Defect retrieval methods and systems applied to polycrystalline systems

Abstract

This invention discloses a defect retrieval method and system applied to polycrystalline systems, belonging to the field of grain boundary analysis technology. The method includes: determining the number N of nearest-neighbor atoms in the first shell of the unit cell under test based on the shell definition. p Based on the nearest neighbor number N p The process involves determining a reference vector set and an actual vector set; summing the first reference vectors in the reference vector set pairwise and taking the minimum value to obtain the second reference vector; calculating the scaling parameter λ based on the reference vector set and the actual vector set; and calculating the E-CSP value based on the actual vector in the actual vector set, the second reference vector, and the scaling parameter. This invention improves upon the traditional CSP method, and the improved E-CSP method is applicable to defect retrieval in all crystal systems.

Description

Technical Field

[0001] This invention relates to the field of grain boundary analysis technology, and specifically to a defect retrieval method and system applicable to polycrystalline systems. Background Technology

[0002] The centrosymmetry parameter (CSP) method has a nearest neighbor of 12 for cubic and face-centered cubic crystal systems, and 8 for body-centered cubic systems. When using the CSP method for defect detection, the CSP value is zero for defect-free crystals. However, for defective crystal regions, the atomic field typically has perturbed non-centrosymmetric neighborhoods, resulting in a positive CSP value. By selecting an appropriate threshold, small perturbations due to thermal displacement and elastic strain can be allowed, and defect atoms can be identified through coloring. However, this method is only applicable to centrosymmetric atoms; for non-centrosymmetric atoms, such as HCP atoms, the error is too large. Furthermore, the threshold is manually defined, and its selection directly affects the calculation results.

[0003] Nearest neighbor analysis (NDA) is a method that uses bond length thresholds to screen and identify non-centrosymmetric atomic structures, and it is applicable to all crystal systems. However, the selection of the number of nearest neighbor atoms directly affects the calculation results, and different crystal systems may introduce errors if only the nearest neighbor atoms are considered.

[0004] In related technologies, patent application CN 113903406 A discloses a defect retrieval method based on the common nearest neighbor method extended to multiple crystal systems. This method simplifies complex crystal structures and then determines classifications based on the cumulative number of nearest neighbors. By accumulating the number of 12 and 14 nearest neighbors, and using the coordination numbers of known FCC, BCC, and HCP structures, it further filters for defective and defect-free atoms. Then, it uses the DXA method to distinguish between crystal interfaces and stacking fault interfaces, and finally retrieves defects other than those at crystal interfaces and stacking fault interfaces, thus achieving comprehensive defect retrieval for multiple crystal systems. This method uses three indexes to identify defect atoms based on the common nearest neighbor method, which can accurately identify defect atoms. However, it is not a defect retrieval method extended to multiple crystal systems using the CSP method, and it lacks a molecular dynamics-based identification system in terms of program and algorithm. Summary of the Invention

[0005] The technical problem to be solved by this invention is how to extend the CSP method to defect retrieval of all crystalline materials.

[0006] The present invention solves the above-mentioned technical problems through the following technical means:

[0007] On one hand, this invention proposes a defect retrieval method applicable to polycrystalline systems, the method comprising:

[0008] Based on the shell definition, determine the number N of nearest-neighbor atoms in the first shell of the unit cell under test. p The shell is defined as follows: atoms that have the same type of bond as the central atom are said to be in the same shell.

[0009] Based on the number of nearest neighbor atoms N p Determine the reference vector set and the actual vector set;

[0010] The second reference vector is obtained by adding the first reference vectors in the reference vector set pairwise and taking the minimum value.

[0011] Calculate the scaling parameter λ based on the reference vector set and the actual vector set;

[0012] Based on the actual vectors in the actual vector set Second reference vector And the proportional parameter λ, calculate the E-CSP value as follows:

[0013]

[0014] This invention improves upon the traditional CSP method. For centrally asymmetric atomic structures, it first reduces errors by calculating the scaling parameter λ, and then by... The difference is obtained from a value starting from 0, which converts the centrally asymmetric atomic structure into a centrally symmetric structure. Therefore, it is applicable not only to centrally symmetric atomic structures but also to centrally asymmetric atomic structures. The improved E-CSP method is applicable to defect retrieval in all crystal systems.

