Two-gradient decoupling method for atomic-scale deformation fields based on geometric phase analysis

Abstract

The present invention provides a two-gradient decoupling method for atomic-scale deformation fields based on geometric phase analysis, which includes: (1) obtaining the original data after crystal deformation through high-resolution transmission electron microscope images; (2) performing Fourier transform on the original data to obtain reciprocal space information, selecting diffraction spots in the reciprocal space information of different crystal orientations for inverse Fourier transform to obtain the phase information of the local lattice, and obtaining the atomic displacement field inside the grain based on the phase information; (3) decomposing the atomic displacement field into a first-order affine displacement gradient tensor and a second-order non-affine displacement gradient tensor, and respectively decomposing them to obtain the deformation components of their respective basic localization events; (4) defining the participation degree of atomic-scale basic localization events, and analyzing the atomic-scale physical mechanism of microdefect evolution. The present invention has a reasonable concept and can effectively solve the multi-scale problem of regulating macroscopic properties by the current microevolution mechanism of materials.

Description

Technical Field

[0001] The present invention relates to the technical field of crystal material defect deformation field analysis, and particularly relates to a two-gradient decoupling method for atomic-scale deformation fields based on geometric phase analysis. Background Art

[0002] The macroscopic mechanical properties of crystal materials are largely affected by the evolution of their microscopic defects. The type, distribution, and dynamic behavior of microscopic defects directly determine the response characteristics of materials under external forces. Therefore, in-depth understanding and analysis of the structural evolution of crystal materials at the micro-nano scale are of great significance for improving material properties and developing new high-performance materials.

[0003] At the micro-nano scale, the displacement field in crystal materials is caused by small changes in atomic arrangement. These changes are usually manifested as the movement and interaction of microscopic defects such as dislocations, interfaces, and phase boundaries. Accurately measuring and analyzing these displacement fields can reveal the microscopic structural characteristics and their evolution laws of materials, thereby providing a scientific basis for material design.

[0004] Traditional characterization techniques, such as transmission electron microscopy (TEM) and high-resolution transmission electron microscopy (HRTEM), although capable of providing nano-scale structural information, how to effectively extract and quantify displacement field information from these images remains a technical challenge. Geometric phase analysis (GPA), as an advanced image processing technique, can accurately extract displacement field information through Fourier space analysis of HRTEM images. However, existing GPA techniques mainly focus on the acquisition of displacement fields and are not yet perfect for further decomposing and analyzing the components of these displacement fields (such as rotation fields, dilation fields, and shear fields). Summary of the Invention

[0005] In view of the technical problems existing in the above background art, the present invention proposes an analysis method for decomposing the micro-nano scale deformation field of crystal materials to solve the multi-scale problems of regulating macroscopic properties by the current microscopic evolution mechanism of materials, especially the problems of difficult analysis of microscopic defect evolution mechanisms, complex atomic motions, and interaction mechanisms of multiple defects.

[0006] To solve the above technical problems, a two-gradient decoupling method for atomic-scale deformation fields based on geometric phase analysis provided by the present invention is characterized by mainly including the following steps:

[0007] (1) Observe a pre-selected material region with a high-resolution transmission electron microscope to obtain a high-resolution transmission electron microscope image, and obtain the original data of the crystal after deformation based on the high-resolution transmission electron microscope image;

[0008] (2) Fourier transform the original data after crystal deformation to obtain reciprocal space information. Select diffraction spots in the reciprocal space information of different crystal orientations for inverse Fourier transform to obtain the phase information of the local lattice, and then calculate the atomic displacement field inside the grain according to the phase information of the local lattice;

[0009] (3) Perform two-term gradient decomposition on the calculated atomic displacement field, decompose it into a first-order affine displacement gradient tensor containing local affine deformation and a second-order non-affine displacement gradient tensor containing local non-affine deformation, and decompose the first-order affine displacement gradient tensor and the second-order non-affine displacement gradient tensor respectively to obtain the deformation components of their respective basic localization events. After superimposing the two terms, obtain the basic localization event component that comprehensively considers local affine deformation and non-affine deformation;

[0010] (4) According to the deformation components of the obtained basic localization events, define the respective participation degrees in atomic motion, analyze the spatio-temporal motion pattern of atoms during the evolution of material crystal defects, and determine the atomic-scale physical mechanism of micro-defect evolution.

