reciprocal space data with sufficient signal-to-noise ratio.

[0045] Nearest neighbor (NN) atomic distance constraint is a key physical constraint in inverse Monte Carlo (RMC) simulations, used to ensure the physical plausibility of the atomic model during optimization. This constraint prevents non-physical overlap of atoms during random movements or exchanges by setting a minimum allowable distance (hard sphere radius) between different element pairs. The constraint value is typically set based on known atomic radii, crystallographic databases, or first-principles calculations, and is checked immediately after each RMC movement attempt. This constraint not only maintains the basic atomic geometry of the material but also ensures the plausibility of the local coordination environment, which is crucial for obtaining interpretable short-range chemical order parameters.

[0046] The nearest neighbor window constraint is a crucial constraint in inverse Monte Carlo (RMC) simulations used to control the rationality of local coordination environments. This constraint defines a range of permissible nearest neighbor atoms (i.e., the coordination number window) for each atom, typically relaxed appropriately based on the known crystallographic coordination number of the material to accommodate disorder and thermal fluctuations. After each atom move attempt, the system checks whether the coordination number of the affected atom exceeds the preset window; if so, the move is rejected. This constraint prevents non-physical configurations such as coordination number anomalies (e.g., isolated atoms or over-coordination) from occurring during the simulation, thus maintaining the structural stability and chemical rationality of the material. It is particularly important for the quantitative analysis of coordination tendencies between different elements in chemically short-range ordered systems.

[0047] Nearest neighbor cutoff distance: This is the maximum search radius used to define the "nearest neighbor" atom when calculating the radial distribution function (RDF) or analyzing the local environment of atoms. This distance is typically determined based on the location of the first minimum value of the RDF (the first nearest neighbor valley), treating atoms smaller than this distance as nearest neighbors while ignoring more distant second-nearest neighbors and outermost atoms. In the calculation of short-range chemical order parameters, the choice of cutoff distance directly affects the accuracy of nearest neighbor statistics: if the distance is too small, some nearest neighbors will be missed; if it is too large, interference from second-nearest neighbors will be introduced.

[0048] Supercell models are large-scale atomic models constructed by periodically expanding the crystallographic unit cell of a material in three dimensions. Their core objective is to obtain a sufficient number of atoms (typically tens of thousands to millions) to meet the needs of statistical physics analysis and computational simulations while maintaining crystal symmetry and periodicity. Supercell models effectively reduce surface and finite-size effects, providing properties closer to the bulk properties of macroscopic bulk materials, while allowing the study of phenomena that cannot be described at the unit cell scale, such as local structural fluctuations, defect interactions, and short-range chemical order.

[0049] Example 1

[0050] As shown in Figure 1, this embodiment provides a chemical short-range order measurement method based on the atomic pair distribution function. The method includes the following steps:

[0051] S1: Conduct a total scattering experiment on the pre-prepared polycrystalline powder sample to obtain total scattering data, and obtain the scattering function and atom pair distribution function based on the total scattering data; construct an initial three-dimensional atomic structure model based on the total scattering data;

[0052] Specifically,

[0053] Since the short-range chemically ordered structure of materials is primarily submicron and micron in size, the corresponding structural information is mainly contained within the signal of the atom-pair distribution function at lower real space distances. To obtain high-quality signals of the atom-pair distribution function at these lower real space distances, requirements are placed on the total scattering data acquired during the experimental acquisition process. Total scattering data is the experimental test data used to obtain the atom-pair distribution function. To acquire high-quality total scattering data, a large reciprocal space range needs to be acquired during the experiment, and a good signal-to-noise ratio must be ensured at higher reciprocal space locations.

[0054] Specifically,

[0055] To ensure a sufficiently large inverted space range for data acquisition, the experiment should be configured as follows:

[0056] 1. The sample to be tested needs to be placed as close to the detector as possible. Considering the beam blocker between the sample and the detector, this distance should be set to within 100cm, so that the flat panel detector can collect a larger inverted space signal in a limited space.

