A quantitative analysis method based on correlation between EDS element distribution and atomic strain field

Abstract

The application provides a quantitative analysis method based on correlation between EDS element distribution and atomic strain field, which comprises the following steps: 1) obtaining a spherical aberration corrected transmission electron microscope image and a corresponding EDS element distribution energy spectrum image, and performing spatial registration on the images; 2) performing noise suppression and filtering processing on the EDS element distribution energy spectrum image respectively, and through a preset calibration relationship, normalizing the element intensity to obtain a normalized EDS signal image; 3) converting each pixel site of the normalized EDS signal image into a relative volume fraction distribution image; 4) obtaining atomic strain field images of body expansion strain components, shear strain components and lattice rotation components; 5) generating a correlation coefficient image; and 6) outputting the correlation result between the element distribution and the atomic strain field. The application can quantitatively reveal the coupling relationship between the element distribution and the atomic scale deformation mode, and has the advantages of strong non-concentration error suppression capacity, good result repeatability, wide application range and the like.

Description

Technical Field

[0001] This invention relates to the field of quantitative characterization technology of material microstructure, specifically to a quantitative analysis method based on the correlation between EDS elemental distribution and atomic strain field. Background Technology

[0002] In the field of material microstructure characterization and quantitative analysis of deformation mechanisms, in order to reveal the quantitative relationship between the fluctuation or distribution of element atoms and the three basic deformations of volume expansion, shearing and rotation during plastic deformation, and to distinguish the main roles played by different types of elements in plastic deformation, there is an urgent need to provide effective analytical methods and tools for material failure analysis and material design.

[0003] Currently, the main techniques for measuring elemental distribution include the following:

[0004] (1) EDS (Energy-Dispersive X-ray Spectroscopy): It mainly uses electron beams to bombard samples to excite each element to generate X-rays with characteristic energies, detects and distinguishes these characteristic peaks according to energy to identify and quantify elements, so as to realize the elemental composition analysis and elemental surface distribution of materials at the micro / nano scale; however, its disadvantages are: ① it is easy to drift and be unstable during the surface scanning process; ② it is seriously affected by the sample thickness, surface effect, internal defects, etc.

[0005] (2) Synchrotron radiation technology: It can perform elemental distribution in thicker samples and can perform larger field of view; the disadvantage is that it depends on large scientific facilities and has high threshold for experimental resources.

[0006] (3) APT (Atomic Probe): True three-dimensional atomic-level elemental distribution (suitable for observing segregation, clusters, SRO / solute atmosphere, etc.); disadvantages include small field of view, difficult sample preparation, and deviations in the reconstruction and quantification of certain materials / phases.

[0007] Current methods for atomic deformation field analysis mainly include the GPA (Geometric Phase Analysis) method, which is based on lattice fringe images obtained by HRTEM / AC-TEM (High Resolution Transmission Electron Microscopy / Aberration-Corrected Transmission Electron Microscopy). It performs Fourier transforms on selected reciprocal lattice vectors and extracts phase changes to invert the lattice displacement field and its derivative strain. However, current atomic field decomposition techniques only consider affine deformation, meaning they assume that local atomic displacements can be described by an approximately constant linear mapping (deformation gradient) within a small neighborhood. But non-affine deformation is also essential for discrete atomic deformation, especially in defects, interfaces, and strongly localized regions (such as dislocation cores, stacking faults / twin boundaries, phase boundaries, shear band fronts, etc.), where non-affine displacements commonly occur.

[0008] In conclusion, it is necessary to further innovate existing technologies. Summary of the Invention

[0009] To address the technical problems existing in the background art, this invention proposes a quantitative analysis method based on the correlation between EDS elemental distribution and atomic-scale expansion / shear / rotation strain field. This method can quantitatively reveal the coupling relationship between elemental distribution and atomic-scale deformation modes, and has the advantages of strong suppression of non-concentration errors, good repeatability of results, and wide applicability.

[0010] To address the aforementioned technical problems, this invention provides a quantitative analysis method based on the correlation between EDS elemental distribution and atomic strain field, comprising the following steps:

[0011] 1) Acquire spherical aberration-corrected transmission electron microscope (TEM) images and corresponding EDS element distribution energy spectra under the same field of view, and spatially register the spherical aberration-corrected TEM images and EDS element distribution energy spectra.

[0012] 2) The energy spectrum of each element in the EDS is subjected to median filtering and Gaussian smoothing noise suppression processing, then filtered again, and the intensity of each element is normalized through a preset calibration relationship to obtain a normalized EDS signal image.

[0013] 3) Statistically analyze each pixel location of the normalized EDS signal map and convert it into a relative volume fraction distribution map of each element to eliminate the influence of sample thickness and defects on the EDS signal;

[0014] 4) Perform geometric phase analysis on the spherical aberration transmission electron microscope images of the same region to obtain the atomic displacement field. Then, use the binomial gradient model to decouple the obtained atomic displacement field to obtain atomic strain field images of the bulk dilatation strain component, shear strain component, and lattice rotation component.