[0011] The two-term gradient decoupling method of atomic-scale deformation field based on geometric phase analysis, wherein the specific process of the step (2) is as follows:

[0012] (2.1) Perform Fourier transform on the high-resolution transmission electron microscope image to obtain the reciprocal space image

[0013] (2.2) Select different basis vectors in the reciprocal space to perform masking processing on the diffraction points of the target, and perform inverse Fourier transform on the selected diffraction points to reconstruct the intensity distribution information as:

[0014]

[0015] wherein, in the above formula, g1 and g2 are the coordinates of the selected reciprocal space basis vectors, I is the real space intensity distribution information obtained after inverse Fourier transform, A g and P g respectively represent the amplitude and phase of different diffraction points, and A0 represents the base value of the real space intensity;

[0016] (2.3) According to the reconstructed real space intensity distribution information, obtain the phase change information P g , and solve to obtain the displacement field that causes the periodic change of the phase.

[0017] The two-term gradient decoupling method of atomic-scale deformation field based on geometric phase analysis, wherein the specific process of the step (2.2) is:

[0018] (2.2.1) Select the diffraction points of the target in the reciprocal space with respect to the basis vectors ;

[0019] (2.2.2) After mask processing, select specific frequency components and perform power spectrum analysis to select specific peaks and extract the periodic information and lattice structure information in the image

[0020] (2.2.3) Perform Fourier transform on the obtained to obtain the in the real space, where and are the image intensity information after performing inverse Fourier transform respectively after

[0021] mask processing; for the displacement generated, the phase change is:

[0022] Thus, the correlation formula between the displacement and the phase information is obtained, that is, the displacement field formula generated by the phase change is:

[0023]

[0024] where, in the above formula, u x and u y are the displacements in the horizontal and vertical directions in the high-resolution transmission electron microscope image respectively; g 1x , g 1y , g 2x and g 2y are the horizontal and vertical coordinates of the basis vectors taking and respectively; and are and the periodic phase changes in the

[0025] The two-gradient decoupling method of the atomic-scale deformation field based on geometric phase analysis, wherein the specific process of performing second-order gradient decomposition on the calculated atomic displacement field in step (3) is:

[0026] (3.1) To better analyze the relationship between the microscopic displacement field and the structural crystal orientation, perform coordinate transformation on the displacement to become a rectangular coordinate system parallel to representing the crystal orientation and perpendicular to ;

[0027] (3.2) Perform Taylor expansion on the displacement after coordinate transformation Calculate the first-order affine displacement gradient tensor $\mathbf{F}$ and the second-order non-affine displacement gradient tensor $\boldsymbol{\eta}$ respectively; among them, the expansion form of the first-order affine displacement gradient tensor is The second-order non-affine displacement gradient tensor is expressed as

[0028] (3.3) Decomposition of the first-order affine displacement gradient tensor basic localization deformation events for two-dimensional space:

[0029]

[0030] Among them, in the above formula are the components of the three basic localization events of volume expansion, shear and rotation in affine deformation respectively;

[0031] Decompose the second-order non-affine displacement gradient tensor of two-dimensional space into basic localization deformation events:

[0032]

[0033] And in the above formula are the volume expansion, shear and rotation components in non-affine deformation respectively;

[0034] (3.4) Superimpose the volume expansion, rotation and shear components of affine deformation and non-affine deformation:

[0035]

[0036] Among them, in the above formula $a$ i is a first-order binomial tensor, where $a_1$ is parallel to the basis vector $\mathbf{g}_1$, and its modulus is equal to the interplanar spacing in its crystal direction, $a_2$ is perpendicular to $a_1$, and its modulus is equal to the interplanar spacing perpendicular to the crystal direction of $a_1$; and are the volume expansion, shear and rotation components of the dimensionless second-order non-affine deformation respectively; $D$, $S$, $R$ respectively represent the components of the three basic localization event components of volume expansion, shear and rotation considering the first-order affine deformation and the second-order non-affine deformation comprehensively.