[0057] 2. The X-ray source selected for the test must have high energy to produce extremely short wavelength X-rays for data acquisition. Considering the layout of existing synchrotron radiation source facilities, the X-ray source energy should be selected in the hard X-ray range, at least 30 keV, corresponding to an X-ray wavelength less than 0.4133 Å.

[0058] 3. Choosing a large-size flat panel detector allows for the acquisition of a larger inverted space range in a single exposure.

[0059] 4. Considering the overall experimental setup and X-ray source energy selection, the final reciprocal space range should be within 15 Å. -1 This is how the optimal resolution is achieved.

[0060] Preferred,

[0061] To ensure a good signal-to-noise ratio for signals acquired at high inverted space locations, the experiment should be set up as follows:

[0062] Extend the exposure time of a single acquisition to ensure that the total scattering image has a longer exposure time, and ensure that the signal-to-noise ratio of the diffraction signal acquired at the high cuboid position to the background signal is at least greater than 2.

[0063] If the signal-to-noise ratio of a single exposure is not good, multiple diffraction images can be acquired, and the counts can be averaged through post-processing to ensure that the data has the best average count statistics.

[0064] By combining detector selection and exposure time settings, the signal-to-noise ratio of a single two-dimensional diffraction image is ensured to be greater than 2.

[0065] Preferred,

[0066] To accurately calibrate the sample-to-detector distance and the scattering caused by air and the sample container, two additional sets of data were acquired. Using the same parameters and configuration selected during sample testing, data were acquired for standard powder samples (such as Si, Ni, LaB6, CeO2) and empty sample containers for distance calibration and background subtraction in post-processing.

[0067] Preferred,

[0068] If the signal-to-noise ratio of the diffraction signal acquired at the high inverted space position does not meet the requirements with the background signal, multiple two-dimensional diffraction images are acquired, and the influence of the background and detector background count at the high inverted space position is reduced by averaging the multiple two-dimensional diffraction images to obtain better average count statistics.

[0069] S2: Calculate the fitting quality factor based on the scattering function and the atomic pair distribution function, and reconstruct the initial three-dimensional atomic structure model by minimizing the fitting quality factor to obtain the reconstructed three-dimensional atomic structure model.

[0070] Specifically,

[0071] To investigate the short-range chemical ordering phenomenon in the local structure of a sample, it is necessary to fit and reconstruct its three-dimensional atomic structure model. Inverse Monte Carlo, as a method for fitting total scattering data, can meet the requirements for fitting large-scale three-dimensional atomic structure models. Therefore, this application chooses to use the inverse Monte Carlo method to fit the three-dimensional atomic structure model. In the initial input three-dimensional atomic structure model, different types of atoms are randomly dispersed. The inverse Monte Carlo method fits the atomic pair distribution function G(r) and scattering function F(Q) obtained from the test of the target sample. The fitting process is affected by the fitting quality factor. Control:

[0072]

[0073] Where K is the structure factor and L is the radial distribution function. and Let be the experimental error function. During the fitting process, each time an atom is randomly selected and moved by a random amount, the corresponding value is calculated. .if Less than If the move is successful, the move is accepted. Greater than Then it follows the probability exponent. A decision is made regarding whether to accept the move. This fitting process continues until... The fit converges when it almost stops decreasing.

[0074] The methods for obtaining the structure factor, radial distribution function, scattering function, and atom pair distribution function are all well-known in this field;

[0075] The scattering function I(Q) refers to the coherent scattering intensity directly measured in the total scattering experiment and corrected by background subtraction and other methods.

[0076] The structure factor is a dimensionless function in reciprocal space that describes the positional correlation of atoms and is obtained by normalizing the scattering function I(Q).

[0077] The atom pair distribution function G(r) is obtained by Fourier transform of the structure factor after processing. It refers to the deviation of the number of atom pairs per unit length at a real space distance r centered on any reference atom from a completely random distribution, characterized by gradually converging to 0 at higher r.

[0078] The radial distribution function g(r), similar in concept to the atom pair distribution function G(r), refers to the relative probability density of finding another atom at a real space distance r with any reference atom as the center. Its characteristic is that it gradually converges to 1 at higher r.