[0015] Furthermore, based on the shell definition, the number N of nearest-neighbor atoms in the first shell of the unit cell under test is determined. p ,include:

[0016] Based on the shell definition, the shells of the 14 Bravais lattices are classified to obtain the shell classification results.

[0017] The number of bond types satisfied by each shell in the shell classification results is counted, and a reference table of shell bonding and atomic number of unit cell is constructed.

[0018] Based on the unit cell structure and the reference table of shell bonding and atomic number of the unit cell, the number N of nearest-neighbor atoms in the first shell of the unit cell to be tested is determined. p .

[0019] Furthermore, the method based on the number of nearest neighbor atoms N pDetermine the reference vector set and the actual vector set, including:

[0020] Based on the coordinates of the central atom after expanding the octet, N is selected. p / 2 For the first reference vector, construct the reference vector set of the central atom.

[0021] Based on the actual measurement results of the central atom, find the nearest N p 1 actual vector, construct the actual vector set

[0022] The first reference vector and the actual vector are sorted based on their magnitudes, respectively.

[0023] Furthermore, the formula for obtaining the second reference vector by adding the first reference vectors in the reference vector set pairwise and taking the minimum value is expressed as:

[0024]

[0025] Further, the calculation of the scaling parameter λ based on the reference vector set and the actual vector set includes:

[0026] Based on the one-to-one correspondence between the sorted first reference vector and the sorted actual vector, the scaling parameter λ is calculated, and the formula is expressed as follows:

[0027]

[0028] in, Let j be the magnitude of the sorted actual vector. Let be the magnitude of the j-th first reference vector after sorting.

[0029] Furthermore, the actual vectors based on the actual vector set Second reference vector And the proportional parameter λ, calculate the E-CSP value, including:

[0030] Perform a full permutation of all vectors in the actual vector set to obtain the full permutation result;

[0031] For each of the second reference vectors, find the following from the full permutation results: Make The minimum value corresponding to the second reference vector is taken as the E-CSP value, k≠l, k,l∈[1,N]. P ];

[0032] The total E-CSP value is calculated based on the E-CSP value corresponding to each of the second reference vectors.

[0033] Furthermore, based on the shell definition, the number N of nearest-neighbor atoms in the first shell of the unit cell under test is determined. p Previously, the method also included:

[0034] The defect-free atoms in the unit cell under test are identified using the E-CNA method, and then the defect-free atoms are removed.

[0035] Furthermore, the method also includes:

[0036] Based on the E-CSP values, defects in polycrystalline systems are classified by coloring.

[0037] Furthermore, this invention also proposes a defect retrieval system applicable to polycrystalline systems, the system comprising:

[0038] The nearest neighbor atom number determination module is used to determine the number N of nearest neighbor atoms in the first shell of the unit cell under test based on the shell definition. p The shell is defined as: atoms with the same type of bond as the central atom are in the same shell;

[0039] The vector set determination module is used to determine the nearest neighbor atom number N. p Determine the reference vector set and the actual vector set;

[0040] The reference vector determination module is used to add the first reference vectors in the reference vector set pairwise and take the minimum value to obtain the second reference vector.

[0041] The scaling parameter calculation module is used to calculate the scaling parameter λ based on the reference vector set and the actual vector set;

[0042] The E-CSP value calculation module is used to calculate the actual vectors in the actual vector set. Second reference vector And the proportional parameter λ, calculate the E-CSP value as follows:

[0043]

[0044] The coloring classification module is used to classify defects in polycrystalline systems by coloring according to the E-CSP value.

[0045] Furthermore, the nearest neighbor atom number determination module includes:

[0046] A shell classification unit is used to classify the shells of the 14 Bravais lattices based on the shell definition to obtain the shell classification results;

[0047] The reference table construction unit is used to count the number of bond types satisfied by each shell in the shell classification results and construct a reference table of shell bonding and atomic number of unit cell.

[0048] The nearest neighbor atom number determination unit is used to determine the nearest neighbor atom number N of the first shell of the unit cell under test based on the unit cell structure and a reference table of shell bonding and atom number of the unit cell. p .