[0037] The two-gradient decoupling method of the atomic-scale deformation field based on geometric phase analysis, among which, the definition of the participation degrees of volume expansion, shear and rotation in different regions during the atomic motion in step (4) is:

[0038]

[0039] Among them, in the above formula $P$ D , $P$ S and $P$ RThey respectively represent the degrees of participation of atomic dilatation, shear, and rotational deformation events in the defect evolution process, and measure the main deformation modes leading to defect evolution;

[0040] By comparing and analyzing the degrees of participation of the three basic deformation events of dilatation, shear, and rotation in different stages of defect evolution, the spatio-temporal motion pattern of atoms in the process of defect generation and evolution is obtained, and the physical mechanism of defect evolution is obtained.

[0041] Adopting the above technical solution, the present invention has the following beneficial effects:

[0042] The present invention has a reasonable concept, can accurately and completely describe local deformation information, and helps to deeply understand the microscopic structure evolution and deformation mechanism of crystal materials. The present invention can effectively solve the multi-scale problems of regulating macroscopic properties by the current microscopic evolution mechanism of materials, especially challenges such as difficult analysis of microscopic defect evolution mechanism, complex atomic motion patterns, and interaction mechanisms of multiple defects; at the same time, it can solve the multi-scale problems of regulating macroscopic properties by the current microscopic evolution mechanism of materials, especially problems such as difficult analysis of microscopic defect evolution mechanism, complex atomic motion, and interaction mechanisms of multiple defects.

[0043] Compared with the prior art, the present invention has the following characteristics and advantages:

[0044] (1) Combined with macroscopic freezing tests, it can analyze the temporal sequence problem of atomic motion at different evolution stages of micro-nano defects, realize cross-scale analysis of the deformation mechanism of materials. Compared with traditional geometric phase analysis methods, the advantage is that it comprehensively considers the affine and non-affine motions of atoms and has more comprehensive motion information;

[0045] (2) The decomposition of the traditional deformation field mainly only defines the von Mises strain for affine deformation, which will inevitably cause the loss of deformation information and cannot be completely described to a certain extent, especially the motion pattern at the microscopic discrete atomic scale. By comprehensively considering the first-order affine deformation and second-order non-affine deformation of atoms, it is decomposed into three basic localized deformation events of dilatation, shear, and rotation, and the degrees of participation of the three types of events are defined, which can deeply analyze the dominant mode of atomic motion, deeply analyze the spatio-temporal motion law of atoms during the deformation process, overcome the limitation of complex atomic motion during the defect evolution process, and describe the microscopic defect evolution process in a new way;

[0046] (3) Compared with current atomic-scale analysis methods, such as molecular dynamics simulation, our method is more combined with experiments, and the analysis of the actual deformed specimen is closer to the actual situation. Especially for the action mechanism of multiple defects, we can comprehensively consider complex atomic motions and provide an effective experimental auxiliary means for revealing the atomic-scale deformation mechanism;

[0047] (4) The current deformation decomposition mainly considers affine motion, resulting in the loss of deformation information. Our decomposition method also provides a new idea for the decomposition of other deformation fields.

