Method for reconstructing three-dimensional atomic configuration of special interface

Abstract

The invention provides a method for reconstructing a three-dimensional atomic configuration of a special interface, and the method comprises the steps: combining actual representation data with theoretical calculation, generating a theoretical template, and carrying out the matching with an actual image, thereby improving the precision of atomic coordinate extraction; the position of each atom is calibrated through Gaussian fitting, and it is ensured that the precision reaches the sub-angstrom scale; atomic phase information in a two-dimensional transmission electron microscope image is utilized, and a direction matrix and coordinate transformation are combined to realize reconstruction from a two-dimensional atomic projection image to a three-dimensional crystal structure.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of three-dimensional atomic structure reconstruction, and particularly relates to a method for reconstructing three-dimensional atomic configuration of special interface. BACKGROUND

[0002] Accurate extraction of two-dimensional atomic phase projection information: existing transmission electron microscopy (TEM) technology faces problems such as image noise, optical aberration and electron beam scattering when obtaining high-resolution two-dimensional atomic structure images, which will affect the accurate extraction of atomic coordinates. Existing methods often cannot accurately locate the atomic positions under the influence of these factors, so how to accurately extract atomic coordinates from two-dimensional atomic projection images under the influence of noise and imaging distortion is still a technical problem.

[0003] Accurate positioning of atomic coordinates in multi-layer structure: for complex materials containing multi-layer structure, existing technology cannot distinguish the atoms in the overlapping layers in the two-dimensional projection image, resulting in inaccurate positioning of atomic coordinates in different layers. How to accurately distinguish and locate the coordinates of atoms in each layer in the multi-layer overlapping projection image is one of the current technical difficulties.

[0004] Automatic and high-precision three-dimensional atomic structure reconstruction: existing three-dimensional reconstruction technology usually relies on manual analysis and processing of two-dimensional projection data, which is tedious and prone to human error. In addition, how to convert the atomic coordinates obtained from the two-dimensional projection image into accurate three-dimensional atomic structure through high-precision matching and calibration algorithm, while improving the automation level of the whole process, is also a problem to be solved in the current technology. SUMMARY

[0005] In view of the defects and deficiencies of the prior art, the application provides a two-dimensional atomic coordinate acquisition and three-dimensional space reconstruction method based on spherical aberration corrected transmission electron microscopy (AC-TEM) characterization data and theoretical crystal structure calculation.

[0006] The technical scheme adopted by the application to solve the technical problems is as follows:

[0007] A method for reconstructing three-dimensional atomic configuration of special interface: combining actual characterization data with theoretical calculation, generating a theoretical template and matching it with the actual image to improve the accuracy of atomic coordinate extraction; using Gaussian fitting to calibrate the position of each atom to ensure that the accuracy reaches the sub-angstrom scale; using the atomic phase information in the two-dimensional transmission electron microscopy image, combining the direction matrix and coordinate transformation to realize the reconstruction from the two-dimensional atomic projection image to the three-dimensional crystal structure.

[0008] Further, the spherical aberration corrected transmission electron microscope is used to collect the atomic structure image of the sample and perform structure characterization to obtain the two-dimensional atomic projection image of the sample.

[0009] Obtaining crystal structure parameters matched with the sample, calculating fractional coordinates of each atom based on the cell parameters and atomic coordinates through symmetry operation rules, and converting the fractional coordinates into actual cell coordinates through a stretching and rotation matrix;

[0010] Simulating the HAADF / iDPC image of the template according to the cell coordinates and atomic numbers;

[0011] Identifying the matching region by calculating the cross-correlation between the template and the target image, assigning the corresponding atomic coordinates according to the position of the matching region, and performing Gaussian fitting on the target image to realize atomic position calibration;

[0012] After all the atomic positions are calibrated, the final atomic coordinate data is exported, and the exported data at least includes the cell size and atomic coordinates.

[0013] Further, the specific process of calculating the fractional coordinates of each atom based on the cell parameters and atomic coordinates through symmetry operation rules, and converting the fractional coordinates into actual cell coordinates through a stretching and rotation matrix is as follows:

[0014] Calculating the direction matrix of the crystal orientation through the characterization angle and the crystal orientation of the sample, the direction matrix is used to describe the crystal structure of the sample under different orientations, and the cell coordinates of the crystal are converted to the current characterization direction;

[0015] According to the crystal direction matrix and the cell parameters, the theoretical atomic coordinates of the sample under the current orientation are calculated; then the theoretical cell coordinates are converted to the spatial coordinate system under the actual characterization direction to obtain the atomic distribution information related to the current orientation; through the original fractional coordinates of the atoms and the symmetry operation of the sample, the complete fractional coordinates of the sample under the theoretical cell are obtained.

[0016] Periodically expanding the fractional coordinates and retaining the fractional coordinates within a specified range; converting the atomic fractional coordinates in the cell coordinate system into the rectangular coordinate system in the actual space.