[0049] Furthermore, the E-CSP value calculation module includes:

[0050] A permutation unit is used to perform a full permutation of all vectors in the actual vector set to obtain a full permutation result.

[0051] A search unit is configured to, for each of the second reference vectors, find from the full permutation results... Make The minimum value corresponding to the second reference vector is taken as the E-CSP value, k≠l, k,l∈[1,N]. P ];

[0052] The calculation unit is used to calculate the total E-CSP value based on the E-CSP value corresponding to each of the second reference vectors.

[0053] The advantages of this invention are:

[0054] (1) This invention improves upon the traditional CSP method. For centrally asymmetric atomic structures, it first reduces errors by calculating the scaling parameter λ, and then by... The difference is obtained from a value starting from 0, which converts the centrally asymmetric atomic structure into a centrally symmetric structure. Therefore, it is applicable not only to centrally symmetric atomic structures but also to centrally asymmetric atomic structures. The improved E-CSP method is applicable to defect retrieval in all crystal systems.

[0055] (2) The improved E-CSP method uses a numerical value to measure the atomic state of the defect, and the entire value is monotonically decreasing from 0, which facilitates the coloring and classification of defects in the later stage.

[0056] Additional aspects and advantages of the invention will be set forth in part in the description which follows, and in part will be obvious from the description, or may be learned by practice of the invention. Attached Figure Description

[0057] Figure 1 This is a flowchart illustrating a defect retrieval method applied to polycrystalline systems in one embodiment of the present invention;

[0058] Figure 2 This is a schematic diagram of the shell definition in this invention;

[0059] Figure 3 This is a comparison diagram of the 14 Bravais lattice bonding types and the number of bonds in each layer in this invention;

[0060] Figure 4 This is a comparison diagram of the shell bonding and atomic number of the five unit cells in this invention;

[0061] Figure 5 This is a schematic diagram of the expansion of a single cell into an eight-cell structure in this invention, where the left side of the diagram shows eight small bottom-centered unit cells, and the right side shows the expanded large unit cell.

[0062] Figure 6 This is a schematic diagram illustrating the defect identification generated after stretching the Zr block of the HCP structure in this invention.

[0063] Figure 7 This is a schematic diagram of a defect retrieval system applied to a polycrystalline system in another embodiment of the present invention. Detailed Implementation

[0064] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below in conjunction with the embodiments of the present invention. Obviously, the described embodiments are only some embodiments of the present invention, not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0065] like Figure 1 As shown in the figure, this invention proposes a defect retrieval method for polycrystalline systems, the method comprising the following steps:

[0066] S10. Based on the shell definition, determine the number N of nearest-neighbor atoms in the first shell of the unit cell to be tested. p The shell is defined as follows: atoms that have the same type of bond as the central atom are said to be in the same shell.

[0067] For the bottom core structure: there are 4 M3 bonds in the first shell, 6 M1 bonds in the second shell, 8 M4 bonds in the third shell, and 12 M5 bonds in the fourth shell.

[0068] S20, Based on the number of nearest neighbor atoms N p Determine the reference vector set and the actual vector set.

[0069] S30. Add the first reference vectors in the reference vector set pairwise and take the minimum value to obtain the second reference vector.

[0070] S40. Calculate the scaling parameter λ based on the reference vector set and the actual vector set.

[0071] S50. Based on the actual vectors in the actual vector set the second reference vector and the proportional parameter λ, calculate the E-CSP value as follows:

[0072]

[0073] In this embodiment, the traditional CSP method is improved. For the central asymmetric atomic structure, the error is first reduced by calculating the proportional parameter λ, and then by subtracting from to obtain a value starting from 0, so that the central asymmetric atomic structure is converted into a central symmetric structure. Therefore, it is not only applicable to the central symmetric atomic structure, but also applicable to the central asymmetric atomic structure. The improved E-CSP method is applicable to the defect retrieval of all crystal systems.

[0074] In one embodiment, in the step S10, the following sub-steps are included:

[0075] S11. Based on the shell definition, classify the shells of 14 Bravais lattices to obtain a shell classification result.

[0076] Among them, the schematic diagram of the shell definition refers to Figure 2 , where M3 < M1 < M4 < M5 < 2*M1, where M1 represents edge-edge, M2 represents edge-body center, M3 represents edge-face center, M4 represents edge-base center, and M5 represents diagonal plane.