[0048] Meanwhile, the present invention also has the following advantages:

[0049] (1) Analyze the atomic motion mechanism of the evolution of microscopic defects and reveal the physical mechanism of the formation and evolution of microscopic defects;

[0050] (2) The present invention is helpful for material design and optimization and promotes the research and development of new high-performance materials;

[0051] (3) Combine with technologies such as freeze tests and molecular dynamics simulations to improve research efficiency;

[0052] (4) The present invention is applicable to the deformation analysis of various crystal materials and has important value not only in basic research but also can be used in fields such as micro-nano technology, semiconductor material analysis, and composite materials, and has a wide application prospect. BRIEF DESCRIPTION OF THE DRAWINGS

[0053] In order to more clearly illustrate the specific embodiments of the present invention or the technical solutions in the prior art, the following will briefly introduce the drawings required for the description of the specific embodiments or the prior art. Obviously, the drawings in the following description are some embodiments of the present invention. For those of ordinary skill in the art, without creative efforts, other drawings can also be obtained based on these drawings.

[0054] Figure 1 is a flowchart of the analysis method for the decomposition of the micro-nano scale deformation field of the crystal material of the present invention;

[0055] Figure 2 is a schematic diagram of the displacement field extracted by geometric phase analysis involved in the analysis method for the decomposition of the micro-nano scale deformation field of the crystal material of the present invention. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0056] The following will clearly and completely describe the technical solutions of the present invention in conjunction with the drawings. Obviously, the described embodiments are some embodiments of the present invention, rather than all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative efforts belong to the scope of protection of the present invention.

[0057] The following further explains and illustrates the present invention in conjunction with specific embodiments.

[0058] An analysis method for decomposing the micro-nano scale deformation field of a crystal material provided by this embodiment first obtains the original data of the deformed crystal through a high-resolution transmission electron microscope image, and performs a Fourier transform on it to obtain reciprocal space information; then, selects diffraction spots in the reciprocal space of different crystal orientations for inverse Fourier transform to obtain the phase information of the local lattice, and then obtains the atomic displacement field inside the crystal grain through geometric phase analysis; then, performs a two-term gradient decomposition on the calculated atomic displacement field, decomposing it into a first-order affine displacement gradient tensor containing local affine deformation and a second-order non-affine displacement gradient tensor containing local non-affine deformation, and decomposes the first-order affine displacement gradient tensor and the second-order non-affine displacement gradient tensor respectively, decoupling the three basic localization events of dilation, shear, and rotation from the comprehensive affine and non-affine atomic motions to accurately and completely describe the local deformation information; finally, according to the participation degrees of the three basic localization events of dilation, shear, and rotation in the atomic motion, analyzes the atomic spatio-temporal motion pattern during the evolution of crystal defects in the material to determine the atomic-scale physical mechanism of micro-defect evolution.

[0059] As Figure 1 shown, the analysis method for decomposing the micro-nano scale deformation field of the crystal material of the present invention specifically includes the following steps:

[0060] S100. Select a material area for high-resolution transmission electron microscope observation to obtain a high-resolution transmission electron microscope image

[0061] S200. Perform geometric phase analysis on the high-resolution transmission electron microscope image to obtain the local lattice displacement field of the transmission area through the change of phase information. Among them, the aforementioned geometric phase analysis of the high-resolution transmission electron microscope image is to reconstruct the phase change caused by atomic displacement through the distortion of the diffraction points in the reciprocal space of the high-resolution transmission electron microscope image, and obtain the atomic displacement by taking the inverse; the specific steps are:

[0062] S210. Perform a Fourier transform on the high-resolution transmission electron microscope image to obtain a reciprocal space image

[0063] S220. Select different basis vectors for the diffraction points of the target in the reciprocal space for correct masking processing, and perform an inverse Fourier transform on the selected diffraction points to obtain the phase change information Pg of the local lattice, and reconstruct the intensity distribution information as:

[0064]

[0065] Among them, in the above formula, g1 and g2 are the coordinates for selecting the reciprocal space basis vectors, I is the positive space intensity distribution information obtained after inverse Fourier transform, A g and P g represent the amplitude and phase of different diffraction points respectively, and A0 represents the base value of the positive space intensity;