[0017] Further, the conversion of the atomic fractional coordinates in the cell coordinate system into the rectangular coordinate system in the actual space specifically uses a matrix transformation formula M to map the position in the cell coordinate system to the spatial coordinate system:

[0018] According to the cell parameters a, b, c, α, β, γ of the sample, a conversion matrix M is constructed;

[0019] a = (a, 0, 0)

[0020] b = (b cos γ, b sin γ, 0)

[0021]

[0022] The cell coordinates are converted to the spatial rectangular coordinate system using the direction matrix R and the conversion matrix M:

[0023] Coordinate 空间直角坐标系 = R·M·Coordinate 晶胞坐标系 .

[0024] Further, the calibrating the position of each atom by using Gaussian fitting specifically includes:

[0025] The atomic coordinates and atomic number information obtained by theoretical calculation are used to generate a theoretical HAADF or iDPC image template of the sample in a given orientation by using a Gaussian fitting method;

[0026] The generated theoretical template image is matched with the actual target image to identify the region in the image that meets the template characteristics, so as to determine the accurate position of the atom in the sample: the atomic position in the actual image is preliminarily located by using a normalized cross-correlation calculation;

[0027] According to the template matching result, the coordinate position of each atom in the target image is preliminarily extracted as an initial estimate, and a Gaussian fitting algorithm is used to accurately calibrate the coordinate of each preliminarily extracted atom.

[0028] Further, the atomic coordinates and atomic number information obtained by theoretical calculation are used to generate a theoretical HAADF or iDPC image template of the sample in a given orientation by using a Gaussian fitting method;

[0029] In the HAADF or iDPC image, the imaging intensity is positively correlated with the atomic number z of the atom; the influence area of each atom in the image is simulated by using a Gaussian fitting method; the form of the Gaussian function is set as G(x, y), and the image intensity is represented as:

[0030]

[0031] Wherein, x and y are the coordinates on the two-dimensional plane; x0 and y0 are the coordinates of the center of the Gaussian function; and sigma is the standard deviation;

[0032] Based on the above formula, a Gaussian distribution is generated for each atom; different types of atoms generate different intensity distributions in the simulated image according to their atomic number Z and the value of the fitting control factor r; and the Gaussian distributions of all atoms are accumulated to obtain the overall theoretical template image;

[0033] Intensity = G(x, y)·Z r

[0034] Wherein, G(x, y) is a two-dimensional Gaussian function, used to describe the intensity distribution of atoms; Z is the atomic number; r is a fitting factor, used to adjust the contribution of different types of atoms to the imaging intensity;

[0035] By adjusting the value of the fitting factor r, the generation of the template is optimized to fit the image characteristics of the actual sample.

[0036] Further, the generated theoretical template image is matched with the actual target image to identify the region in the image that meets the template characteristics, thereby determining the precise position of the atoms in the sample:

[0037] By normalizing the cross-correlation, the region in the target image similar to the template image is found:

[0038]

[0039] Wherein, R(i, j) represents the matching degree of the template image at the target image (i, j) position; f(x, y) is the gray value of the target image; t(x, y) is the gray value of the template image; And are the average values of images f and t, respectively;

[0040] By calculating the cross-correlation value R(i, j), the region in the target image that best meets the template characteristics is found;

[0041] In the calculated cross-correlation map, the peak points are found, and whether the peak points represent the atomic positions are verified:

[0042] If multiple peak points are too close, by threshold judgment, the repeated regions are screened and discarded to avoid repeated identification of the same region;

[0043] overlap area =max(0,x min2 -x max1 )×max(0,y min2 -y max1 )

[0044] The above formula indicates that when the overlap of the repeated regions exceeds the set threshold, the repeated peaks in the repeated regions are discarded to avoid redundancy;

[0045] By matching, all regions in the target image that meet the template characteristics are obtained; the peak points of the regions represent the positions of the atoms in the sample.

[0046] Further, according to the template matching result, the coordinate position of each atom in the target image is preliminarily extracted as an initial estimate, and a Gaussian fitting algorithm is used to accurately calibrate each preliminarily extracted atomic coordinate:

[0047] For each preliminary extracted atomic coordinate, a small local area around it is selected as the target area for fitting; the size of the area is adjusted according to the type of the atom and the lattice environment it is in to ensure that the fitting range can cover the entire atomic signal;

[0048] In the selected local area, a two-dimensional Gaussian function is used for fitting to obtain the accurate center position of the atom; the function form of the Gaussian fitting is:

[0049]

[0050] Where: A is the background intensity; B is the peak intensity; (C, D) is the center position; ω1 and ω2 are the widths along the x and y directions; the center position of each atom is calibrated by Gaussian fitting to an accuracy of sub-angstrom scale.

