Method for efficiently and accurately simulating three-dimensional electron diffraction kinetics intensity

Abstract

The invention discloses a method for efficiently and accurately simulating three-dimensional electron diffraction dynamics intensity, and aims to solve the problems of low simulation calculation efficiency and insufficient precision in the prior art. According to the method, a reciprocal vector is rotated by adopting a Rodrigues formula through optimizing a reciprocal space sampling strategy, and a user-defined phase difference or random sampling is introduced in two dimensions of rotation and precession, so that the sampling frequency is remarkably reduced. And meanwhile, the diffraction intensity is accurately calculated by utilizing a Bloch wave method, and the diffraction intensity of the chiral crystal and the enantiomer thereof is calculated at one time by setting the negative thickness, so that repeated calculation is avoided. The invention supports a plurality of diffraction means, including electron diffraction automatic tomography (ADT), rotating electron diffraction (RED), precession electron diffraction tomography (PEDT), continuous rotating electron diffraction (cRED) and continuous rotating precession electron diffraction tomography (cPEDT), and can achieve convergence within 50, 100 and 500 times of sampling of single diffraction. According to the method, the calculation efficiency is improved, the application range of simulation is widened, and reliable technical support is provided for material structure analysis.

Description

Technical Field

[0001] The present invention relates to the technical field of three-dimensional electron diffraction dynamic intensity simulation, and in particular to a method for performing efficient and accurate crystal zone axis reciprocal space sampling by utilizing golden section phase difference, thereby performing computational simulation quickly and accurately. Background Art

[0002] Three-dimensional electron diffraction technology is a submicron crystal structure analysis technology that has developed rapidly in recent years. However, the existence of dynamic effects has caused great difficulties in the structure analysis and refinement of three-dimensional electron diffraction. Accurate simulation and calculation of the dynamic intensity of electron diffraction is the basis for making full use of the information contained in electron diffraction and effectively refining it. The existing structure refinement method is based on the Bloch wave method, which linearly samples the trajectory of the electron diffraction crystal axis. It can simulate and refine the data collection method of the continuous change of the electron beam or the goniometer alone, obtain the precise structural information of the sample, and determine the absolute configuration of chiral molecules, and has been widely used. However, the following problems still exist:

[0003] For the continuous rotation and precession electron diffraction tomography method that combines the continuous rotation of the goniometer with the precession of the incident electron beam, there is no targeted simulation method, and it is impossible to further study or even refine its numerical properties due to the serious oversampling of the crystal zone axis during data collection, the number of samples in the simulation process is too large, and the calculation is limited. The calculation and refinement process for the chiral structure is also cumbersome, and it is impossible to perform a fast one-time calculation of the enantiomer.

[0004] Therefore, an efficient and accurate three-dimensional electron diffraction dynamic intensity simulation method is urgently needed to solve the above problems. Summary of the invention

[0005] In view of the shortcomings of the prior art, the present invention proposes a method for efficiently and accurately simulating the three-dimensional electron diffraction dynamic intensity. The method significantly improves the efficiency and accuracy of the simulation by optimizing the reciprocal space sampling strategy, introducing phase difference or random sampling strategy, and using the Bloch wave method to calculate the diffraction intensity.

[0006] The present invention is achieved by the following steps:

[0007] S01: Accurately calculate the structure factor of the sample and obtain the electron wavelength, rotation axis direction, diffraction frame number, crystal band axis direction of each frame, sample thickness, diffraction resolution, and specific diffraction method information;

[0008] S02: According to the direction of each frame obtained in S01, determine the total number of simulations of electron diffraction for each frame, calculate the direction of the crystal zone axis when considering rotation and precession in each simulation, and calculate the corresponding excitation error. When considering rotation and precession at the same time, they are 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. It also supports random sampling of the two dimensions of rotation and precession.

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

[0010] S04: Select to integrate the excitation error using the trapezoidal method, and further kinematically combine the diffraction data of each frame calculated in S03 into a set of hkl intensities.

[0011] Furthermore, the simulation method of the three-dimensional electron diffraction dynamic intensity adopts a three-dimensional unit vector to simulate the crystal band axis direction; uses the Rodrigues formula to rotate the crystal band axis vector; adopts two dimensions of rotation and precession to sample the crystal band axis direction; between different rotation and precession samples, there is an adjustable phase difference at the starting point or random sampling is performed; uses the Bloch wave method to calculate the single electron diffraction intensity; calculates the diffraction intensity of the chiral enantiomer by setting a negative thickness; and uses the trapezoidal method to integrate to obtain the kinematically reduced intensity.

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

[0013] Furthermore, the specific diffraction means include automatic electron diffraction tomography (ADT), rotational electron diffraction (RED), precession electron diffraction tomography (PEDT), continuous rotational electron diffraction (cRED) and continuous rotation precession electron diffraction tomography (cPEDT).