[0066] The specific steps are as follows:

[0067] S221. Select the diffraction points of the target in the reciprocal space at the basis vectors ;

[0068] S222. After performing mask processing on g1 and g2, select specific frequency components, perform power spectrum analysis to select specific peaks, and extract the periodic information and lattice structure information in the image

[0069] S223. Perform inverse Fourier transform on the obtained to obtain the in the positive space. Among them, and are the image intensity information obtained by performing inverse Fourier transform after mask processing for the selected ;

[0070] For the displacement , the phase change is:

[0071]

[0072] Thus, the correlation formula between the displacement and the phase information is obtained:

[0073]

[0074] Among them, in the above formula, u x , u y are the displacements in the horizontal and vertical directions in the high-resolution transmission electron microscope image respectively; g 1x , g 1y , g 2x and g 2y are the horizontal and vertical coordinates of the basis vectors taking and respectively; and are the periodic phase changes in the and directions respectively, and are functions of the positive space coordinates (x, y).

[0075] S230. Based on the reconstructed positive space intensity distribution information, the displacement formula caused by the phase change, that is, the above-mentioned correlation formula between displacement and phase information, can be obtained. Among them, the phase information contains the periodicity of the crystal lattice. The original perfect crystal lattice has a consistent periodicity. During the defect evolution process, atomic displacements occur, and the periodicity changes locally. The atomic displacement field can be deduced inversely from the periodic changes.

[0076] S300. Expand the displacement information along the main crystallographic directions into a two-term gradient model including the first-order displacement gradient and the second-order displacement gradient, and decompose the rotation R xy , dilation D, and shear S xy which are the deformation components of local elementary events. The specific steps are as follows:

[0077] S301. To better analyze the relationship between the microscopic displacement field and the crystal structure orientation, transform the displacement into a right-angle coordinate system parallel to representing the crystal orientation and perpendicular to .

[0078] S302. Perform a Taylor expansion on the displacement after coordinate transformation, and calculate the first-order affine displacement gradient tensor F and the second-order non-affine displacement gradient tensor η respectively. Among them, the expansion form of the first-order affine displacement gradient tensor is The second-order non-affine displacement gradient tensor is expressed as The two-term gradient model refers to the addition of the first-order and second-order terms, representing the affine term and the non-affine term.

[0079] Generally, when decomposing the deformation field, the von Mises strain defined mainly for affine deformation will inevitably cause the loss of deformation information and cannot completely describe the local affine deformation field to a certain extent, especially the motion mode at the microscopic discrete atomic scale. Generally speaking, local rotation events (similar to vortex motion) can be represented by linear transformation and belong to the affine-dominated part, while the dilation and shear motions of atoms are dominated by severe irregular distortions and belong to the non-affine part of the deformation. Therefore, in order to completely describe the local deformation field information and decouple three basic localization events from it, it is necessary to comprehensively consider the affine and non-affine parts.

[0080] S303. Decomposition of the first-order affine displacement gradient tensor for basic localization deformation events in two-dimensional space:

[0081]

[0082] Among them, in the above formula are the components of the three basic localization events of dilation, shear, and rotation in affine deformation respectively;

[0083] Decompose the fundamental localized deformation events of the second-order non-affine displacement gradient tensor in two-dimensional space:

[0084]

[0085] Similarly, the above are respectively the dilatation, shear, and rotation components in non-affine deformation;

[0086] S304. Superimpose the dilatation, rotation, and shear components of affine deformation and non-affine deformation:

[0087]

