A method for efficiently and accurately simulating three-dimensional electron diffraction dynamic intensity

Abstract

The application discloses a kind of high-efficiency accurate simulation three-dimensional electron diffraction dynamics intensity method, to solve the problem of low efficiency in prior art simulation calculation, insufficient accuracy.The method is by optimizing the strategy of inverse space sampling, using Rodrigues formula to rotate inverse vector, and introducing self-defined phase difference or random sampling in rotation and spin two dimensions, significantly reduce the sampling number.At the same time, the diffraction intensity is accurately calculated by using Bloch wave method, and the diffraction intensity of chiral crystal and its enantiomer is calculated by setting negative thickness once, which avoids repeated calculation.The application supports a variety of diffraction methods, including electron diffraction automatic tomography (ADT), rotating electron diffraction (RED), spin electron diffraction tomography (PEDT), continuous rotation electron diffraction (cRED) and continuous rotation spin electron diffraction tomography (cPEDT), and can reach convergence within 50, 100, 500 times sampling of a single diffraction.The method not only improves the calculation efficiency, but also widens the scope of simulation, and provides reliable technical support for material structure analysis.

Description

Technical Field

[0001] This invention relates to the field of three-dimensional electron diffraction dynamics intensity simulation technology, and in particular to a method for efficient and accurate zone axis inverted space sampling using the golden ratio phase difference, thereby enabling rapid and accurate computational simulation. Background Technology

[0002] Three-dimensional electron diffraction (3D electron diffraction) is a rapidly developing technique for analyzing the structure of submicron crystals. However, the existence of kinetic effects poses significant challenges to the analysis and refinement of 3D electron diffraction structures. Accurate simulation and calculation of the kinetic intensity of electron diffraction are fundamental to fully utilizing the information contained within electron diffraction and effectively refining its structure. Existing structure refinement methods, based on the Bloch wave method, linearly sample the zone axis trajectory of electron diffraction. This allows for simulation and refinement of data collection methods that allow for continuous changes in the electron beam or goniometer, enabling the acquisition of precise structural information of samples and determination of the absolute configuration of chiral molecules, leading to widespread applications. However, the following problems still exist:

[0003] For the continuous rotating precession electron diffraction tomography method, which combines continuous rotation of the goniometer stage with precession of the incident electron beam, the oversampling of the zone axis during data collection results in an excessively large number of samples during simulation, limiting computation. There is currently no specific simulation method, and further research or refinement of its numerical properties is impossible. The calculation and refinement process for chiral structures is also quite cumbersome, making rapid, one-time calculation of enantiomeric structures impossible.

[0004] Therefore, there is an urgent need for an efficient and accurate three-dimensional electron diffraction dynamics intensity simulation method to solve the above problems. Summary of the Invention

[0005] To address the shortcomings of existing technologies, this invention proposes a method for efficiently and accurately simulating the dynamic intensity of three-dimensional electron diffraction. This method significantly improves the efficiency and accuracy of the simulation by optimizing the reciprocal sampling strategy, introducing phase difference or random sampling strategies, and using the Bloch wave method to calculate the diffraction intensity.

[0006] This invention is achieved through the following steps:

[0007] S01: Accurately calculate the structure factor of the sample and obtain information on electron wavelength, rotation axis direction, number of diffraction frames, zone axis direction of each frame, sample thickness, diffraction resolution, and specific diffraction methods.

[0008] S02: Based on the frame directions obtained in S01, determine the total number of simulations for each frame of electron diffraction, calculate the zone axis direction when considering rotation and precession in each simulation, and calculate the corresponding excitation error. When considering rotation and precession simultaneously, they are treated as two independent variables. However, when sampling different precession rings, there is a custom interval between the starting position of each ring and the previous ring. This interval can be 0 or any input value. Random sampling of the two dimensions of rotation and precession is also supported.

[0009] S03: Construct a structure matrix from the information obtained in S02, solve the characteristic equation and calculate the diffraction intensity using the Bloch wave method, and take the average value of the diffraction intensities of the directions contained in the corresponding diffraction frame to obtain the final intensity. When the thickness is set to a negative number, the result is consistent with its opposite for non-chiral structures, while for chiral structures, the diffraction intensity of its enantiomer is calculated.

[0010] S04: The trapezoidal method is selected to integrate the excitation error, and the kinematics of the diffraction data of each frame calculated in S03 are further combined into a set of hkl intensities.