[0079] In the formula for calculating the inverse Monte Carlo quality factor, the structure factor and radial distribution function can be used as upper limits for summation. This refers to the simultaneous fitting of multiple sets of data obtained from the same material system under different test conditions to the model. Therefore, the summation method is used to accumulate the fitting quality factor among multiple sets of data.

[0080] Preferred,

[0081] To ensure fitting quality, the following settings should be made when fitting the three-dimensional atomic structure model:

[0082] 1. The lattice constant and atomic positions of the material's unit cell were obtained using the Ritwald refinement results of X-ray diffraction.

[0083] The initial three-dimensional atomic structure model for fitting should use a supercell model built from a single cell. The established three-dimensional atomic structure model should contain at least 10,000 atoms to ensure statistical averaging during the fitting process, and a sufficiently large lattice size for the periodic mapping of the model.

[0084] 2. Nearest neighbor atom distance constraints and atom nearest neighbor window constraints are adopted to ensure that the rigid network structure of the material is not destroyed during the fitting process.

[0085] 3. By employing atomic position exchange operations, the three-dimensional atomic structure model swaps atoms of different element types at the same lattice sites during the fitting process, thus reconstructing a chemically ordered short-range arrangement that conforms to experimental data.

[0086] A single fit generates at least 1 million valid atom movement attempts, and the fit is repeated 5 times while keeping the fitting parameters unchanged to ensure the robustness of the fit.

[0087] S3: Based on the reconstructed three-dimensional atomic structure model, calculate the radial distribution function and the bulk average distribution concentration of atoms of different elements; based on the radial distribution function, determine the cutoff distance of nearest neighbor atoms, and calculate the cutoff by setting the chemical short-range order parameter based on the cutoff distance of nearest neighbor atoms; further calculate the probability of each atom finding other types of atoms under the cutoff of the chemical short-range order parameter; calculate the chemical short-range order parameter based on the probability and the bulk average distribution concentration.

[0088] Specifically,

[0089] After obtaining the fitted three-dimensional atomic structure model, the chemical short-range ordering parameter of the multi-component system was used to explore the chemical short-range ordering phenomenon in the target material. The multi-component chemical short-range ordering parameter describes the local distribution of element pairs in a multi-component system and is defined as follows:

[0090] (𝑖=𝑗, to count atoms of the same kind)

[0091] (i≠j, calculate different types of atoms)

[0092] in This represents the probability of finding a class i atom near a class j atom within the m-shell. This represents the average concentration of class j atoms within the system. A negative value indicates that there is clustering between type j atoms and type i atoms, while a positive value indicates that type j atoms tend to be separated from type i atoms. If it is 0, it indicates that type i atoms and type j atoms are completely randomly distributed.

[0093] Preferred,

[0094] The calculation process for chemical short-range order parameters is shown below:

[0095] 1) Calculate the radial distribution function based on the input three-dimensional atomic structure model.

[0096] 2) Based on the calculated radial distribution function, the nearest neighbor atom cutoff distance is determined, and the chemical short-range order parameter is set accordingly to calculate the cutoff. In solid material systems, the calculated cutoff is generally selected from 0.1 Å to the cutoff position of the first nearest neighbor peak.

[0097] 3) Based on the input three-dimensional atomic structure model, calculate the bulk average concentration of atoms of different elements. .

[0098] 4) Based on the input 3D atomic structure model, calculate the probability that each atom will find other types of atoms within the computational truncation. .

[0099] 5) Calculate the chemical short-range ordering parameters based on the multi-component chemical short-range ordering formula.

[0100] Further analysis was conducted based on the three-dimensional atomic structure model and chemical short-range order parameters to examine the chemical short-range order phenomenon in the material and its distribution in three-dimensional space.

[0101] Example 2

[0102] This embodiment provides a chemical short-range ordered measurement system based on the atomic pair distribution function, including a memory and a processor. The memory stores a computer program, and the processor calls the computer program to execute the steps of any of the methods in Embodiment 1.

[0103] Improvements of this invention:

[0104] 1) Provide and guide high-quality total scattering data collection strategies to obtain high-quality atom pair distribution functions.