[0015] 5) Align the relative volume fraction distribution map of each element obtained in step 3) with the atomic strain field image obtained in step 4) on the same pixel grid. Using pixels as statistical units, perform correlation analysis between element volume fraction and each strain component using Pearson correlation coefficient, and generate a correlation coefficient map.

[0016] 6) Based on the sign and magnitude of the correlation coefficients in the correlation score graph, identify the local deformation type corresponding to each element and output the correlation results between the element distribution and the atomic strain field.

[0017] As a preferred embodiment of the present invention: the spherical aberration transmission electron microscope image and the EDS energy distribution spectrum of each element are obtained at the same location. After determining the location to be captured by the spherical aberration transmission electron microscope image, the spherical aberration transmission electron microscope image is captured, and the EDS scan is performed randomly at that location to obtain the energy distribution spectrum of each element in that region.

[0018] As a preferred embodiment of the present invention, the specific process of step 2) is as follows:

[0019] For the energy spectrum of each element in EDS, the intensity is:

[0020] (1);

[0021] In the above formula, the subscript 'e' is the element type index; (x, y) represents the pixel coordinates, which measure the spatial position. This represents the initial intensity of element e at pixel position (x, y);

[0022] Median filtering is applied to the energy spectrum of each element in the EDS based on the initial scan quality of the material to eliminate noise. The median filtering formula is as follows:

[0023] (2);

[0024] In the above formula, This represents the intensity after median filtering; the median function is the formula for calculating the median, which means that the internal data are arranged from largest to smallest and the median value is taken. The neighborhood window is centered at (x, y) and has a size of k x k. The value of k is determined based on the initial scan quality. If the initial scan quality is good, it is 1 or 3; if the quality is poor, it is 5 or 7. (i, j) is the pixel coordinate index inside the window. Let (x, y) be the initial set of intensity values ​​for the neighborhood window centered at (x, y) with a window size of k x k.

[0025] After removing noise through median filtering, the energy distribution spectra of each element in the EDS after noise removal are then Gaussian smoothed to suppress statistical noise in the EDS energy distribution spectra. The formula is as follows:

[0026] (3);

[0027] In the above formula, the subscript 'e' is the element type index; (x, y) represents the pixel coordinates, which measure the spatial position. Indicates the intensity after Gaussian smoothing; These represent the offset of the convolution kernel coordinates (x, y), and represent the displacement of the kernel relative to the center. This represents the weighting coefficient of the two-dimensional Gaussian kernel at the offset (u, v), where , Use Gaussian standard deviation to control smoothing intensity. r represents the radius of the convolution kernel. ;

[0028] As a preferred embodiment of the present invention: in step 2), the elemental distribution maps of the EDS measurement results are normalized and statistically calibrated using standard samples or samples with known average composition, and the linearized structure results of the EDS elemental distribution energy spectrum are output. The EDS elemental distribution energy spectrum after median filtering and Gaussian smoothing is then normalized, and its intensity is linearly calibrated.

[0029] (4);

[0030] In the above formula, This refers to the calibrated element content; This indicates the intensity after median filtering and Gaussian smoothing. and The linear fitting parameters are obtained from calibration using standard samples; that is, when the calibration sample is a single-element pure metal of the element to be tested, the measured intensity value is... ,at this time When the calibration sample is a single-element pure metal with other elements as its components, the measured strength value is... ,at this time By combining the two, we can obtain and .

[0031] As a preferred embodiment of the present invention: in step 2), a mask or weight attenuation is set for the low signal region to eliminate non-true concentration-dominant regions caused by severe thinning, porosity, or severe diffusion of the sample.

[0032] As a preferred embodiment of the present invention, the mask processing procedure is as follows:

[0033] Due to defects such as severe sample thinning or porosity, the intensity of EDS images in unreliable regions may be extremely high or low. Users can check the intensity range of these unreliable regions and perform binary masking.

[0034] (5);

[0035] In the above formula, This is a binary mask function; 1 indicates that values ​​should be retained, and 0 indicates that values ​​should be removed. The initial intensity of element e at pixel position (x, y), where T is the range of values ​​for the untrusted region, is obtained by applying a mask:

[0036] (6);

[0037] This is the data after masking.

[0038] As a preferred embodiment of the present invention, the weight attenuation process is as follows:

[0039] If the untrusted region is relatively small and its location is important, weight decay can be applied to ensure spatial continuity; define the weight coefficient. Define the form of the weighting coefficients according to the image quality:

[0040] (7);

[0041] In the above formula, The threshold for the completely untrusted region. The threshold for the fully trustworthy region;

[0042] The weighted decay function applied to the EDS intensity is as follows:

[0043] (8);

[0044] This is the data after weight decay.