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

[0015] Compared with the prior art, the present invention has the following beneficial effects:

[0016] 1. Simulation accuracy:

[0017] Accurate simulation of multiple diffraction intensities: For the first time, the accurate simulation of the intensity of continuous rotation and precession electron diffraction tomography was achieved, and the intensity of multiple specific diffraction methods such as automatic electron diffraction tomography (ADT), rotation electron diffraction (RED), precession electron diffraction tomography (PEDT), and continuous rotation electron diffraction (cRED) can be accurately calculated. For example, in material structure analysis, for complex crystal structures, the electron diffraction intensity can be accurately simulated to provide reliable data for subsequent structural analysis.

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

[0019] 2. Computational efficiency:

[0020] Efficient sampling in the crystal zone axis direction: The sampling in the crystal zone axis direction is more efficient, and the rotation and precession dimensions are sampled at the same time, and the total number of sampling times is reduced by the phase difference between the starting points of adjacent precession rings. For example, when dealing with simulation tasks with large amounts of data, compared with traditional methods, it can significantly reduce the amount of calculation and shorten the calculation time. For continuous rotation electron diffraction, precession electron diffraction tomography, and continuous rotation precession electron diffraction tomography, convergence can be achieved within 50, 100, and 500 samplings of a single diffraction, respectively, and accurate results can be obtained quickly.

[0021] Avoid repeated calculations: By setting the thickness to a negative number, the diffraction intensity of the chiral crystal and its enantiomer is calculated at one time, avoiding repeated matrix diagonalization processes and effectively improving the calculation efficiency. For example, when studying the crystal structure of chiral drug molecules, there is no need to repeatedly calculate the chiral enantiomers, saving a lot of computing resources and time.

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

[0023] Multiple thicknesses can be simulated: The diffraction intensity of multiple thicknesses can be simulated at the same time, which broadens the scope of application of the simulation. When studying the electron diffraction characteristics of samples of different thicknesses, there is no need to perform multiple simulations separately. The results of multiple thicknesses can be obtained in one operation, which improves the research efficiency.

[0024] Kinematically merged data: You can choose to use the trapezoidal method to integrate the excitation error and kinematically merge the calculated diffraction data of each frame into a set of HKL intensities, further enriching the means of data processing and analysis, and providing more possibilities for in-depth research on the structure and properties of materials. BRIEF DESCRIPTION OF THE DRAWINGS

[0025] Figure 1 : The relative deviation of the PbSO4 electron diffraction intensity in different directions in Example 1 from the theoretical reference value.

[0026] Figure 2 : Example of the trapezoidal integration method for kinematic reduction of kinetic intensity in Example 1.

[0027] Figure 3 : In Example 2, the thickness of L-alanine is set to The relative deviation of the calculated value of different thickness of its enantiomer.

[0028] Figure 4 : The crystal band axis errors of the eight crystals in different diffraction methods in Example 3 cause relative deviations from the standard intensity.

[0029] Figure 5 : Schematic diagram of the sampling strategy in the crystal band axis direction during the three-dimensional electron diffraction dynamic intensity simulation, showing the spatial relationship between the goniometer rotation trajectory, the electron beam precession direction and the sample position. DETAILED DESCRIPTION

[0030] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0031] Example 1

[0032] The simulation calculation and kinematic reduction steps of the electron diffraction intensity of the lead sulfate (PbSO4) crystal along a specific rotation axis and one frame per 1° are as follows:

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

[0034] S02: For each frame average crystal zone axis index determined in S01, calculate the start and end positions of the angle measuring stage rotation, and evenly divide the rotation trajectory to take 16 points. For each of these n sampling points, calculate the circular deviation angle as the precession angle. 32 sampling points of , where the starting point of each ring is offset by the golden ratio (0.618) divisions relative to the previous ring, and the crystal zone axis index corresponding to the above 16×32 sampling points is calculated respectively;

[0035] S03: Calculate the corresponding excitation error for the crystal zone axis index of each sampling point calculated in S02, select the diffraction that meets the standard of resolution and excitation error, construct the structure matrix, calculate the eigenvalue and eigenvector of the structure matrix, use the above results to calculate the form of Bloch wave in the crystal and the conversion matrix with plane wave, calculate the form of the incident wave according to the sample thickness, convert it into a plane wave, the square of the plane wave amplitude corresponding to the reciprocal direction is the diffraction intensity of a single sampling point, and take the average value of 512 sampling points in each frame as the diffraction intensity of each frame;

[0036] S04: The intensity calculated for the same diffraction peak in different frames is integrated and normalized with respect to the excitation error of the average position of each frame, so that the kinematically restored continuous rotation precession electron diffraction tomography intensity can be obtained, which is expressed as a hkl list.

[0037] The dynamic intensity calculated by the example 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 intensity collected by different methods for chiral crystal L-alanine and its enantiomers includes the following steps:

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

[0041] S02: Based on the average crystal zone axis index of each frame determined in S01, the sampling points of the continuous rotation of the goniometer stage, the precession of the electron beam and the combination of the two are calculated, and the total number of sampling times of the three is 50 times, 128 times and 512 times respectively;

[0042] S03: Calculate the corresponding excitation error for the crystal band axis index of each sampling point calculated in S02, select the diffraction that meets the standard of resolution and excitation error, construct the structure matrix, solve the eigenvalue and eigenvector of the structure matrix, use the above results to calculate the form of Bloch wave in the crystal and the conversion matrix with plane wave, calculate the form of incident wave according to the sample thickness, and convert it into plane wave, wherein the sample thickness can be set to a negative value, corresponding to the diffraction intensity of the enantiomer, the square of the plane wave amplitude 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: Direct calculation of the enantiomeric thickness of L-alanine is The diffraction intensity of each method is calculated, and its deviation from the intensity in S03 is calculated. It is proved that for the three methods, its difference with the thickness setting is The calculated intensities are equal under these conditions.