[0051] Compared with the prior art, the present application and its preferred schemes improve the reconstruction efficiency and accuracy of the three-dimensional atomic configuration of the unit cell structure. The core innovations include: combining actual characterization data with theoretical calculations, improving the accuracy of atomic coordinate extraction through simulation and matching; using Gaussian fitting to calibrate the atomic position to ensure an accuracy of sub-angstrom scale; ultimately realizing the reconstruction from two-dimensional atomic projection images to three-dimensional crystal structure.

[0052] The main innovations and advantages include:

[0053] The innovative multi-step process combines characterization and simulation: quantitative matching of actual characterization data obtained by a spherical aberration-corrected transmission electron microscope with theoretical simulation images can efficiently and accurately obtain and accurately calibrate atomic coordinates. This method is more accurate than traditional analysis relying on single characterization data, significantly improving the efficiency and accuracy of data processing.

[0054] High-precision fitting: after preliminary acquisition of atomic coordinates, further accurate calibration is performed using Gaussian fitting. This process can significantly improve the accuracy of atomic coordinates.

[0055] Realize two-dimensional to three-dimensional space reconstruction: the core innovation of this method is to reconstruct the crystal structure in three-dimensional space through the atomic phase information in the two-dimensional transmission electron microscope image. This technology solves the problem of accurately restoring three-dimensional structures from two-dimensional images at the atomic scale.

[0056] The present application is applied to the fields of structure analysis of crystal materials, calculation of atomic distribution, simulation of crystal growth, etc., and is suitable for scenarios of accurate analysis of complex crystal structures. It effectively combines characterization techniques, image processing, theoretical calculations, and high-precision fitting algorithms to realize an efficient process from characterization to modeling. BRIEF DESCRIPTION OF DRAWINGS

[0057] The application is further described in detail below with reference to the drawings and specific embodiments.

[0058] Figure 1 WCΣ2 grain boundary iDPC image for the embodiment of the application;

[0059] Figure 2 Visual drawing using MATLAB for the embodiment of the application Atomic coordinate diagram;

[0060] Figure 3 Visual drawing using MATLAB for the embodiment of the application Atomic coordinate diagram;

[0061] Figure 4 Template example generated by adjusting the value of fitting factor r for optimizing template generation for the embodiment of the application Figure 1 ;

[0062] Figure 5 Template example generated by adjusting the value of fitting factor r for optimizing template generation for the embodiment of the application Figure 2 ;

[0063] Figure 6 Correlation matching diagram of template example 1 for the embodiment of the application;

[0064] Figure 7 Recognition area diagram of template example 1 for the embodiment of the application;

[0065] Figure 8 Correlation matching diagram of template example 2 for the embodiment of the application;

[0066] Figure 9 Recognition area diagram of template example 2 for the embodiment of the application;

[0067] Figure 10 Atomic coordinate preliminary assignment diagram for the embodiment of the application;

[0068] Figure 11 Atomic coordinate accurate calibration diagram for the embodiment of the application;

[0069] Figure 12 WCΣ2 grain boundary reconstruction model - characterization direction diagram for the embodiment of the application;

[0070] Figure 13 WCΣ2 grain boundary reconstruction model - vertical characterization direction diagram for the embodiment of the application;

[0071] Figure 14 Overall flowchart for the embodiment of the application. DETAILED DESCRIPTION

[0072] In order to make the features and advantages of the present application more apparent, the following detailed examples are given, described in detail as follows.

[0073] It should be noted that the following detailed description is exemplary in nature and is intended to provide further description of the application. Unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this application belongs.

[0074] It should be noted that the terms used herein are merely for the purpose of describing specific embodiments and are not intended to limit the exemplary embodiments according to the present application. As used herein, the singular form is intended to include the plural form unless the context clearly indicates otherwise, and it should also be understood that the terms "comprise" and / or "include" as used herein indicate the presence of the features, steps, operations, devices, components and / or combinations thereof.

[0075] The embodiments of the present application realize the reconstruction of the special interface three-dimensional atomic configuration by the following steps:

[0076] Atomic scale characterization of spherical aberration-corrected transmission electron microscopy:

[0077] Firstly, atomic scale characterization of the target sample is performed, and high-resolution two-dimensional atomic structure projection images of the sample are collected by using spherical aberration-corrected transmission electron microscopy (AC-TEM). By using spherical aberration correction technology, the aberration in the image can be greatly reduced, so that the imaging of the atomic position is more clear and accurate. These high-resolution two-dimensional projection images provide important experimental basis data for subsequent three-dimensional reconstruction.

[0078] Figure 1 An example of the iDPC image of the WCΣ2 grain boundary.

[0079] Cell parameter acquisition:

[0080] After the sample characterization is completed, the cell parameters and atomic information of the crystal are obtained by reading the crystal information file (such as CIF file) of the sample. The specific steps are as follows:

[0081] The CIF file of the WC sample is read using MATLAB, and the cell constants, atomic species, symmetry operations and initial positions of the atoms contained therein are extracted. These data will be used as the basis information for subsequent theoretical atomic coordinate calculation.