[0011] Furthermore, the simulation method for the three-dimensional electron diffraction dynamics intensity employs a three-dimensional unit vector to simulate the zone axis direction; uses the Rodrigues formula to rotate the zone axis vector; samples the zone axis direction using both rotation and precession dimensions; between different rotation and precession sampling, there is an adjustable phase difference at the starting point or random sampling is performed; the Bloch wave method is used to calculate the single-sheet electron diffraction intensity; the diffraction intensity of the chiral enantiomer is calculated by setting a negative thickness; and the kinematically reduced intensity is obtained by integrating using the trapezoidal method.

[0012] Furthermore, the customized interval is the golden ratio (0.618).

[0013] Furthermore, the specific diffraction methods include automated electron diffraction tomography (ADT), rotating electron diffraction (RED), precession electron diffraction tomography (PEDT), continuous rotating electron diffraction (cRED), and continuous rotating precession electron diffraction tomography (cPEDT).

[0014] Furthermore, for continuous rotating electron diffraction, precession electron diffraction tomography, and continuous rotating precession electron diffraction tomography, convergence can be achieved for a single diffraction pattern within 50, 100, and 500 samples, respectively.

[0015] Compared with the prior art, the beneficial effects of the present invention are:

[0016] 1. Regarding simulation accuracy:

[0017] Accurate Simulation of Multiple Diffraction Intensities: For the first time, accurate simulation of continuous rotating precession electron diffraction tomography intensity has been achieved. It can also accurately calculate the intensities of various specific diffraction techniques, including automated electron diffraction tomography (ADT), rotating electron diffraction (RED), precession electron diffraction tomography (PEDT), and continuous rotating electron diffraction (cRED). For example, in material structure analysis, for complex crystal structures, it can accurately simulate their electron diffraction intensity, providing reliable data for subsequent structural analysis.

[0018] Multiple factors are considered: During the simulation process, the structure factor of the sample is accurately calculated, and information such as electron wavelength, rotation axis direction, diffraction frame number, zone axis direction, sample thickness, and diffraction resolution are comprehensively considered to make the simulation results more consistent with reality. For example, when studying crystal materials with specific orientations, accurate information on the rotation axis direction and zone axis direction can ensure that the simulated diffraction intensity matches the actual situation.

[0019] 2. Computational efficiency:

[0020] Efficient zone axis sampling: Sampling along the zone axis is more efficient, sampling both rotation and precession dimensions simultaneously, and reducing the total number of samples by utilizing the phase difference between the starting points of adjacent precession rings. For example, in simulation tasks handling large amounts of data, this significantly reduces computational load and shortens computation time compared to traditional methods. For continuous rotating electron diffraction, precession electron diffraction tomography, and continuous rotating precession electron diffraction tomography, convergence can be achieved within 50, 100, and 500 samples per diffraction sheet, respectively, providing rapid and accurate results.

[0021] Avoiding redundant calculations: By setting the thickness to a negative number, the diffraction intensity of the chiral crystal and its enantiomers is calculated in one step, avoiding repeated matrix diagonalization processes and effectively improving computational efficiency. For example, when studying the crystal structure of chiral drug molecules, there is no need to repeatedly calculate the chiral enantiomers, saving a significant amount of computational resources and time.

[0022] 3. Scope of application and functional expansion:

[0023] Simulates multiple thicknesses: It can simultaneously simulate the diffraction intensity of multiple thicknesses, broadening the applicability of the simulation. When studying the electron diffraction characteristics of samples with different thicknesses, it is not necessary to perform multiple simulations separately; results for multiple thicknesses can be obtained in a single operation, improving research efficiency.

[0024] Kinematic data merging: The trapezoidal method can be used to integrate the excitation error and merge the kinematic data of each frame of diffraction into a set of hkl intensities, which further enriches the means of data processing and analysis and provides more possibilities for in-depth research on the structure and properties of materials. Attached Figure Description

[0025] Figure 1 The relative deviations between the electron diffraction intensities of PbSO4 in different directions and the theoretical reference values ​​in Example 1.

[0026] Figure 2 Example of the trapezoidal integral method for kinematic reduction of dynamic intensity in Example 1.

[0027] Figure 3 In Example 2, the L-alanine thickness was set to... The relative deviation between the calculated values ​​of the time and its enantiomer at different thicknesses.

[0028] Figure 4 In Example 3, the zone axis errors of the eight crystals using different diffraction methods caused relative deviations from the standard intensity.