[0045] As a preferred embodiment of the present invention, the specific process of converting each pixel site of the normalized EDS signal map into a relative volume fraction distribution map of each element in step 3) is as follows:

[0046] For any pixel (i, j) in the image matrix, where i and j represent the horizontal and vertical coordinates of the image matrix, respectively, the relative volume fraction of at least two different elements at this pixel is statistically calculated; now, element A is used as the normalized element distribution content and denoted as... Then the relative volume fraction of element A at pixel (i, j) Calculate using the following formula:

[0047] ;

[0048] In the above formula, This is the sum of the normalized contents of all elements at pixel (i, j); the relative volume fractions of other elements at this pixel are calculated in the same way. By statistically calculating the relative volume fractions, the relative contents of each element at each pixel position are obtained.

[0049] As a preferred embodiment of the present invention, the method for decoupling the obtained atomic displacement field using a binomial gradient model in step 4) is as follows: through geometric phase analysis, the aberration-corrected transmission electron microscope image is subjected to Fourier transform to obtain the reciprocal space phase information, and the phase information is converted into atomic-scale displacement gradient. Then, using a binomial gradient model, the displacement gradient is decomposed 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 deformation decoupling is performed respectively to obtain the spatial distribution maps of volumetric strain, shear strain and rotational strain.

[0050] As a preferred embodiment of the present invention, the specific process of using the Pearson correlation coefficient to perform correlation analysis between the element volume fraction and each strain component in step 5) is as follows:

[0051] The correlation coefficients between element A and the volumetric expansion, shear, and rotational strain components are defined as follows:

[0052] ;

[0053] ;

[0054] ;

[0055] In the above formula, , , These are the correlation coefficients between element A and the volumetric expansion, shear, and rotational strain components, respectively. A value greater than 0 indicates a positive correlation, a value less than 0 indicates a negative correlation, and a value equal to 0 indicates no correlation. , , These are the volumetric dilatation, shear, and rotational strain components at pixel location (i, j), respectively. , , These represent the average volumetric expansion, shear, and rotational strain within the statistical region, respectively. Let A be the relative volume fraction of element A at pixel location (i, j). The average relative volume fraction of element A within the statistical region;

[0056] The numerator of the above three formulas , , These represent the covariances of volumetric expansion, shear, and rotational strain with the relative volume fraction of element A, respectively, to measure the magnitude of the deviation of deformation from the element distribution in the same or opposite direction.

[0057] The denominator of the above three formulas , , These represent the products of the standard deviations of volumetric expansion, shear, and rotational strain and the standard deviation of the relative volume fraction of element A, respectively. They are used to normalize the covariance to eliminate the effects of dimensional and scale differences.

[0058] By adopting the above technical solution, the present invention has the following beneficial effects:

[0059] This invention presents a well-designed quantitative analysis method based on the correlation between elemental distribution and atomic strain field in EDS (Electronic Data Sequencing). The EDS scan data post-processing operation normalizes and weights the results, eliminating errors introduced by the sample and the measurement itself. Two gradient deformation field decomposition techniques based on geometric phase analysis consider both affine and non-affine deformation, providing a more comprehensive decomposition of atomic volumetric rotation and shear deformation fields. The defined correlation between elemental distribution and deformation field effectively quantifies the involvement of different deformation types. This invention can quantitatively reveal the coupling relationship between elemental distribution and atomic-scale deformation modes, offering advantages such as strong suppression of non-concentration errors, good repeatability, and wide applicability.

[0060] This invention uses EDS elemental scanning technology to obtain elemental distribution information. To eliminate the inherent drawbacks of EDS, such as instability and severe influence from sample quality and internal defects, normalization and weighting are used to obtain the weighted content of different elements at different locations. This eliminates errors caused by the sample and measurement process. For example, scanning CoCrNi yields the distribution surfaces of Co, Cr, and Ni. Due to sample and measurement errors, the intensity at different locations is affected not only by the energy emitted by the elements themselves but also by many other interfering factors. Therefore, after normalization, the weighted proportions of the three elements can be taken to eliminate errors caused by the sample and measurement process itself.

[0061] In addition, an important factor in selecting EDS is its combination with the next step of atomic deformation field analysis; EDS can be combined with HRTEM / ACTEM (high-resolution transmission electron microscopy / spherical aberration-corrected transmission electron microscopy) to provide possibilities for subsequent correlation analysis.

[0062] To investigate the roles of different chemical elements in plastic deformation, this invention employs AC-TEM+EDS to obtain two-dimensional (2D) element distribution maps. Simultaneously, it uses the AC-TEM+GPA+binomial gradient model to generate distribution maps for volumetric expansion, shear, and rotational deformation. Correlation coefficients between each element and each deformation field are then defined for these two types of maps to measure which type of deformation each element participates in more and is more correlated with. This reveals the roles of elements in plastic deformation and provides a basis for material design. Attached Figure Description

[0063] To more clearly illustrate the specific embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the specific embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of the present invention. For those skilled in the art, other drawings can be obtained from these drawings without creative effort.