[0088] In the above formula, a i is a first-order binomial tensor, where a1 is parallel to the basis vector g1, and its modulus is equal to the interplanar spacing in its crystal direction. a2 is perpendicular to a1, and its modulus is equal to the interplanar spacing perpendicular to the crystal direction of a1; and are respectively the dilatation, shear, and rotation components of the dimensionless second-order non-affine deformation; D, S, and R respectively represent the components of the three fundamental localized event components of dilatation, shear, and rotation considering both first-order affine deformation and second-order non-affine deformation. Here, the superscript A represents the affine deformation component, and the superscript N represents the non-affine deformation component. Among them, the affine deformation A is a dimensionless quantity, and the dimension of the non-affine deformation is [L -1 . Considering both affine deformation and non-affine deformation and superimposing them, it is necessary to integrate the non-affine variables to unify the dimensions for superposition. Taking dilatation as an example: the dilatation of the non-affine deformation quantity is: represents the integral of the non-affine deformation field at the i direction around the atom to measure the non-affine deformation of the atom, which is a dimensionless quantity; however, in the program calculation, it is simplified to a i / 2 represents the characteristic value of the integral of the interplanar spacing.

[0089] S400. Define the participation degrees of rotation, dilatation, and shear during the atomic movement process, and analyze the main spatio-temporal movement patterns of atoms during the defect evolution process; among them, the definitions of the participation degrees of dilatation, shear, and rotation in different regions during the atomic movement process are:

[0090]

[0091] Among them, in the above formula, P D , P S and P R respectively represent the magnitudes of the participation degrees of atomic dilatation, shear, and rotation deformation events during the defect evolution process, measuring the main deformation patterns leading to defect evolution;

[0092] By comparatively analyzing the participation degrees of three basic deformation events, namely volume expansion, shear, and rotation, in different stages of defect evolution, the spatio-temporal motion pattern of atoms during the defect generation and evolution processes is obtained, and the physical mechanism of defect evolution is acquired.

[0093] The concept of the present invention is reasonable and can effectively solve the multi-scale problem of regulating the macroscopic properties by the microscopic evolution mechanism of materials at present, especially challenges such as the difficulty in analyzing the microscopic defect evolution mechanism, the complex atomic motion pattern, and the interaction mechanism of multiple defects.

[0094] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those of ordinary skill in the art should understand that they can still modify the technical solutions described in the foregoing embodiments, or perform equivalent replacements on some or all of the technical features; and these modifications or replacements do not make the essence of the corresponding technical solutions deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. An atomic-scale deformation field two-gradient decoupling method based on geometric phase analysis, characterized in that , mainly including the following steps: (1) Observe the pre-selected material area with a high-resolution transmission electron microscope to obtain a high-resolution transmission electron microscope image, and obtain the original data after crystal deformation based on the high-resolution transmission electron microscope image; (2) Perform a Fourier transform on the original data after crystal deformation to obtain reciprocal space information, select diffraction spots in the reciprocal space information of different crystal orientations for inverse Fourier transform to obtain the phase information of the local lattice, and then calculate the atomic displacement field inside the grain according to the phase information of the local lattice; (3) Perform two-term gradient decomposition on the calculated atomic displacement field, decompose it into a first-order affine displacement gradient tensor containing local affine deformation and a second-order non-affine displacement gradient tensor containing local non-affine deformation, and decompose the first-order affine displacement gradient tensor and the second-order non-affine displacement gradient tensor respectively to obtain the deformation components of their respective basic localization events. After superimposing the two terms, the basic localization event component considering both local affine deformation and non-affine deformation is obtained; (4) According to the deformation components of the obtained basic localization events, define the respective participation degrees in the atomic movement, and analyze the atomic spatio-temporal movement pattern during the evolution of material crystal defects to determine the physical mechanism at the atomic scale of microdefect evolution.

2. The two-gradient decoupling method for atomic-scale deformation fields based on geometric phase analysis according to claim 1, wherein The specific process of step (2) is as follows: (2.1) Perform Fourier transform on the high-resolution transmission electron microscope image to obtain the reciprocal space image (2.2) Select different basis vectors in the reciprocal space Perform masking processing on the diffraction points of the target, and perform inverse Fourier transform on the selected diffraction points to reconstruct the intensity distribution information as: Among them, in the above formula, g1 and g2 are the coordinates for selecting the reciprocal space basis vectors, I is the positive space intensity distribution information obtained after inverse Fourier transform, A g and P g represent the amplitude and phase of different diffraction points respectively, and A0 represents the base value of the positive space intensity; (2.3) Obtain the phase change information P based on the reconstructed positive-space intensity distribution information g , and solve to obtain the displacement field that causes the periodic change of the phase.