[0029] Figure 5 This is a schematic diagram of the sampling strategy along the zone axis during the three-dimensional electron diffraction dynamics intensity simulation, illustrating the spatial relationship between the rotation trajectory of the goniometer, the electron beam precession direction, and the sample position. Detailed Implementation

[0030] 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. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0031] Example 1

[0032] The simulation calculation and kinematic reduction steps for the rotational precession electron diffraction intensity of lead sulfate (PbSO4) crystals along a specific rotation axis, with each frame representing 1° of rotation, are shown below:

[0033] S01: Read the atomic coordinates, temperature factor, and unit cell parameters of lead sulfate crystal, calculate its electron diffraction structure factor, calculate its rotation axis representation in Cartesian coordinates, and determine the zone axis index of the average position of each frame of electron diffraction.

[0034] S02: For the average zone axis index of each frame determined in S01, calculate the start and end positions of the goniometer rotation, and divide the rotation trajectory into 16 points. For each of these n sampling points, calculate the circumferential deviation angle as the precession angle. The 32 sampling points are used, and the starting position of each ring is offset from the previous ring by the golden ratio (0.618) intervals. The zone axis index corresponding to the above 16×32 sampling points is calculated respectively.

[0035] S03: Calculate the excitation error corresponding to the zone axis index of each sampling point calculated in S02, screen diffractions that meet the standard resolution and excitation error, construct the structure matrix, find the eigenvalues ​​and eigenvectors of the structure matrix, use the above results to calculate the form of the Bloch wave in the crystal and the conversion matrix with the plane wave, find the form of the emitted wave according to the sample thickness, convert it into a plane wave, and the square of the plane wave amplitude in the reciprocal direction is the diffraction intensity of a single sampling point. The average value of the 512 sampling points in each frame is recorded as the diffraction intensity of each frame.

[0036] S04: By integrating and normalizing the intensity of the same diffraction peak calculated on different frames with respect to the excitation error of the average position of each frame, the kinematically reduced continuous rotational precession electron diffraction tomography intensity can be obtained, which is represented as an hkl list.

[0037] The dynamic intensity obtained from the example calculation is compared with the theoretical reference intensity simulated 360×50 times in each frame in the precession and continuous rotation directions. The maximum value of the relative deviation is less than 10%, which can be regarded as convergence.

[0038] Example 2

[0039] The calculation of the electron diffraction dynamics intensities of chiral L-alanine and its enantiomers collected by different methods includes the following steps:

[0040] S01: Read the atomic coordinates, temperature factor, and unit cell parameters of the L-alanine crystal, calculate the structure factor of its electron diffraction, calculate the representation of its rotation axis in the Cartesian coordinate system, and determine the zone axis index of the average position of each frame of electron diffraction.

[0041] S02: Based on the average zone axis index of each frame determined in S01, calculate the sampling points of continuous rotation of the goniometer stage, electron beam precession and the combination of the two. The total number of samplings for the three are 50, 128 and 512, respectively.

[0042] S03: Calculate the excitation error corresponding to the zone axis index of each sampling point calculated in S02, screen diffractions that meet the standard resolution and excitation error, construct the structure matrix, solve the eigenvalues ​​and eigenvectors of the structure matrix, use the above results to calculate the form of the Bloch wave in the crystal and the transformation matrix with the plane wave, calculate the form of the emitted wave according to the sample thickness, convert it into a plane wave, where the sample thickness can be set to a negative value, the square of the plane wave amplitude corresponding to the enantiomer diffraction intensity in the reciprocal direction is the diffraction intensity of a single sampling point, and the average value of the sampling points in each frame is recorded as the diffraction intensity of each frame;

[0043] S04: Directly calculate the enantiomeric thickness of L-alanine. The diffraction intensities of each method are calculated, and their deviations from the intensities in SO3 are determined. It is proven that for the three methods, the deviation is consistent with the thickness set to... The calculated strengths are equal under the same conditions.

[0044] Examples were calculated for electron diffraction dynamics with thicknesses set to positive and negative values. It can be proven that, for chiral crystals, setting the thickness to a negative value calculates the diffraction intensity of its enantiomer. Therefore, it is not necessary to calculate the structure factor and structure matrix separately; the diffraction intensity of the chiral crystal and its enantiomer can be calculated in one step.

[0045] Example 3

[0046] The calculation of diffraction intensity for eight crystals, including sodium chloride and lead sulfate (PbSO4), along a specific rotation axis using different diffraction methods, including random errors in zone axis direction, includes the following steps:

[0047] S01: Read the atomic coordinates, temperature factors, and unit cell parameters of eight crystals, calculate their electron diffraction structure factors, calculate the representation of their rotation axes in Cartesian coordinates, and determine the zone axis index of the average position of each frame of electron diffraction. After obtaining the zone axis direction in Cartesian coordinates, deflect it in a random direction by a normal random angle within 0.05°, while retaining the case without deflection as the standard value.