[0082] The extracted cell parameters include the length and angle information of the cell, for example:

[0083] Cell parameters:

[0084] _cell_length_a 2.902(1)

[0085] _cell_length_b 2.902(1)

[0086] _cell_length_c 2.831(1)

[0087] _cell_angle_alpha 90.

[0088] _cell_angle_beta 90.

[0089] _cell_angle_gamma 120.

[0090] Atom species and their original fractional coordinates: These coordinates describe the relative position of each atom in the unit cell, for example:

[0091] Atom information:

[0092] W1: Tungsten atom, fractional coordinates (0, 0, 0), occupancy 1.0.

[0093] C1: Carbon atom, fractional coordinates (0.6667, 0.3333, 0.5), occupancy 1.0.

[0094] _atom_site_label

[0095] _atom_site_type_symbol

[0096] _atom_site_symmetry_multiplicity

[0097] _atom_site_Wyckoff_symbol

[0098] _atom_site_fract_x

[0099] _atom_site_fract_y

[0100] _atom_site_fract_z

[0101] _atom_site_occupancy

[0102] _atom_site_attached_hydrogens

[0103] W1 W0+1a 0001.0

[0104] C1 C0+1f0.66670.33330.51.0

[0105] Symmetry operation: the symmetry operation rules of the sample extraction, which clearly shows the atomic distribution in different symmetry positions. For example, the symmetry operation of WC sample includes the following:

[0106] _symmetry_equiv_pos_site_id

[0107] _symmetry_equiv_pos_as_xyz

[0108] 1' x, x-y, -z'

[0109] 2' -x+y, y, -z'

[0110] 3' -y, -x, -z'

[0111] 4' x, x-y, z'

[0112] 5' -x+y, y, z'

[0113] 6' -y, -x, z'

[0114] 7' -x+y, -x, -z'

[0115] 8' -y, x-y, -z'

[0116] 9' x, y, -z'

[0117] 10' -x+y, -x, z'

[0118] 11' -y, x-y, z'

[0119] 12' x, y, z'

[0120] These symmetry operations describe the spatial symmetry in the crystal structure, which is used to generate the theoretical positions of all atoms, and is one of the core steps to achieve three-dimensional structure reconstruction.

[0121] Calculation of direction matrix of crystal orientation:

[0122] By knowing the characterization angle and crystal orientation of the sample, the corresponding direction matrix can be calculated. This direction matrix is used to convert the unit cell coordinate system of the crystal to the current characterization direction, so that subsequent theoretical calculations can be consistent with the actual characterization data. In order to accurately describe the crystal orientation, the grain projection vector and upward vector of Vesta software are used to determine the orientation of the sample.

[0123] Example analysis: for WCΣ2 grain boundary, the crystal orientations of the two sides of the grain are known, which are

[0001] and The corresponding cell orientation matrix (Orientation Matrix) can be generated by Vesta software:

[0124] Direction matrix R1 corresponds to

[0001] Orientation:

[0125]

[0126] Direction matrix R2 corresponds to Orientation:

[0127]

[0128] These direction matrices are used to describe the crystal structure of the sample in different orientations, and to convert the cell coordinates of the crystal to the current observation direction.

[0129] Theoretical coordinate calculation:

[0130] According to the known crystal direction matrix and cell parameters, the theoretical atomic coordinates of the sample in the current orientation are calculated. This includes converting from the theoretical cell coordinate system to the spatial coordinate system in the actual characterization direction to obtain atomic distribution information related to the current orientation.

[0131] 1. Atomic fraction coordinate calculation based on symmetry operation

[0132] Through the original fraction coordinates of atoms and the symmetry operation of the sample, the complete fraction coordinates of the sample in the theoretical cell can be obtained. The following is the specific calculation steps of WC sample as an example:

[0133] Original initial fraction coordinates:

[0134] Tungsten atom (W): (0, 0, 0)

[0135] Carbon atom (C): (0.6667, 0.3333, 0.5)

[0136] Symmetry operation: The symmetry operation of the sample describes how to generate equivalent atomic positions in the crystal structure. For example, for WC, the symmetry operation includes:

[0137] 'x, x-y, -z', '-x+y, y, -z', '-y, -x, -z', 'x, x-y, z', etc., a total of 12 symmetry operations.

[0138] Calculation result: By bringing the original fraction coordinates into these symmetry operations, the complete fraction coordinates of the atoms in the cell can be obtained.

[0139] For example:

[0140] Symmetry operation result of W atom: (0, 0, 0).

[0141] Symmetry operations on C atoms: (0.667, 0.333, 0.500), (0.667, 0.333, -0.500), (-0.333, 0.333, 0.500), (-0.333, 0.333, -0.500), (-0.333, -0.667, 0.500), (-0.333, -0.667, -0.500)

[0142] 2. Periodic extension and cell extension

[0143] In order to accurately describe the repetition in the crystal structure, the fractional coordinates obtained above are periodically extended, and the fractional coordinates within the specified range are retained. For example, the extension is carried out in the [0, n] [0, n] [0, n] interval, so as to obtain the fractional coordinates of the atoms extended by n periods. This process can facilitate the subsequent steps to better describe the crystal structure.

