A method and system for calculating bcc metal and alloy vacancy cluster dislocation loops

Abstract

The application discloses a BCC metal and alloy vacancy cluster dislocation loop calculation method and system, and belongs to the technical field of computational materials science. The application provides a BCC lattice with reference site identification, a discrete search actual vacancy number equal to a target value of a dislocation loop deletion position set, and an initial state of a vacancy cluster is deleted by an element deletion vector constraint, so that the total number of initial and final state atoms and the element-by-element counting are consistent. After relaxation, the final state is verified according to the closed dislocation connected component, the Burgers vector and the vacancy attribute. The common reference site is used as a topological anchor point, and the remaining same element atoms are periodically and globally matched one by one, the atomic identity is unified, and an elastic band path is generated. According to the residual force, image continuity and climbing image convergence state, the diagnostic path, NEB path peak value or convergence saddle point energy barrier is graded and output. The application is suitable for batch atomic scale simulation of multi-component BCC alloy irradiation defect transformation.

Description

Technical Field

[0001] This invention belongs to the fields of computational materials science, atomic-scale simulation and high-performance computing technology. It relates to a calculation method and system for BCC-based metal and alloy vacancy cluster dislocation loops. The system is used to accurately construct the initial state of vacancy clusters and the final state of vacancy-type a<100> dislocation loops, constrain chemical composition, perform relaxation topological verification, maintain atomic identity mapping, generate elastic band paths and calculate the transition energy barrier. Background Technology

[0002] Vacancy clusters and vacancy-type dislocation loops are significant defects that form in metals and alloys during irradiation, quenching, plastic deformation, and high-temperature service. The transformation of vacancy clusters from a three-dimensional aggregated state to planar vacancy plates or prismatic dislocation loops alters defect migration patterns, trapping sections, and elastic interactions, thereby affecting the material's radiation hardening, swelling, embrittlement, and long-term service performance. Obtaining the reaction pathways and energy characteristics of this transformation process through atomic-scale simulations is crucial for understanding defect evolution mechanisms and evaluating the radiation resistance of alloys.

[0003] The NEB-type elastic band method requires that the initial and final states have the same total number of atoms, the same element-by-element atomic count, and a defined one-to-one atomic correspondence. In elemental systems, atomic identity constraints are relatively simple; however, in multi-component random alloys, the initial state of vacancy clusters and the final state of dislocation loops often lack different reference lattice positions. Even if the total number of vacancies is the same, the elemental composition corresponding to the deleted positions may still be different, resulting in inconsistent element-by-element counts at the endpoints, or destroying the chemical identity of atoms when forcibly unifying the numbering.

[0004] If the atom numbers from two independent structure files are directly used, or if atom-by-atom local nearest neighbor matching is employed, mismatches of dissimilar elements, competition among multiple source atoms for the same target atom, and pseudo-long-distance movements across periodic boundaries can easily occur. For non-orthogonal periodic cells, if the shortest periodic displacement is not determined according to the cell geometry, the mapping error may be further amplified. These problems can cause atomic overlap, local high strain, and anomalously high-energy structures in the interpolated path image, reducing the numerical stability of path optimization and the physical interpretability of the resulting energy path.

[0005] The construction of dislocation loops also exhibits discreteness. A continuously varying geometric radius does not correspond to a continuously varying number of deleted atoms; the actual number of vacancies generated for a given radius may deviate from the target value. For small-sized multi-element dislocation loops, the local chemical environment and potential function characteristics may also cause the constructed state to collapse, split, open, or transform into other Burgers vector defects after energy minimization. Therefore, merely checking the geometric parameters before construction cannot guarantee that the final state is a valid vacancy-type a<100> dislocation loop.

[0006] Furthermore, completing the preset iterations in NEB calculations does not equate to obtaining a convergence saddle point. If the path residual force is still large, the structure between images is discontinuous, or the CI-NEB climbing image has not reached the convergence condition, the obtained peak value should not be directly expressed as the convergence saddle point energy barrier. Existing calculation workflows typically handle endpoint construction, dislocation identification, atom mapping, and path calculation separately. Without a unified verification mechanism throughout all steps, it is not conducive to repeatable comparisons between different material systems, vacancy numbers, and chemical random seeds.