3. The two-gradient decoupling method for atomic-scale deformation fields based on geometric phase analysis according to claim 2, characterized in that The specific process of step (2.2) is: (2.2.1) Select the diffraction point of the target in the reciprocal space at the basis vector ; (2.2.2) After mask processing, select specific frequency components and perform power spectrum analysis to select specific peaks and extract periodic information and lattice structure information in the image. (2.2.3) Perform Fourier transform on the obtained to obtain in the real space where H g1 ' and H g2 ' are respectively the image intensity information after inverse Fourier transform is performed on the selected mask-processed image.​ For generating displacement The phase change is: Thus, the correlation formula between displacement and phase information is obtained, that is, the displacement field formula generated by phase change is: Among them, u in the above formula x , u y are the displacements in the horizontal and vertical directions in the high-resolution transmission electron microscope image, respectively; g 1x , g 1y , g 2x and g 2y are the horizontal and vertical coordinates of the basis vectors taking and , respectively; and are the periodic phase changes in the directions of and , respectively, and are functions of the positive space coordinates (x, y).

4. The two-gradient decoupling method for atomic-scale deformation fields based on geometric phase analysis according to claim 1, wherein The specific process of performing second-order gradient decomposition on the calculated atomic displacement field in step (3) is: (3.1) To better analyze the relationship between the microscopic displacement field and the crystal orientation of the structure, the displacement is subjected to a coordinate transformation to become a rectangular coordinate system parallel to representing the crystal orientation and perpendicular to ; (3.2) Taylor-expand the displacements after coordinate transformation, calculate the first-order affine displacement gradient tensor F and the second-order non-affine displacement gradient tensor η respectively; among them, the expansion form of the first-order affine displacement gradient tensor is The second-order non-affine displacement gradient tensor is expressed as (3.3) Decomposition of the basic localization deformation event of the first-order affine displacement gradient tensor in two-dimensional space: wherein, in the above formula are respectively the components of the three basic localization events of volumetric expansion, shear, and rotation in the affine transformation Decompose the second-order non-affine displacement gradient tensor in two-dimensional space into basic localization deformation events: and in the above formula are respectively the volumetric dilation, shear, and rotation components in the non-affine deformation; (3.4) Superimpose the volume expansion, rotation, and shear components of affine deformation and non-affine deformation: where, in the above formula, a i is a first-order binomial tensor, where a1 is parallel to the basis vector g1, and its modulus is equal to the interplanar spacing in its crystal direction, a2 is perpendicular to a1, and its modulus is equal to the interplanar spacing perpendicular to the crystal direction of a1; and are the volumetric dilation, shear, and rotation components of the dimensionless second-order non-affine deformation respectively; D, S, and R represent the volumetric dilation, shear, and rotation components of the three basic localization event components that comprehensively consider the first-order affine deformation and the second-order non-affine deformation respectively.

5. The two-gradient decoupling method for atomic-scale deformation fields based on geometric phase analysis according to claim 1, characterized in that The definitions of the participation degrees of volume expansion, shear, and rotation in different regions during the atomic movement in step (4) are: Among them, P in the above formula D , P S and P R respectively represent the degrees of participation of atomic dilation, shear, and rotational deformation events in the process of defect evolution, and measure the main deformation modes leading to defect evolution; By comparing and analyzing the magnitudes of the participation degrees of the three basic deformation events of volume expansion, shear, and rotation in different stages of defect evolution, obtain the atomic spatio-temporal movement pattern during the generation and evolution of defects, and obtain the physical mechanism of defect evolution.

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