[0064] Figure 1 This is a flowchart of the quantitative analysis method based on the correlation between EDS elemental distribution and atomic strain field of the present invention;

[0065] Figure 2 The image shows the initial results of spherical aberration electron microscopy observation and EDS scanning of a medium-entropy alloy CoCrNi sample after dynamic deformation, as per the present invention.

[0066] Figure 3 This is the result of preprocessing and normalizing the energy spectrum of the three elements in EDS according to the present invention.

[0067] Figure 4 The present invention relates to a result image obtained by decomposing the deformation field based on the spherical aberration transmission electron microscopy result image;

[0068] Figure 5 This is a schematic diagram showing the statistical analysis of the selective substitution determination region involved in this invention, extracting data from the elemental distribution field and deformation field, respectively.

[0069] Figure 6 The invention relates to the above. Figure 5 The data is substituted into the correlation coefficient calculation to obtain the correlation coefficient graph. Detailed Implementation

[0070] The technical solution of the present invention will now be clearly and completely described with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of the present invention. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0071] The present invention will be further explained below with reference to specific embodiments.

[0072] like Figure 1 As shown in the figure, this embodiment provides a quantitative analysis method based on the correlation between EDS elemental distribution and atomic strain field. The specific process is as follows:

[0073] S100. Acquire spherical aberration-corrected transmission electron microscope (AC-TEM) images and corresponding EDS element distribution energy spectra under the same field of view, and spatially register the spherical aberration-corrected AC-TEM images and EDS element distribution energy spectra. Specifically, the spherical aberration-corrected AC-TEM images and EDS element distribution energy spectra are acquired at the same location. After determining the location to be captured for the AC-TEM images, the AC-TEM images are captured, and EDS scans are randomly performed at that location to acquire the element distribution energy spectra of that region.

[0074] S200. The energy spectrum distributions of each element in the EDS are subjected to noise suppression processing such as median filtering and Gaussian smoothing. After filtering, the intensity of each element is normalized using a preset calibration relationship to obtain a normalized EDS signal image. The specific process is as follows:

[0075] For the energy spectrum of each element in EDS, the intensities are:

[0076] (1);

[0077] Where, the subscript 'e' is the element type index (e.g., in the CoCrNi alloy, 'e' refers to the three elements Co, Cr, and Ni, while CO, Cr, and Ni are element symbols); (x,y) represents the pixel coordinates, which measure the spatial position. The initial intensity of element e at pixel position (x, y).

[0078] Median filtering is performed on the energy spectrum of each element in the EDS based on the initial scan quality of the material. The purpose is to eliminate noise. The median filtering formula is as follows:

[0079] (2);

[0080] in, This represents the intensity after median filtering; median(.) is the formula for calculating the median, which means taking the median value when the internal data are arranged from largest to smallest. The neighborhood window centered at (x, y) has a size of k x k. The value of k can be determined based on the initial scan quality. If the initial scan quality is good, it can be 3 or even 1 (when it is 1, no median filtering operation is performed). If the quality is poor, it can be 5 or 7. It is not recommended to have a larger value, as it may cause distortion. (i, j) is the pixel coordinate index inside the window. Let (x, y) be the initial set of intensity values ​​for the neighborhood window centered at (x, y) with a window size of k x k.

[0081] After median filtering removes some noise, the next step, to suppress statistical noise in the EDS image and improve stability, is to perform Gaussian smoothing on the energy distribution spectra of each element in the EDS image after noise removal. The formula is as follows:

[0082] (3);

[0083] Where, the subscript 'e' is the element type index (e.g., in CoCrNi alloy, 'e' refers to the three elements Co, Cr, and Ni respectively); (x,y) represents the pixel coordinates, which measure the spatial position. Indicates the intensity after Gaussian smoothing; These represent the offset of the convolution kernel coordinates (x, y), and represent the displacement of the kernel relative to the center. This represents the weighting coefficient of the two-dimensional Gaussian kernel at the offset (u, v), where , Use Gaussian standard deviation to control smoothing intensity. The larger the value, the stronger the smoothing and the lower the noise, but the more blurred the boundaries. To preserve the details of the EDS image, a value of 0.6-1.0 is generally used for mild noise reduction. r represents the radius of the convolution kernel. .

[0084] In step S200, the elemental distribution maps of the EDS measurement results are normalized and statistically calibrated using standard samples or samples with known average composition, and the linearized structure results of the EDS elemental distribution energy spectra are output. The EDS elemental distribution energy spectra after median filtering and Gaussian smoothing are then normalized, and their intensity magnitudes are linearly calibrated.

[0085] (4);

[0086] in, This refers to the calibrated element content. This represents the intensity after a series of preprocessing steps (median filtering + Gaussian smoothing). and The linear fitting parameters are obtained through calibration using standard samples (pure metals of different elements). Specifically, when the calibration sample is a single-element pure metal of the element to be tested, the measured intensity value is... ,at this time When the calibration sample is a single-element pure metal with other elements as its components, the measured strength value is... ,at this time By combining the two, we can obtain and .