[0077] S12. Count the number of types of bonds satisfied by each shell in the shell classification result, and construct a comparison table of shell bonding and atomic numbers of the unit cell.

[0078] In this embodiment, through the definition of the shell, the shells of 14 Bravais lattices are newly classified, and the number of types of bonds satisfied by each shell is correspondingly counted, obtaining a comparison table of bonding types and the number of bonds per layer of 14 Bravais lattices as shown in Figure 3 , and from this, a comparison table of shell bonding and atomic numbers of five types of unit cells as shown in Figure 4 is obtained.

[0079] S13. Based on the crystal cell structure and the comparison table of shell bonding and atomic numbers of the unit cell, determine the number of nearest neighbor atoms N of the first shell of the待测晶胞 (to be determined crystal cell) p .

[0080] It should be noted that in the traditional CSP method, Np is only the number of nearest-neighbor atoms for different crystal systems. However, for non-cubic and hexagonal structures, the selection of Np is highly uncertain. The E-CSP method proposed in this embodiment defines a shell as atoms with the same type of bond as the central atom. Based on this definition, the shells of the 14 Bravais lattices are reclassified, and the number of bond types satisfied by each shell is statistically analyzed. The number of Np atoms can be directly determined according to the summary table. For example, for... Figure 4 The cell structure shown allows for the selection of the number of atoms in the first shell: Np = 6 for a simple (non-hexagonal) structure, Np = 12 for a simple (hexagonal) structure, Np = 8 for a body-centered structure, Np = 12 for a face-centered structure, and Np = 4 for a bottom-centered structure. The selection of Np is also determined for both non-cubic and hexagonal structures, and the selection of Np using the traditional CSP method is also included.

[0081] In one embodiment, step S20 specifically includes the following sub-steps:

[0082] S21. Based on the coordinates of the central atom after expanding the octet, select N. p / 2 For the first reference vector, construct the reference vector set of the central atom.

[0083] It should be noted that, as Figure 5 As shown, we can directly select the large unit cell after expanding a single cell into an octet, and select Np / 2 pairs of vectors (with opposite directions) to obtain a total of Np / 2 pairs of first reference vectors, thereby constructing a reference vector set.

[0084] S22. Based on the actual measurement results of the central atom, find the nearest N. p 1 actual vector, construct the actual vector set

[0085] S23. Sort the first reference vector and the actual vector according to their magnitudes, respectively.

[0086] It should be noted that the first reference vector in the reference vector set is obtained by sorting it according to its magnitude. The actual vectors in the actual vector set are sorted according to their magnitudes to obtain... in, After sorting according to the module length After sorting according to the module length

[0087] In this embodiment, the number of Np vectors is directly determined according to the summarized reference table. The Np vectors closest to the central atom are selected by number, and can be directly sorted according to distance. for It also allows you to directly sort and select by distance, without needing to compare sizes.

[0088] In one embodiment, in step S30, the formula for calculating the second reference vector is:

[0089]

[0090] It should be noted that the second reference vector is taken as... The minimum sum of any pair of elements can be found by iterating through and eliminating elements.

[0091] In the reference vector set Select the first reference vector by distance. And search through the remaining first reference vector in the reference vector set. Make Minimum, and remove and Select by distance And search through the remaining first reference vector in the reference vector set. Make Minimum, remove again and Thus, after traversing all the elements, we can obtain Np / 2. And the calculated Sort by modulus length to obtain

[0092] In one embodiment, step S40 specifically includes:

[0093] Based on the one-to-one correspondence between the sorted first reference vector and the sorted actual vector, the scaling parameter λ is calculated, and the formula is expressed as follows:

[0094]

[0095] in, Let j be the magnitude of the sorted actual vector. Let be the magnitude of the j-th first reference vector after sorting.

[0096] It should be noted that although the calculation form of the proportionality coefficient λ in this embodiment is the same as that in the nearest neighbor analysis method, due to Np, The selection of the proportionality coefficient λ differs from that of the nearest neighbor analysis method, therefore the calculation of the proportionality coefficient λ is more accurate in this embodiment.