[0144] 3. Coordinate conversion to spatial rectangular coordinate system

[0145] The fractional coordinates of the atoms in the cell coordinate system are converted to the rectangular coordinate system in the actual space. This conversion uses a matrix transformation formula M, which maps the position in the cell coordinate system to the spatial coordinate system. The specific steps are as follows:

[0146] a) Construct the conversion matrix M according to the cell parameters a, b, c, α, β, γ of the sample;

[0147] a = (a, 0, 0)

[0148] b = (b cos γ, b sin γ, 0)

[0149]

[0150]

[0151] b) Use the direction matrix R and the conversion matrix M to convert the cell coordinates to the spatial rectangular coordinate system:

[0152] Corrdinate 空间直角坐标系 = R·M·Coordinate 晶胞坐标系

[0153] 4. MATLAB visualization and atom selection

[0154] After obtaining the spatial coordinates of all atoms, MATLAB is used for visualization drawing. In the drawing image, the tungsten atom (W) is marked in red, and the carbon atom (C) is marked in blue. In the visualization result, according to the research requirements, a part of the target atoms is selected to form a template (Template) for further analysis,Figure 2 、 Figure 3 Two template examples are given.

[0155] Template simulation:

[0156] The atomic coordinates and atomic number information obtained by theoretical calculation are used to generate a theoretical HAADF (high-angle annular dark-field imaging) or iDPC (integral-differential phase contrast imaging) image template of the sample in a given orientation by using the Gaussian fitting method. The template effectively simulates the projection of the atomic structure in the specified orientation, providing a standard reference for subsequent matching with actual characterization data.

[0157] Steps for generating a simulated image

[0158] 1. Relationship between atomic intensity and Gaussian function

[0159] In the HAADF or iDPC image, the imaging intensity is positively correlated with the atomic number Z of the atom. Therefore, the influence area of each atom in the image is simulated by the Gaussian fitting method. Assuming that the form of the Gaussian function is G(x, y), the image intensity can be represented as:

[0160]

[0161] where x and y are the coordinates on the two-dimensional plane; x0 and y0 are the coordinates of the center of the Gaussian function; and σ is the standard deviation.

[0162] 2. Generation of template image

[0163] A Gaussian distribution is generated for each atom based on the above formula by using MATLAB. Different types of atoms generate different intensity distributions in the simulated image according to their atomic number Z and the value of the fitting control factor r. Finally, the Gaussian distributions of all atoms are added to obtain the overall theoretical template image.

[0164] Intensity = G(x, y) · Z r

[0165] where G(x, y) is a two-dimensional Gaussian function used to describe the intensity distribution of the atom; Z is the atomic number; and r is a fitting control factor used to adjust the contribution of different types of atoms to the imaging intensity.

[0166] 3. Fitting control

[0167] By adjusting the value of the fitting factor r, the generation of the template can be optimized to make it more close to the image features of the actual sample, Figure 4 、 Figure 5 Two template examples are given.

[0168] Template matching:

[0169] The generated theoretical template image is matched with the actually acquired target image to identify regions in the image that match the template features, thereby determining the precise positions of atoms in the sample.

[0170] Matching process

[0171] 1. Normalized cross-correlation calculation

[0172] Using an image matching algorithm, the region in the target image that is similar to the template image is found by means of normalized cross-correlation (NCC). The formula for normalized cross-correlation is:

[0173]

[0174] where R(i,j) represents the matching degree of the template image at the position (i,j) of the target image; f(x,y) is the grayscale value of the target image; t(x,y) is the grayscale value of the template image; and are the average values of images f and t, respectively.

[0175] By calculating the cross-correlation value R(i,j), the region in the target image that best matches the template features can be found.

[0176] 2. Peak point selection and repeated detection

[0177] In the calculated cross-correlation map, peak points are sought, which represent possible atomic positions. To ensure the accuracy of the detection results, the selected target regions are further verified:

[0178] Repeated region detection: If multiple peak points are too close together, it may indicate that the same region is repeatedly identified. At this time, a threshold needs to be set to screen and discard the repeated regions.

[0179] Threshold judgment: When the overlap of repeated regions exceeds the set threshold, the repeated peaks are discarded to avoid redundancy.

[0180] overlap area = max(0, x min2 -x max1 ) x max(0, y min2 -y max1 )

[0181] Output results

[0182] Finally, through the above matching process, all regions in the target image that match the template features can be obtained. The peak points of these regions represent the precise positions of atoms in the sample, providing a data basis for subsequent three-dimensional reconstruction and structural analysis,Figure 6 、 Figure 7 , and Figure 8 、 Figure 9 Two groups of template examples are given respectively.