[0087] In step S200 above, a mask or weight attenuation is applied to the low-signal region to eliminate areas where the concentration is not true, caused by severe thinning, porosity, or severe diffusion of the sample. Masking or weight attenuation is an optional data processing method. Since the sample may have unreliable areas due to defects such as severe thinning or porosity leading to non-true concentrations, a masking process can be performed before median filtering and Gaussian smoothing, directly removing these areas as invalid regions. However, if this part is very important and removal would compromise its continuity, weight attenuation can be performed, as detailed below:

[0088] ① Masking

[0089] Due to defects such as severe sample thinning or porosity, the intensity of EDS images in unreliable regions may be extremely high or low. Users can check the intensity range of these unreliable regions and perform binary masking.

[0090] (5);

[0091] in, This is a binary mask function, where 1 represents retaining the values ​​and 0 represents removing the values. The initial intensity of element e at pixel position (x, y), where T is the range of values ​​for the untrusted region. Applying a mask results in:

[0092] (6);

[0093] This is the data after masking.

[0094] ② Weight decay

[0095] If the untrusted region is relatively small and its location is important, weight decay can be applied to ensure spatial continuity; define the weight coefficient. The weighting coefficients can be defined according to the image quality; for example, a linear weighting coefficient:

[0096] (7);

[0097] in, The threshold for the completely untrusted region. The threshold for the fully trustworthy region. The definition of the threshold depends on the actual EDS data.

[0098] The weighted decay function applied to the EDS intensity is as follows:

[0099] (8);

[0100] This is the data after weight decay.

[0101] S300. Statistically analyze each pixel site of the normalized EDS signal image and convert it into a relative volume fraction distribution map of each element to eliminate the influence of sample thickness and defects on the EDS signal (since the EDS energy spectrum image determines the distribution of multiple elements and is measured simultaneously at the same location, the intensity of the EDS image of multiple elements is consistent with the influence of the sample and the drift during the measurement process, so the error of this part can be eliminated when taking the relative volume fraction).

[0102] The method described above for converting the data into a relative volume fraction distribution map of each element is as follows:

[0103] For any pixel (x, y) in the normalized image matrix, where x and y represent the horizontal and vertical coordinates of the image matrix, respectively, the normalized element distribution content of at least two different elements A, B, C, etc. at this pixel is denoted as follows: , , If so, then the relative volume fraction of element A at the pixel point (x, y) is... Calculate using the following formula:

[0104] (9);

[0105] in, This is the sum of the normalized values ​​of all elements at the pixel (x, y).

[0106] The relative volume fractions of other elements at that pixel are calculated in the same way;

[0107] By statistically calculating the relative volume fractions, the relative content of each element at each pixel location can be obtained, effectively reducing or eliminating spatial absolute intensity errors caused by factors such as lattice defects and sample thickness variations, thereby enabling more accurate comparison and characterization of the spatial distribution characteristics of different elements.

[0108] S400. Perform geometric phase analysis on the AC-TEM of the same region to obtain the atomic displacement field. Then, use the binomial gradient model to decouple the obtained atomic displacement field to obtain atomic strain field images of the bulk dilatation strain component, shear strain component, and lattice rotation component.

[0109] The above-mentioned method for decoupling the obtained atomic displacement field using a binomial gradient model includes: using geometric phase analysis, performing Fourier transform on the aberration-corrected transmission electron microscope image to obtain reciprocal space phase information, and converting the phase information into atomic-scale displacement gradients. Using a binomial gradient model, the displacement gradient is decomposed 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 deformation decoupling is performed separately to obtain spatial distribution maps of volumetric strain, shear strain, and rotational strain.

[0110] The decoupling process between geometric phase analysis and the binomial gradient model is as follows:

[0111] Based on the high-resolution images obtained from transmission electron microscopy, we obtained the transmission image information of the crystal after deformation. After performing a Fourier transform, the deont space is obtained, and the reciprocal space information is acquired by selecting different basis vectors. , The target's diffraction points are masked, and the intensity distribution information is reconstructed by performing an inverse Fourier transform on the selected diffraction points:

[0112] (10);

[0113] I represents the positive space intensity distribution information obtained after the inverse Fourier transform, Ag and Pg represent the amplitude and phase of different diffraction points, respectively, and A0 represents the basic value of the positive space intensity. A vector represents a spatial location in positive space. , The selected basis vectors are respectively and .

[0114] The displacement field formula is derived based on the phase change:

[0115] (11);

[0116] Where, u in the above formula x u y These represent the horizontal and vertical displacements in the high-resolution transmission electron microscope image, respectively. , , and Take the basis vectors respectively and The horizontal and vertical coordinates; and They are respectively and The periodic phase change in the direction is about the positive space coordinates. The function.