[0105] 2) Provide a chemical short-range order fitting strategy based on total scattering data to obtain a three-dimensional atomic structure model containing chemical short-range order.

[0106] 3) Provide a chemical short-range ordering calculation method based on a three-dimensional atomic structure model to analyze the chemical short-range ordering distribution characteristics of materials.

[0107] The beneficial effects of this invention are as follows:

[0108] (1) The experimental collection strategy for total scattering data can ensure the acquisition of high-quality atom pair distribution functions under limited experimental conditions. Using the recommended flat panel detector and experimental setup, large-scale and high signal-to-noise ratio reciprocal total scattering data can be collected in a short time. High-quality total scattering data will reveal more information about the local structure of materials, laying a good data foundation for subsequent fitting of three-dimensional atomic structure models.

[0109] (2) The inverse Monte Carlo method is used to fit and reconstruct the three-dimensional atomic structure model based on total scattering data. This method can reveal the spatial distribution of short-range chemical order in the three-dimensional atomic structure model. Compared with the traditional single-cell fitting method for total scattering data, the fitting of the three-dimensional atomic structure model uses a supercell structure containing tens of thousands of atoms to characterize the local atomic distribution. This is beneficial for exploring the local structure of atoms of different element types at the same lattice site. In addition, by performing position exchange operations on atoms of different types occupying the same lattice site during the fitting process, the distribution of short-range chemical order associated with the element can be explored, and a three-dimensional atomic structure model containing short-range chemical order can be obtained for further analysis.

[0110] (3) The multi-component chemical short-range ordering formula is used to calculate the chemical short-range ordering phenomenon in the material. Compared with the traditional Warrencowley short-range ordering parameter, the multi-component chemical short-range ordering formula used in this application can distinguish different elements at the anion and cation sites during calculation, eliminate interference from elements that do not participate in the chemical short-range ordering distribution, and focus only on the chemical short-range ordering distribution phenomenon at a certain lattice site, thus analyzing the element distribution in three-dimensional space. On this basis, the chemical short-range ordering between element clusters can also be calculated. In addition to traditional crystalline materials, this method can also characterize the chemical short-range ordering phenomenon in amorphous clusters without periodic boundaries.

[0111] (4) This invention calculates the fitting quality factor and the residual between the fitting and the experiment, which can quantitatively measure the quality of the fitting model and further explore the chemical short-range ordering phenomenon. During the calculation process, the scattering function and the atom pair distribution function are optimized at the same time, and the signal-to-noise ratio between different data is unified so as to obtain more reliable chemical short-range ordering parameters and explore the chemical short-range ordering parameters in the material.

[0112] The preferred embodiments of the present invention have been described in detail above. It should be understood that those skilled in the art can make numerous modifications and variations based on the concept of the present invention without creative effort. Therefore, all technical solutions that can be obtained by those skilled in the art based on the concept of the present invention through logical analysis, reasoning, or limited experimentation on the basis of existing technology should be within the scope of protection defined by the claims.

Claims

1. A chemical short-range ordered measurement method based on the atomic pair distribution function, characterized in that, include: A total scattering experiment was conducted on a pre-prepared polycrystalline powder sample to obtain total scattering data, and the scattering function and atom pair distribution function were obtained based on the total scattering data. An initial three-dimensional atomic structure model was constructed based on the total scattering data. A good fit factor was calculated based on the scattering function and atom pair distribution function, and the initial three-dimensional atomic structure model was reconstructed using the inverse Monte Carlo method with the goal of minimizing the good fit factor, resulting in a reconstructed three-dimensional atomic structure model. Based on the reconstructed three-dimensional atomic structure model, the radial distribution function and the bulk average distribution concentration of atoms of different elements were calculated. The nearest neighbor atom cutoff distance was calculated based on the radial distribution function, and a chemical short-range order parameter was set based on the nearest neighbor atom cutoff distance to calculate the cutoff. The probability that each atom would find other types of atoms under the cutoff calculated by the chemical short-range order parameter was further calculated. The chemical short-range order parameter was calculated based on the probability and the bulk average distribution concentration.