[0097] In one embodiment, step S50 specifically includes the following sub-steps:

[0098] S51. Perform a full permutation of all vectors in the actual vector set to obtain the full permutation result;

[0099] S52. For each of the second reference vectors, find the permutation result from the full permutation result. Make The minimum value corresponding to the second reference vector is taken as the E-CSP value, k≠l, k,l∈[1,N]. P ];

[0100] S53. Calculate the total E-CSP value based on the E-CSP value corresponding to each of the second reference vectors.

[0101] It should be noted that the E-CSP value corresponding to each second reference vector is calculated and then summed to obtain the total E-CSP value.

[0102] In one embodiment, the method further includes the following steps:

[0103] Based on the E-CSP values, defects in polycrystalline systems are classified by coloring.

[0104] It should be noted that because the values ​​calculated using the E-CSP method monotonically decrease from 0, it facilitates subsequent defect coloring and classification. This embodiment can express defects in non-centrosymmetric atomic structures through coloring, and by filtering the numerical peaks of E-CSP, defect atoms can be classified and represented. For example, the identification of defects generated after stretching a Zr bulk structure with an HCP structure is as follows: Figure 6 As shown, in Figure 6 In the diagram, (a) is a schematic diagram of the total material coloring using the E-CSP method, (b) is a schematic diagram of the total material after the determination of atoms in the total material is deleted using the E-CNA method, (c) is a schematic diagram of atoms after the first peak value is deleted according to the E-CSP value, and (d) is a schematic diagram of atoms after the second peak value is deleted according to the E-CSP value.

[0105] In one embodiment, prior to step S10, the method further includes the following steps:

[0106] The defect-free atoms in the unit cell under test are identified using the E-CNA method, and then the defect-free atoms are removed.

[0107] It should be noted that the E-CNA method described in this embodiment refers to the scheme described in the invention patent application with publication number CN 113903406 A. In this embodiment, the E-CNA method is used to identify and delete defect-free atoms. Then, the method of this embodiment is used to calculate the remaining atoms, delete atoms within the error range, and further analyze the defective atoms by coloring. This can achieve accurate identification and classification of defective atoms.

[0108] In addition, such as Figure 7 As shown, another embodiment of the present invention also proposes a defect retrieval system applicable to polycrystalline systems, the system comprising:

[0109] The nearest neighbor atom number determination module 10 is used to determine the nearest neighbor atom number N of the first shell of the unit cell under test based on the shell definition. p The shell is defined as: atoms with the same type of bond as the central atom are in the same shell;

[0110] Vector set determination module 20, used to determine the vector set based on the number of nearest neighbor atoms N p Determine the reference vector set and the actual vector set;

[0111] The reference vector determination module 30 is used to add the first reference vectors in the reference vector set pairwise and take the minimum value to obtain the second reference vector.

[0112] The scaling parameter calculation module 40 is used to calculate the scaling parameter λ based on the reference vector set and the actual vector set;

[0113] E-CSP value calculation module 50, used to calculate the actual vector in the actual vector set. Second reference vector And the proportional parameter λ, calculate the E-CSP value as follows:

[0114]

[0115] In this embodiment, the traditional CSP method is improved. For centrally asymmetric atomic structures, the error is first reduced by calculating the scaling parameter λ, and then by... The difference is obtained from a value starting from 0, which converts the centrally asymmetric atomic structure into a centrally symmetric structure. Therefore, it is applicable not only to centrally symmetric atomic structures but also to centrally asymmetric atomic structures. The improved E-CSP method is applicable to defect retrieval in all crystal systems.

[0116] In one embodiment, the nearest neighbor atom number determination module 10 includes:

[0117] A shell classification unit is used to classify the shells of the 14 Bravais lattices based on the shell definition to obtain the shell classification results;

[0118] The reference table construction unit is used to count the number of bond types satisfied by each shell in the shell classification results and construct a reference table of shell bonding and atomic number of unit cell.

[0119] The nearest neighbor atom number determination unit is used to determine the nearest neighbor atom number N of the first shell of the unit cell under test based on the unit cell structure and a reference table of shell bonding and atom number of the unit cell. p .

[0120] In one embodiment, the vector set determination module 20 includes:

[0121] Reference vector set determination unit, used to select N based on the coordinates of the central atom after octet expansion. p / 2 For the first reference vector, construct the reference vector set of the central atom.