[0117] Then perform Taylor expansion on the displacement. (12);

[0118] Calculate the first-order affine displacement gradient tensor F and the second-order non-affine displacement gradient tensor η respectively; where the expansion form of the first-order affine displacement gradient tensor is: The second-order non-affine displacement gradient tensor is represented as:

[0119] ;

[0120] Decomposition of the basic localized deformation events of the first-order affine displacement gradient tensor in two-dimensional space:

[0121] ;

[0122] In the above formula These are the components of the three basic localization events—volume dilation, shearing, and rotation—in affine deformation, respectively, and the function tr(F) represents these components. ij ) represents solving for tensor F ij traces, This is equivalent to the sum of the principal deformation gradients, reflecting the volume expansion localization event of the tensor;

[0123] Decomposition of basic localized deformation events in the second-order non-affine displacement gradient tensor in two-dimensional space:

[0124] ;

[0125] And in the above formula These represent the volume dilation, shear, and rotational components in non-affine deformation, respectively. The Kronecker function is used to perform index replacement or component selection in tensor operations. i and j are the indices of the tensor;

[0126] The volume dilation, rotation, and shear components of affine and non-affine deformations are superimposed:

[0127] ;

[0128] in, , , These are the volume expansion, shear, and rotational components that are comprehensively considered in both affine and non-affine deformation. Let be a first-order binomial tensor, where With basis vectors Parallel, its modulus is equal to the interplanar spacing pointing downwards. Perpendicular to Modulus equal to vertical The interplanar spacing facing downwards; , and These are the volume dilation, shear, and rotation components of the dimensionless second-order nonaffine deformation, respectively.

[0129] S500. Align the relative volume fraction distribution map of each element obtained in step S300 with the atomic strain field image obtained in step S400 on the same pixel grid. Using pixels as statistical units, perform correlation analysis between element volume fraction and each strain component using Pearson correlation coefficient, and generate a correlation coefficient map (the horizontal axis of the correlation coefficient map is the deformation type, the vertical axis is the element distribution, and it is divided into several grids, with the grid value being the correlation coefficient).

[0130] The specific process of using the Pearson correlation coefficient to perform correlation analysis between elemental volume fraction and each strain component (volume expansion, shear, and rotational strain components) is as follows:

[0131] The correlation coefficients between element A and the volumetric expansion, shear, and rotational strain components are defined as follows:

[0132] ;

[0133] ;

[0134] ;

[0135] In the above formula, , , These are the correlation coefficients between element A and the volumetric dilatation, shear, and rotational strain components, respectively. A value greater than 0 indicates a positive correlation, less than 0 indicates a negative correlation, and 0 indicates no correlation. , , Let represent the volumetric dilatation, shear, and rotational strain components at pixel location (i, j). , , The average volumetric expansion, shear, and rotational strain within the statistical region. Let A be the relative volume fraction of element A at pixel location (i, j). The average relative volume fraction of element A within the statistical region; the numerator of the above three formulas. , , Let $\mathbf{A}$ represent the covariances of volumetric expansion, shear, and rotational strain with the relative volume fraction of element A, respectively, to measure the magnitude of the deviation of deformation from the element distribution in the same or opposite direction. The denominator is... , , These represent the products of the standard deviations of volumetric expansion, shear, and rotational strain and the standard deviation of the relative volume fraction of element A, respectively. They are used to normalize the covariance to eliminate the effects of dimensional and scale differences.

[0136] S600. Based on the sign and magnitude of the correlation coefficients in the correlation score graph, identify the local deformation type corresponding to each element: n element types (e.g., A1, A2, A3…, An) and 3 deformation types (volume dilation, shear, and rotation) can be calculated pairwise, resulting in 3*n correlation coefficients, namely A1-volume dilation, A1-shear, A1-rotation, A2-volume dilation… The value range of these correlation coefficients is [-1, 1], with both positive and negative values. When the coefficient is greater than zero, it indicates a positive correlation, and a coefficient greater than 0.5 indicates a strong positive correlation; when the coefficient is less than zero, it indicates a negative correlation, and a coefficient less than -0.5 indicates a strong negative correlation. In terms of physical interpretation, for example, when the correlation coefficient between element A1 and shear deformation is 0.8, then element A1 dominates shear deformation during the entire deformation process. If the correlation coefficient between element A2 and rotational deformation is -0.8, then element A2 basically does not participate in rotational motion during the deformation process. The correlation result between element distribution and atomic strain field is output (this correlation result is the value of r, which indicates the correlation between element distribution and deformation distribution, meaning which type of element participates more in which motion).