2. The chemical short-range ordered measurement method based on the atomic pair distribution function according to claim 1, characterized in that, The fitting and reconstruction process specifically includes: each time, randomly selecting an atom and moving it by a random amount, calculating the corresponding new fitting quality factor; if it is less than the current fitting quality factor, the move is accepted, and the current fitting quality factor is replaced with the new fitting quality factor; if the new fitting quality factor after the move is greater than the current fitting quality factor, a probability exponent is used to determine whether to accept the move and replace the current fitting quality factor with the new one; continuously calculating the new fitting quality factor and comparing it with the current fitting quality factor until the fitting quality factor no longer decreases, at which point the fitting convergence is achieved; the calculation expression for the fitting quality factor is: Where K is the structure factor and L is the radial distribution function. and Let be the experimental error function. and The scattering functions are obtained from calculation and experiment, respectively. and These are the atomic pair distribution functions obtained through calculation and experiment, respectively. This represents the i-th reciprocal space sampling point. This represents the i-th real space distance sampling point.

3. The chemical short-range ordered measurement method based on the atomic pair distribution function according to claim 2, characterized in that, In the process of fitting and reconstruction, an atomic position exchange operation is used to exchange atoms of different element types located at the same lattice site in order to explore the chemical short-range ordered arrangement phenomenon in the polycrystalline powder sample.

4. The chemical short-range ordered measurement method based on the atomic pair distribution function according to claim 1, characterized in that, The formula for calculating the chemical short-range ordering parameter is as follows: ,𝑖=𝑗 , i≠j, where This represents the probability of finding a class i atom near a class j atom within the m-shell. This represents the average concentration of class j atoms within the system; A negative value indicates that there is an aggregation between type j atoms and type i atoms, while a positive value indicates that type j atoms and type i atoms tend to be separated; if it is 0, it indicates that type i atoms and type j atoms are completely randomly distributed.

5. The chemical short-range ordered measurement method based on the atomic pair distribution function according to claim 1, characterized in that, Further analysis of the chemical short-range ordering phenomenon in the polycrystalline powder sample was conducted based on the fitted and reconstructed three-dimensional atomic structure model and the chemical short-range ordering parameters.

6. The chemical short-range ordered measurement method based on the atomic pair distribution function according to claim 1, characterized in that, The total scattering data was refined using Ritwald to obtain the lattice constant and atomic positions of the unit cell in the polycrystalline powder sample, and then an initial three-dimensional atomic model was constructed based on the lattice constant and atomic positions.

7. The chemical short-range ordered measurement method based on the atomic pair distribution function according to claim 1, characterized in that, During the total scattering experiment: an X-ray source with energy in the hard X-ray range is selected to collect data in a reciprocal space range greater than a preset value, thereby obtaining total scattering data with optimal resolution; the exposure time of a single acquisition of a two-dimensional diffraction image is extended to ensure that the signal-to-noise ratio of the diffraction signal and the background signal acquired at a high reciprocal space position is greater than a preset value.

8. The chemical short-range ordered measurement method based on the atomic pair distribution function according to claim 7, characterized in that, If the signal-to-noise ratio of the diffraction signal and the background signal acquired at the high inverted space position does not meet the requirements, multiple two-dimensional diffraction images are acquired, and the influence of the background and detector background count at the high inverted space position is reduced by averaging the multiple two-dimensional diffraction images to obtain better average count statistics.

9. The chemical short-range ordered measurement method based on the atomic pair distribution function according to claim 1, characterized in that, During the total scattering experiment, the same experimental parameters and configuration were used, and total scattering data were additionally collected from the standard powder sample and the empty sample container to calibrate the distance from the pre-prepared polycrystalline powder sample to the detector and to remove experimental errors caused by scattering from the air and the sample container itself.

10. A chemical short-range ordered measurement system based on the atomic pair distribution function, characterized in that, It includes a memory and a processor, the memory storing a computer program, the processor invoking the computer program to perform the steps of the method as described in any one of claims 1 to 9.

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