[0044] The example calculates the electron diffraction dynamic intensity when the thickness is set to positive and negative values. It can be proved that for chiral crystals, when the thickness is set to negative, the diffraction intensity of its enantiomer is calculated. Therefore, it is not necessary to calculate the structure factor and structure matrix separately, and the diffraction intensity of the chiral crystal and its enantiomer can be calculated at one time.

[0045] Example 3

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

[0047] S01: Read the atomic coordinates, temperature factors and unit cell parameters of eight crystals, calculate the structure factor of their electron diffraction, calculate the representation of their rotation axis in the Cartesian coordinate system, and determine the crystal zone axis index of the average position of each frame of electron diffraction. After obtaining the crystal zone axis direction in the Cartesian coordinate system, deflect it in a random direction by a normal random angle within 0.05°, and keep the non-deflected situation as the standard value.

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

[0049] S03: Calculate the corresponding excitation error for the crystal band axis index of each sampling point calculated in S02, screen the diffraction that meets the standards of resolution and excitation error, construct the structure matrix, calculate the eigenvalues ​​and eigenvectors of the structure matrix, and use the above results to calculate the form of the Bloch wave in the crystal and the conversion matrix with the plane wave. According to the sample thickness, the form of the incident wave is calculated and converted into a plane wave. The square of the plane wave amplitude corresponding to 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 rotation axis error.

[0051] The example calculated the diffraction intensity with crystal zone axis error under different diffraction methods. Compared with the standard intensity, the relative error of continuous rotation and precession electron diffraction tomography is the smallest. It is proved that the intensity error caused by the zone axis error is the smallest when the goniometer is continuously rotated and the electron beam is precessed, and the calculation result is the most stable.

[0052] The above description is only a preferred specific implementation manner of the present invention, but the protection scope of the present invention is not limited thereto. Any technician familiar with the technical field can make equivalent replacements or changes according to the technical scheme and inventive concept of the present invention within the technical scope disclosed by the present invention, which should be covered by the protection scope of the present invention.

Claims

1. A method for efficiently and accurately simulating the three-dimensional electron diffraction dynamics intensity, characterized in that: The following steps are involved: S01: Accurately calculate the structure factor of the sample and obtain the electron wavelength, rotation axis direction, diffraction frame number, crystal band axis direction of each frame, sample thickness, diffraction resolution, and specific diffraction method information; S02: According to the direction of each frame obtained in S01, determine the total number of simulations of electron diffraction for each frame, calculate the direction of the crystal zone axis when considering rotation and precession in each simulation, and calculate the corresponding excitation error. When considering rotation and precession at the same time, they are 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. It also supports random sampling of the two dimensions of rotation and precession. S03: construct a structure matrix based on the information obtained in S02, solve the characteristic equation and calculate the diffraction intensity by the Bloch wave method, and take the average value of the diffraction intensity in the direction contained in the corresponding diffraction frame to obtain the final intensity. When the thickness is set to a negative number, the result for the non-chiral structure is consistent with its opposite number, and for the chiral structure, the diffraction intensity of its enantiomer is calculated; S04: Select to integrate the excitation error using the trapezoidal method, and further kinematically combine the diffraction data of each frame calculated in S03 into a set of hkl intensities.

2. The method for simulating three-dimensional electron diffraction dynamic intensity according to claim 1, characterized in that: Use three-dimensional unit vectors to simulate the crystal band axis direction; use Rodrigues formula to rotate the crystal band axis vector; use rotation and precession to sample the crystal band axis direction; between different rotation and precession sampling, there is an adjustable phase difference at the starting point or random sampling; use Bloch wave method to calculate the single electron diffraction intensity; calculate the diffraction intensity of chiral enantiomers by setting negative thickness; The strength of the kinematic reduction is obtained by integration using the trapezoidal method.

3. The method for simulating three-dimensional electron diffraction dynamic intensity according to claim 1 or 2, characterized in that: The customized interval is the golden ratio.

4. The method for simulating three-dimensional electron diffraction dynamic intensity according to claim 1, characterized in that: The specific diffraction means include automated electron diffraction tomography (ADT), rotational electron diffraction (RED), precession electron diffraction tomography (PEDT), continuous rotational electron diffraction (cRED) and continuous rotation precession electron diffraction tomography (cPEDT).

5. The method for simulating three-dimensional electron diffraction dynamics intensity according to any one of claims 1 to 4, characterized in that: For continuous rotation electron diffraction, precession electron diffraction tomography and continuous rotation precession electron diffraction tomography, convergence can be achieved within 50, 100 and 500 sampling times for a single diffraction, respectively.

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