[0122] The actual vector set determination unit is used to find the nearest N based on the actual measurement results of the central atom. p 1 actual vector, construct the actual vector set

[0123] The sorting unit is used to sort the first reference vector and the actual vector based on the magnitudes of the reference vector and the actual vector, respectively.

[0124] In one embodiment, the formula for calculating the second reference vector in the reference vector determination module 30 is as follows:

[0125]

[0126] It should be noted that the second reference vector is taken as... The minimum sum of any pair of elements can be found by iterating through and eliminating elements.

[0127] In the reference vector set Select the first reference vector by distance. And search through the remaining first reference vector in the reference vector set. Make Minimum, and remove and Select by distance And search through the remaining first reference vector in the reference vector set. Make Minimum, remove again and Thus, after traversing all the elements, we can obtain Np / 2. And the calculated Sort by modulus length to obtain

[0128] In one embodiment, the proportional parameter calculation module 40 is specifically used for:

[0129] Based on the one-to-one correspondence between the sorted first reference vector and the sorted actual vector, the scaling parameter λ is calculated, and the formula is expressed as follows:

[0130]

[0131] in, Let j be the magnitude of the sorted actual vector. Let be the magnitude of the j-th first reference vector after sorting.

[0132] In one embodiment, the E-CSP value calculation module 50 includes:

[0133] A permutation unit is used to perform a full permutation of all vectors in the actual vector set to obtain a full permutation result.

[0134] A search unit is configured to, for each of the second reference vectors, find from the full permutation results... This makes the E-CSP value corresponding to each of the second reference vectors Minimum, k≠l, k,l∈[1,N] P ];

[0135] The calculation unit is used to calculate the total E-CSP value based on the E-CSP value corresponding to each of the second reference vectors.

[0136] In one embodiment, the system further includes:

[0137] The coloring classification module is used to classify defects in polycrystalline systems by coloring according to the E-CSP value.

[0138] In one embodiment, the system further includes:

[0139] The identification module is used to identify defect-free atoms in the unit cell under test using the E-CNA method and to delete defect-free atoms.

[0140] It should be noted that other embodiments or implementation methods of the defect retrieval system applied to polycrystalline systems described in this invention can refer to the above-described method embodiments, and will not be repeated here.

[0141] In the description of this specification, references to terms such as "one embodiment," "some embodiments," "example," "specific example," or "some examples," etc., indicate that a specific feature, structure, material, or characteristic described in connection with that embodiment or example is included in at least one embodiment or example of the invention. In this specification, the illustrative expressions of the above terms do not necessarily refer to the same embodiment or example. Furthermore, the specific features, structures, materials, or characteristics described may be combined in any suitable manner in one or more embodiments or examples.

[0142] Furthermore, the terms "first" and "second" are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of technical features indicated. Thus, a feature defined as "first" or "second" may explicitly or implicitly include at least one of that feature. In the description of this invention, "a plurality of" means at least two, such as two, three, etc., unless otherwise explicitly specified.

[0143] Although embodiments of the present invention have been shown and described above, it is understood that the above embodiments are exemplary and should not be construed as limiting the present invention. Those skilled in the art can make changes, modifications, substitutions and variations to the above embodiments within the scope of the present invention.

Claims

1. A defect retrieval method applied to polycrystalline systems, characterized in that, The method includes: Based on the shell definition, determine the number N of nearest-neighbor atoms in the first shell of the unit cell under test. p The shell is defined as follows: atoms that have the same type of bond as the central atom are said to be in the same shell. Based on the number of nearest neighbor atoms N p Determine the reference vector set and the actual vector set, including: selecting N based on the coordinates of the central atom after expanding the octet. p / 2 pairs of the first reference vectors, constructing the reference vector set for the central atom. Based on the actual measurement results of the central atom, find the nearest N p 1 actual vector, construct the actual vector set The first reference vector and the actual vector are sorted based on their magnitudes, respectively. The second reference vector is obtained by adding the first reference vectors in the reference vector set pairwise and taking the minimum value. The scaling parameter λ is calculated based on the reference vector set and the actual vector set, including: calculating the scaling parameter λ according to the one-to-one correspondence between the sorted first reference vector and the sorted actual vector, as expressed by the following formula: in, Let j be the magnitude of the sorted actual vector. The magnitude of the j-th first reference vector after sorting; Based on the actual vectors in the actual vector set Second reference vector And the proportional parameter λ, calculate the E-CSP value as follows:

2. The defect retrieval method for polycrystalline systems as described in claim 1, characterized in that, The number N of nearest-neighbor atoms in the first shell of the unit cell under test is determined based on the shell definition. p ,include: Based on the shell definition, the shells of the 14 Bravais lattices are classified to obtain the shell classification results. The number of bond types satisfied by each shell in the shell classification results is counted, and a reference table of shell bonding and atomic number of unit cell is constructed. Based on the unit cell structure and the reference table of shell bonding and atomic number of the unit cell, the number N of nearest-neighbor atoms in the first shell of the unit cell to be tested is determined. p .

3. The defect retrieval method for polycrystalline systems as described in claim 1, characterized in that, The formula for obtaining the second reference vector by adding the first reference vectors in the reference vector set pairwise and taking the minimum value is expressed as follows:

4. The defect retrieval method for polycrystalline systems as described in claim 1, characterized in that, The actual vectors based on the actual vector set Second reference vector And the proportional parameter λ, calculate the E-CSP value, including: Perform a full permutation of all vectors in the actual vector set to obtain the full permutation result; For each of the second reference vectors, find the following from the full permutation results: Make The minimum value corresponding to the second reference vector is taken as the E-CSP value, k≠l, k,l∈[1,N]. P ]; The total E-CSP value is calculated based on the E-CSP value corresponding to each of the second reference vectors.

5. The defect retrieval method for polycrystalline systems as described in any one of claims 1-4, characterized in that, Based on the shell definition, the number N of nearest-neighbor atoms in the first shell of the unit cell under test is determined. p Previously, the method also included: The defect-free atoms in the unit cell under test are identified using the E-CNA method, and then the defect-free atoms are removed.

6. The defect retrieval method for polycrystalline systems as described in any one of claims 1-4, characterized in that, The method further includes: Based on the E-CSP values, defects in polycrystalline systems are classified by coloring.

7. A defect retrieval system applied to polycrystalline systems, characterized in that, The system includes: The nearest neighbor atom number determination module is used to determine the number N of nearest neighbor atoms in the first shell of the unit cell under test based on the shell definition. p The shell is defined as: atoms with the same type of bond as the central atom are in the same shell; The vector set determination module is used to determine the nearest neighbor atom number N. p Determine the reference vector set and the actual vector set; The reference vector determination module is used to add the first reference vectors in the reference vector set pairwise and take the minimum value to obtain the second reference vector. The scaling parameter calculation module is used to calculate the scaling parameter λ based on the reference vector set and the actual vector set, including: calculating the scaling parameter λ according to the one-to-one correspondence between the sorted first reference vector and the sorted actual vector, as expressed by the following formula: in, Let j be the magnitude of the sorted actual vector. The magnitude of the j-th first reference vector after sorting; The E-CSP value calculation module is used to calculate the actual vectors in the actual vector set. Second reference vector And the proportional parameter λ, calculate the E-CSP value as follows: The vector set determination module includes: Reference vector set determination unit, used to select N based on the coordinates of the central atom after octet expansion. p / 2 For the first reference vector, construct the reference vector set of the central atom. The actual vector set determination unit is used to find the nearest N based on the actual measurement results of the central atom. p 1 actual vector, construct the actual vector set The sorting unit is used to sort the first reference vector and the actual vector based on the magnitudes of the reference vector and the actual vector, respectively.

8. The defect retrieval system for polycrystalline systems as described in claim 7, characterized in that, The nearest neighbor atom number determination module includes: A shell classification unit is used to classify the shells of the 14 Bravais lattices based on the shell definition to obtain the shell classification results; The reference table construction unit is used to count the number of bond types satisfied by each shell in the shell classification results and construct a reference table of shell bonding and atomic number of unit cell. The nearest neighbor atom number determination unit is used to determine the nearest neighbor atom number N of the first shell of the unit cell under test based on the unit cell structure and a reference table of shell bonding and atom number of the unit cell. p .

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