[0048] S02: Based on the average zone axis index of each frame determined in S01, calculate the sampling points of continuous rotation of the goniometer stage, electron beam precession and the combination of the two. The total number of samplings for the three are 100, 360 and 180×50, respectively.

[0049] S03: Calculate the excitation error corresponding to the zone axis index of each sampling point calculated in S02, screen diffractions that meet the standard resolution and excitation error, construct the structure matrix, find the eigenvalues ​​and eigenvectors of the structure matrix, use the above results to calculate the form of the Bloch wave in the crystal and the transformation matrix with the plane wave, find the form of the emitted wave according to the sample thickness, convert it into a plane wave, and the square of the plane wave amplitude in the reciprocal direction is the diffraction intensity of a single sampling point. The average value of all sampling points in each frame is recorded as the diffraction intensity of each frame.

[0050] S04: Calculate the relative deviation between the standard value in S03 and the strength with shaft error.

[0051] The examples calculated the diffraction intensity containing zone axis errors under different diffraction methods. Compared with the standard intensity, the relative error of continuous rotating precession electron diffraction tomography was the smallest. This proves that the electron diffraction under the conditions of continuous rotation of the goniometer and electron beam precession has the smallest intensity error caused by zone axis error, and the calculation results are the most stable.

[0052] The above description is only a preferred embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any equivalent substitutions or modifications made by those skilled in the art within the scope of the technology disclosed in the present invention, based on the technical solution and inventive concept of the present invention, should be covered within the scope of protection of the present invention.

Claims

1. A method for efficiently and accurately simulating the intensity of three-dimensional electron diffraction dynamics, characterized in that, Includes the following steps: S01: Accurately calculate the structure factor of the sample and obtain information on electron wavelength, rotation axis direction, number of diffraction frames, zone axis direction of each frame, sample thickness, diffraction resolution, and specific diffraction methods. S02: Based on the frame directions obtained in S01, determine the total number of simulations for each frame of electron diffraction, calculate the zone axis direction when considering rotation and precession in each simulation, and calculate the corresponding excitation error. When considering rotation and precession simultaneously, treat rotation and precession as two independent variables. When sampling different precession rings, there is a custom interval between the starting position of each ring and the previous ring. This interval can be 0 or any input value. Random sampling of the two dimensions of rotation and precession is also supported. S03: Construct a structure matrix from the information obtained in S02, solve the characteristic equation and calculate the diffraction intensity using the Bloch wave method, and take the average value of the diffraction intensities of the directions contained in the corresponding diffraction frame to obtain the final intensity. When the thickness is set to a negative number, the result is consistent with its opposite for non-chiral structures, while for chiral structures, the diffraction intensity of its enantiomer is calculated. S04: The trapezoidal method is selected to integrate the excitation error, and the kinematics of the diffraction data of each frame calculated in S03 are further combined into a set of hkl intensities.

2. The method for efficiently and accurately simulating the intensity of three-dimensional electron diffraction dynamics according to claim 1, characterized in that: The zone axis direction is simulated using a three-dimensional unit vector; the zone axis vector is rotated using the Rodrigues formula; the zone axis direction is sampled using two dimensions: rotation and precession; between different rotation and precession sampling, there is an adjustable phase difference at the starting point or random sampling is performed; the Bloch wave method is used to calculate the single-sheet electron diffraction intensity; the diffraction intensity of the chiral enantiomer is calculated by setting a negative thickness. The intensity of the kinematic reduction is obtained by integrating using the trapezoidal method.

3. A method for efficiently and accurately simulating the intensity of three-dimensional electron diffraction dynamics according to claim 1 or 2, characterized in that: The customized interval is based on the golden ratio.

4. The method for efficiently and accurately simulating the intensity of three-dimensional electron diffraction dynamics according to claim 1, characterized in that: The specific diffraction techniques include automated electron diffraction tomography (ADT), rotating electron diffraction (RED), precession electron diffraction tomography (PEDT), continuous rotating electron diffraction (cRED), and continuous rotating precession electron diffraction tomography (cPEDT).

5. A method for efficiently and accurately simulating the intensity of three-dimensional electron diffraction dynamics according to claim 1 or 2, characterized in that: For continuous rotating electron diffraction, precession electron diffraction tomography, and continuous rotating precession electron diffraction tomography, convergence can be achieved for a single diffraction pattern within 50, 100, and 500 samples, respectively.

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