[0183] Preliminary extraction of atomic coordinates

[0184] According to the template matching result, the coordinate position of each atom in the target image is preliminarily extracted. These coordinates are obtained based on the region recognition of template matching, but due to the lattice distortion, thermal disturbance or other physical factors that may exist in the actual sample, the preliminarily extracted coordinate position may have a certain deviation from the actual atomic center. Therefore, the atomic coordinates obtained at this stage are only used as an initial estimate to provide a basis for subsequent accurate calibration, as shown in Figure 10 .

[0185] Coordinate calibration:

[0186] In order to further improve the accuracy of the atomic coordinates, the present application uses a Gaussian fitting algorithm to accurately calibrate each preliminarily extracted atomic coordinate. The specific steps are as follows:

[0187] 1. Local area selection

[0188] For each preliminarily extracted atomic coordinate, a small local area around it is selected as the target area for fitting. The size of this area is adjusted according to the type of the atom and its lattice environment to ensure that the fitting range can cover the entire atomic signal.

[0189] 2. Gaussian fitting algorithm

[0190] In the selected local area, a two-dimensional Gaussian function is used for fitting to obtain the accurate center position of the atom. The function form of Gaussian fitting is:

[0191]

[0192] Where:

[0193] A is the background intensity; B is the peak intensity; (C, D) is the center position; ω1 and ω2 are the widths along the x and y directions

[0194] 3. Accurate calibration result

[0195] Through the Gaussian fitting algorithm, the center position of each atom can be calibrated to achieve a precision of sub-angstrom This process significantly reduces the errors caused by lattice distortion or imaging noise in the preliminary extraction process, thereby improving the accuracy of the overall coordinates, as shown in Figure 11 .

[0196] Coordinate export:

[0197] After completing the precise calibration of all atomic coordinates, the final coordinate data is exported in the commonly used.xsf format. This format is widely used in crystallographic analysis and is compatible with various crystal analysis and visualization software such as Vesta, facilitating subsequent detailed structure analysis. The exported coordinate data includes the type of each atom and its precise spatial position, forming a complete and accurate three-dimensional atomic distribution data set.

[0198] Exported format description

[0199] File format:.xsf (eXtensible Structured Format)

[0200] Data content: includes the coordinates (in units of ) and corresponding atomic numbers of each atom.

[0201] Visualization and analysis: the exported data can be directly loaded into software such as Vesta for further atomic structure analysis, such as bond length measurement, lattice constant calculation, and atomic distance analysis, etc. The obtained result template is shown in Figure 12 、 Figure 13 .

[0202] The present invention combines various technical means and algorithms, significantly improving the reconstruction accuracy and efficiency of three-dimensional atomic configurations in complex unit cell structures. Its core innovations include:

[0203] Combining actual characterization data with theoretical calculations

[0204] Combining experimental data with theoretical calculations, by generating theoretical templates and matching them with actual images, improves the accuracy of extracting atomic coordinates from two-dimensional projections. This method effectively reduces the influence of imaging noise and lattice distortion on the results.

[0205] Gaussian fitting to calibrate atomic positions

[0206] Using Gaussian fitting algorithm to accurately calibrate the position of each atom, the coordinate accuracy reaches sub-angstrom scale. This process greatly reduces the deviation caused by sample characteristics and ensures the high reliability of the final reconstruction results.

[0207] Efficient three-dimensional reconstruction process

[0208] By extracting information from two-dimensional atomic projection images and combining direction matrices and coordinate transformations, efficient conversion from two-dimensional to three-dimensional is achieved. Compared with traditional methods, the present invention significantly improves the efficiency of three-dimensional atomic reconstruction, reduces the steps of manual participation, and thus improves the accuracy and consistency of the reconstruction results.

[0209] In summary, the method proposed in the application not only solves the problems of noise interference and lattice distortion in the technical field, but also significantly improves the overall accuracy of three-dimensional reconstruction of complex crystal structures, thereby providing a powerful tool for the research and analysis of new materials.

[0210] The overall process of the embodiment of the application is shown in Figure 14 and generally includes the following implementation process:

[0211] 1. Characterization of spherical aberration-corrected transmission electron microscope

[0212] First, the target sample is characterized using a spherical aberration-corrected transmission electron microscope (AC-TEM). Through the AC-TEM, two-dimensional atomic projection images of the sample can be obtained. The spherical aberration correction technique can effectively reduce the optical aberration in the image, making the obtained image clearer and accurately displaying the atomic structure of the sample. This step provides the necessary experimental data basis for subsequent automated calculation and matching.

[0213] 2. Cell parameter input

[0214] The CIF file matching the sample is imported into the system. The CIF file contains the crystal information of the sample, including the cell constant, atomic type, symmetry operation, and original fractional coordinates. After importing, the system automatically parses the content in the CIF file and extracts the required crystal structure parameters to provide basic data for the subsequent calculation.

[0215] 3. Automated calculation

[0216] After obtaining the cell parameters, the system automatically performs the following steps:

[0217] According to the symmetry operation rules in the CIF file, the fractional coordinates of all atoms are generated. These fractional coordinates cover all symmetry positions of the sample, ensuring the comprehensiveness of the calculation.