[0137] The morphology of the dynamically deformed CoCrNi alloy specimen was observed by spherical aberration electron microscopy and EDS scanning. The initial results are as follows: Figure 2 As shown;

[0138] The data from the three element distributions of EDS were preprocessed and normalized, and the results are as follows: Figure 3 As shown;

[0139] Based on the spherical aberration transmission electron microscopy results, deformation field decomposition was performed to obtain the following... Figure 4 The results are shown below;

[0140] Statistical analysis was performed on the selected substitution measurement area, and data were extracted from the elemental distribution field and deformation field, respectively. Figure 5 As shown;

[0141] Based on the above data, substituting it into the correlation coefficient calculation, we can obtain 9 correlation coefficients, and create a correlation coefficient graph (e.g.) Figure 6 (As shown in the figure). The horizontal axis represents deformation type, the vertical axis represents element type, and the color of the values ​​represents the correlation coefficient. When the coefficient is greater than zero, it indicates a positive correlation, and a coefficient greater than 0.5 indicates a strong positive correlation. When the coefficient is less than zero, it indicates a negative correlation, and a coefficient less than -0.5 indicates a strong negative correlation. In this example, Cr mainly participates in atomic-scale bulk expansion deformation, while Ni shows a strong negative correlation with bulk expansion, which means that Ni basically does not participate in bulk expansion deformation.

[0142] This invention can quantitatively reveal the coupling relationship between elemental distribution and atomic-scale deformation modes, and has the advantages of strong ability to suppress non-concentration errors, good repeatability of results, and wide applicability.

[0143] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A quantitative analysis method based on the correlation between EDS elemental distribution and atomic strain field, characterized in that, Includes the following steps: 1) Acquire spherical aberration-corrected transmission electron microscope (TEM) images and corresponding EDS element distribution energy spectra under the same field of view, and spatially register the spherical aberration-corrected TEM images and EDS element distribution energy spectra. 2) The energy spectrum of each element in the EDS is subjected to median filtering and Gaussian smoothing noise suppression processing, then filtered again, and the intensity of each element is normalized through a preset calibration relationship to obtain a normalized EDS signal image. 3) Statistically analyze each pixel location of the normalized EDS signal map and convert it into a relative volume fraction distribution map of each element to eliminate the influence of sample thickness and defects on the EDS signal; 4) Perform geometric phase analysis on the spherical aberration transmission electron microscope images of the same region to obtain the atomic displacement field. Then, use the binomial gradient model to decouple the obtained atomic displacement field to obtain atomic strain field images of the bulk dilatation strain component, shear strain component, and lattice rotation component. 5) Align the relative volume fraction distribution map of each element obtained in step 3) with the atomic strain field image obtained in step 4) on the same pixel grid. Using pixels as statistical units, perform correlation analysis between element volume fraction and each strain component using Pearson correlation coefficient, and generate a correlation coefficient map. 6) Based on the sign and magnitude of the correlation coefficients in the correlation score graph, identify the local deformation type corresponding to each element and output the correlation results between the element distribution and the atomic strain field.

2. The quantitative analysis method based on the correlation between EDS elemental distribution and atomic strain field according to claim 1, characterized in that: The spherical aberration transmission electron microscope (TEM) image and the energy spectrum of elemental distribution in EDS are obtained from the same location. After determining the location to be captured for the TEM image, the TEM image is captured, and an EDS scan is performed randomly at that location to obtain the energy spectrum of elemental distribution in that region.

3. The quantitative analysis method based on the correlation between EDS elemental distribution and atomic strain field according to claim 1, characterized in that, The specific process of step 2) is as follows: For the energy spectrum of each element in EDS, the intensity is: （1）； In the above formula, the subscript 'e' is the element type index; (x, y) represents the pixel coordinates, which measure the spatial position. This represents the initial intensity of element e at pixel position (x, y); Median filtering is applied to the energy spectrum of each element in the EDS based on the initial scan quality of the material to eliminate noise. The median filtering formula is as follows: （2）； In the above formula, This represents the intensity after median filtering; the median function is the formula for calculating the median, which means that the internal data are arranged from largest to smallest and the median value is taken. The neighborhood window is centered at (x, y) and has a size of k x k. The value of k is determined based on the initial scan quality. If the initial scan quality is good, it is 1 or 3; if the quality is poor, it is 5 or 7. (i, j) is the pixel coordinate index inside the window. Let (x, y) be the initial set of intensity values ​​for the neighborhood window centered at (x, y) with a window size of k x k. After removing noise through median filtering, the energy distribution spectra of each element in the EDS after noise removal are then Gaussian smoothed to suppress statistical noise in the EDS energy distribution spectra. The formula is as follows: （3）； In the above formula, the subscript 'e' is the element type index; (x, y) represents the pixel coordinates, which measure the spatial position. Indicates the intensity after Gaussian smoothing; These represent the offset of the convolution kernel coordinates (x, y), and represent the displacement of the kernel relative to the center. This represents the weighting coefficient of the two-dimensional Gaussian kernel at the offset (u, v), where , Use Gaussian standard deviation to control smoothing intensity. r represents the radius of the convolution kernel. .