[0218] The system will automatically remove and filter the generated atomic coordinates to ensure the uniqueness of each atomic position and filter out duplicate or invalid coordinates.

[0219] 4. Gaussian fitting and matching

[0220] The system uses the Gaussian fitting method to automatically identify and match the atomic positions in the target image and performs accurate calibration. The specific process is as follows:

[0221] According to the theoretically calculated atomic coordinates and atomic numbers, a simulated image template is generated.

[0222] Using normalized cross-correlation calculation, the atomic positions in the actual image are preliminarily located.

[0223] A local Gaussian fitting is performed around the initial extracted position to refine the position by fitting and get more accurate atomic center coordinates. This process effectively reduces the impact of image noise and lattice distortion on coordinate positioning.

[0224] 5. Coordinate export

[0225] After all the atomic positions are calibrated, the system will export the final atomic coordinate data in a standard format. The exported format is the structure file format of.xsf, so that subsequent detailed research and data analysis can be carried out in Vesta, PyMOL or other professional analysis software.

[0226] It should be noted that, unless otherwise defined, the technical terms or scientific terms used in the present application should be understood as the usual meaning understood by a person with ordinary skills in the art to which the present application belongs. The "first", "second" and similar words used in the present application do not represent any order, quantity or importance, but are only used to distinguish different components. "Include" or "contain" and similar words mean that the elements or objects before the word cover the elements or objects listed after the word and their equivalents, without excluding other elements or objects. "Connected" or "connected" and similar words are not limited to physical or mechanical connection, but can include electrical connection, whether direct or indirect. "Up", "down", "left", "right" and the like are only used to represent relative positional relationship, and when the absolute position of the described object changes, the relative positional relationship may also change accordingly.

[0227] The above is only the preferred embodiment of the present application, and is not intended to limit the other forms of the present application. Any person skilled in the art can use the disclosed technical content to make changes or modifications to equivalent embodiments. However, any simple modification, equivalent change and modification made according to the technical essence of the present application to the above embodiments, without departing from the technical solution content of the present application, still belongs to the protection scope of the present application.

[0228] The present application is not limited to the above best mode, and anyone can derive other various forms of a method for reconstructing a special interface three-dimensional atomic configuration under the inspiration of the present application. Any equivalent change and modification made in accordance with the scope of the present application shall be covered by the present application.

Claims

1. A method for reconstructing special interfacial three-dimensional atomic configurations, characterized by: Combining the actual characterization data with the theoretical calculation, the accuracy of atomic coordinate extraction is improved by generating a theoretical template and matching it with the actual image; the position of each atom is calibrated by Gaussian fitting to ensure that the accuracy reaches the sub-angstrom scale; Using the atomic phase information in the two-dimensional transmission electron microscopy image, combined with the direction matrix and coordinate transformation, the reconstruction from the two-dimensional atomic projection image to the three-dimensional crystal structure is realized.

2. The method for reconstructing a three-dimensional atomic configuration of a special interface according to claim 1, characterized in that: an atomic structure image of the sample is collected using a spherical aberration corrected transmission electron microscope, and structure characterization is performed to obtain a two-dimensional atomic projection image of the sample; crystal structure parameters matching the sample are obtained, and based on the unit cell parameters and atomic coordinates, the fractional coordinates of each atom are calculated through the symmetry operation rules, and then converted to the actual unit cell coordinates through stretching and rotation matrix; HAADF / iDPC images of the template are simulated according to the unit cell coordinates and atomic numbers; the cross-correlation between the template and the target image is calculated to identify the matching area; and the corresponding atomic coordinates are assigned according to the position of the matching area; and Gaussian fitting is performed on the target image to calibrate the atomic positions; After all the atomic positions are calibrated, the final atomic coordinate data is exported, and the exported data at least includes the unit cell size and atomic coordinates.

3. The method for reconstructing a three-dimensional atomic configuration of a special interface according to claim 1, characterized in that: the specific process of converting the fractional coordinates of each atom to the actual unit cell coordinates based on the unit cell parameters and atomic coordinates through the symmetry operation rules is as follows: through the characterization angle and crystal orientation of the sample, the direction matrix of the crystal orientation is calculated, which is used to describe the crystal structure of the sample in different orientations and convert the unit cell coordinates of the crystal to the current characterization direction; the theoretical atomic coordinates of the sample in the current orientation are calculated according to the crystal direction matrix and unit cell parameters; and then converted from the theoretical unit cell coordinate system to the spatial coordinate system in the actual characterization direction to obtain the atomic distribution information related to the current orientation; the complete fractional coordinates of the sample in the theoretical unit cell are obtained through the original fractional coordinates of the atoms and the symmetry operation of the sample; the fractional coordinates are periodically expanded and the fractional coordinates within the specified range are retained; the fractional coordinates of the atoms in the unit cell coordinate system are converted to the rectangular coordinate system in the actual space.