4. The quantitative analysis method based on the correlation between EDS elemental distribution and atomic strain field according to claim 1, characterized in that: In step 2), the elemental distribution maps of the EDS measurement results are normalized and statistically calibrated using standard samples or samples with known average composition. The linearized structure of the EDS elemental distribution energy spectrum is then output. The median-filtered and Gaussian-smoothed EDS elemental distribution energy spectra are normalized, and their intensity magnitudes are linearly calibrated. （4）； In the above formula, This refers to the calibrated element content; This indicates the intensity after median filtering and Gaussian smoothing. and The linear fitting parameters are obtained from calibration using standard samples; that is, when the calibration sample is a single-element pure metal of the element to be tested, the measured intensity value is... ,at this time When the calibration sample is a single-element pure metal with other elements as its components, the measured strength value is... ,at this time By combining the two, we can obtain and .

5. The quantitative analysis method based on the correlation between EDS elemental distribution and atomic strain field according to claim 1, characterized in that: In step 2), a mask or weight attenuation is applied to the low-signal region to eliminate regions that are not dominated by true concentration due to severe thinning, porosity, or severe diffusion of the sample.

6. The quantitative analysis method based on the correlation between EDS elemental distribution and atomic strain field according to claim 5, characterized in that, The mask processing procedure is as follows: Due to defects such as severe sample thinning or porosity, the intensity of EDS images in unreliable regions may be extremely high or low. Users can check the intensity range of these unreliable regions and perform binary masking. （5）； In the above formula, This is a binary mask function; 1 indicates that values ​​should be retained, and 0 indicates that values ​​should be removed. The initial intensity of element e at pixel position (x, y), where T is the range of values ​​for the untrusted region, is obtained by applying a mask: （6）； This is the data after masking.

7. The quantitative analysis method based on the correlation between EDS elemental distribution and atomic strain field according to claim 5, characterized in that, The weight decay process is as follows: If the untrusted region is relatively small and its location is important, weight decay can be applied to ensure spatial continuity; define the weight coefficient. Define the form of the weighting coefficients according to the image quality: （7）； In the above formula, The threshold for the completely untrusted region. The threshold for the fully trustworthy region; The weighted decay function applied to the EDS intensity is as follows: （8）； This is the data after weight decay.

8. The quantitative analysis method based on the correlation between EDS elemental distribution and atomic strain field according to claim 1, characterized in that, The specific process of statistically analyzing each pixel location in the normalized EDS signal map and converting it into a relative volume fraction distribution map of each element in step 3) is as follows: For any pixel (i, j) in the image matrix, where i and j represent the horizontal and vertical coordinates of the image matrix, respectively, the relative volume fraction of at least two different elements at this pixel is statistically calculated; now, element A is used as the normalized element distribution content and denoted as... Then the relative volume fraction of element A at pixel (i, j) Calculate using the following formula: ； In the above formula, This is the sum of the normalized contents of all elements at pixel (i, j); the relative volume fractions of other elements at this pixel are calculated in the same way. By statistically calculating the relative volume fractions, the relative contents of each element at each pixel position are obtained.

9. The quantitative analysis method based on the correlation between EDS elemental distribution and atomic volume dilatation-shear rotational strain field according to claim 1, characterized in that, The method for decoupling the obtained atomic displacement field using the binomial gradient model in step 4) is as follows: through geometric phase analysis, the aberration-corrected transmission electron microscope image is subjected to Fourier transform to obtain the reciprocal space phase information, and the phase information is converted into atomic-scale displacement gradient. Then, using the binomial gradient model, the displacement gradient is decomposed 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 deformation decoupling is performed separately to obtain the spatial distribution maps of volumetric strain, shear strain and rotational strain.

10. The quantitative analysis method based on the correlation between EDS elemental distribution and atomic strain field according to claim 1, characterized in that, The specific process of using the Pearson correlation coefficient to perform correlation analysis between elemental volume fraction and each strain component in step 5) is as follows: The correlation coefficients between element A and the volumetric expansion, shear, and rotational strain components are defined as follows: ； ； ； In the above formula, , , These are the correlation coefficients between element A and the volumetric expansion, shear, and rotational strain components, respectively. A value greater than 0 indicates a positive correlation, a value less than 0 indicates a negative correlation, and a value equal to 0 indicates no correlation. , , These are the volumetric dilatation, shear, and rotational strain components at pixel location (i, j), respectively. , , These represent the average volumetric expansion, shear, and rotational strain within the statistical region, respectively. Let A be the relative volume fraction of element A at pixel location (i, j). The average relative volume fraction of element A within the statistical region; The numerator of the above three formulas , , These represent the covariances of volumetric expansion, shear, and rotational strain with the relative volume fraction of element A, respectively, to measure the magnitude of the deviation of deformation from the element distribution in the same or opposite direction. The denominator of the above three formulas , , These represent the products of the standard deviations of volumetric expansion, shear, and rotational strain and the standard deviation of the relative volume fraction of element A, respectively. They are used to normalize the covariance to eliminate the effects of dimensional and scale differences.

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