4. The method for reconstructing a three-dimensional atomic configuration of a special interface according to claim 3, characterized in that: the conversion of the fractional coordinates of the atoms in the unit cell coordinate system to the rectangular coordinate system in the actual space uses the matrix transformation formula M to map the positions in the unit cell coordinate system to the spatial coordinate system: the conversion matrix M is constructed according to the unit cell parameters a, b, c, α, β, γ of the sample; a = (a, 0, 0) b = (b cos γ, b sin γ, 0) the unit cell coordinates are converted to the spatial rectangular coordinate system using the direction matrix R and the conversion matrix M: Coordinate 空间直角坐标系 = R * M * Coordinate 晶胞坐标系 .

5. The method for reconstructing a three-dimensional atomic configuration of a special interface according to claim 1, characterized in that: The calibration of the position of each atom by Gaussian fitting specifically includes: The atomic coordinates and atomic number information obtained by theoretical calculation are used to generate a theoretical HAADF or iDPC image template of the sample in a given orientation by a Gaussian fitting method; The generated theoretical template image is matched with the actual target image collected to identify the area in the image that meets the template characteristics, thereby determining the accurate position of the atoms in the sample: the atomic position in the actual image is preliminarily located using a normalized cross-correlation calculation; According to the template matching result, the coordinate position of each atom in the target image is preliminarily extracted as an initial estimate, and the Gaussian fitting algorithm is used to accurately calibrate each preliminarily extracted atomic coordinate.

6. The method for reconstructing a three-dimensional atomic configuration of a special interface according to claim 5, characterized in that: The atomic coordinates and atomic number information obtained by theoretical calculation are used to generate a theoretical HAADF or iDPC image template of the sample in a given orientation by a Gaussian fitting method; In the HAADF or iDPC image, the imaging intensity is positively correlated with the atomic number Z of the atom; the influence area of each atom in the image is simulated by a Gaussian fitting method; the form of the Gaussian function is set as G(x, y), and the image intensity is represented as: Where x and y are the coordinates on the two-dimensional plane; x0 and y0 are the coordinates of the center of the Gaussian function; and sigma is the standard deviation; Based on the above formula, a Gaussian distribution is generated for each atom; different types of atoms generate different intensity distributions in the simulated image according to their atomic number z and the value of the fitting control factor r; and the Gaussian distributions of all atoms are accumulated to obtain the overall theoretical template image; Intensity = G(x, y) · Z r Where G(x, y) is a two-dimensional Gaussian function used to describe the intensity distribution of the atom; Z is the atomic number; and r is a fitting control factor used to adjust the contribution of different types of atoms to the imaging intensity; By adjusting the value of the fitting factor r, the generation of the template is optimized to fit the image characteristics of the actual sample.

7. The method for reconstructing a three-dimensional atomic configuration of a special interface according to claim 5, characterized in that: The generated theoretical template image is matched with the actual target image collected to identify the area in the image that meets the template characteristics, thereby determining the accurate position of the atoms in the sample: By means of normalized cross-correlation, a region similar to the template image in the target image is found: Wherein, R(i,j) represents the matching degree of the template image at the target image (i,j) position; f(x,y) is the gray value of the target image; t(x,y) is the gray value of the template image; and are the average values of images f and t, respectively; By calculating the cross-correlation value R(i, j), the region in the target image that best meets the template characteristics is found; In the calculated cross-correlation map, peak points are found, and it is verified whether the peak points represent the atomic positions: If multiple peak points are too close, the repeated regions are screened and discarded by threshold judgment to avoid repeated identification of the same region; overlap area = max(0, x min2 - x max1 ) x max(0, y min2 - y max1 ) The above formula indicates that when the overlap degree of the repeated regions exceeds the set threshold, the repeated peaks in the repeated regions are discarded to avoid redundancy; Through matching, all regions in the target image that meet the template characteristics are obtained; the peak points of the regions represent the positions of the atoms in the sample.

8. The method for reconstructing a three-dimensional atomic configuration of a special interface according to claim 5, characterized in that: According to the template matching result, a coordinate position of each atom in the target image is preliminarily extracted as an initial estimation, and a Gaussian fitting algorithm is used to accurately calibrate each preliminarily extracted atom coordinate: For each preliminarily extracted atom coordinate, a small local area around the atom coordinate is selected as a target area for fitting; the size of the area is adjusted according to the type of the atom and the crystal lattice environment in which the atom is located, so as to ensure that the fitting range can cover the entire atom signal; In the selected local area, a two-dimensional Gaussian function is used for fitting to obtain the accurate center position of the atom; the function form of the Gaussian fitting is: Wherein: A is the background intensity; B is the peak intensity; (C, D) is the center position; ω1 and ω2 are the widths along the x and y directions; The center position of each atom is calibrated through Gaussian fitting, and the accuracy reaches sub-angstrom scale.

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