[0007] Therefore, a technical solution is needed that links discrete lattice topology, post-defect chemical composition, reference site identity, periodic cell geometry, post-relaxation dislocation topology, and path convergence criteria, so that only structures that meet physical endpoint constraints and atomic identity constraints can enter elastic band calculations, and the path results can be output in a traceable hierarchical manner. Summary of the Invention

[0008] This invention aims to solve the following technical problems in the simulation of the transformation of vacancy clusters into vacancy-type a<100> dislocation loops in multi-component BCC alloys: inconsistency between the target number of vacancies and the actual number of constructed vacancies; inconsistency between the number of atoms per element in the initial and final states; errors in atomic identification due to different elements, non-one-to-one mapping, or improper handling of periodic boundaries; collapse, opening, splitting, or incorrect Burgers vector type of the target dislocation loop after relaxation; atomic overlap, excessive local strain, or abnormal energy in the interpolation path image; and misjudging the peak of the non-converged NEB path as the energy barrier of the convergent saddle point.

[0009] The present invention solves the above-mentioned technical problems through the following technical solutions: This invention provides a method for calculating dislocation loops in BCC-based metal and alloy vacancy clusters, comprising: Establish a BCC reference lattice with periodic cell information, element type, and reference lattice site identifier; Based on the target number of vacancies, dislocation loop orientation, loop center, and geometric parameters, the discrete lattice topology of candidate dislocation loops is searched to obtain the set of dislocation loop deletion positions where the actual number of deletion positions is strictly equal to the target number of vacancies. The number of element deletions in the set of dislocation loop deletion positions is counted, and the initial state of vacancy clusters is constructed on the reference structure with the same number of element deletions, so that the initial state of vacancy clusters is consistent with the total number of remaining atoms and the number of atoms of each element in the final state of dislocation loops. The initial and final states of the dislocation loop were relaxed under the same periodic boundary conditions and the same interatomic interaction model. The final state of the dislocation loop was verified based on the closed connectivity, Burgers vector and vacancy properties of the relaxed dislocation line network. Atoms with the same reference site identifier and element type in the initial and final states are used as topological anchor points to directly establish a correspondence. For the remaining atoms, global one-to-one matching based on the periodic shortest displacement is performed according to element type. Based on the topological anchor points and global one-to-one matching to unify the initial and final state atom identities and atom numbers, generate and verify the elastic band path image, perform ordinary NEB path optimization, and perform CI-NEB path optimization on the basis of ordinary NEB when necessary; Based on path residual force, image continuity, and climbing image convergence status, the diagnostic path, NEB path peak, or convergence saddle point energy barrier are output.

[0010] Furthermore, the BCC reference lattice consists of BCC conventional unit cell repetitions in three directions. , , With the unit cell matrix H determined, the number of atoms in the perfect reference lattice satisfies Each ideal lattice location is assigned a unique reference site identifier that remains unchanged throughout the process of endpoint construction, atomic mapping, and result tracing.

[0011] Furthermore, the search method for the discrete lattice topology includes: changing at least one of the following within a preset candidate parameter space: the radius of the dislocation loop, the offset of the loop center relative to the lattice plane, and the number of lattice layers to be deleted; and calculating the set of actual deletion positions for each candidate structure. and its cardinality; only those that satisfy Candidate structures as target number of vacancies Acceptable candidates; when no exact match exists, expand the candidate parameter space or output a hint that the target number of empty spaces cannot be achieved in the current parameter space.

[0012] Furthermore, the element type allocation adopts either a post-defect composition constraint mode or a perfect lattice composition constraint mode. In the post-defect composition constraint mode, the geometric position of the dislocation loop deletion site set is first determined, and the remaining reference sites are allocated to integers according to the target composition ratio to obtain the target element-wise atomic number of the defect structure. Then, elements are allocated to the dislocation loop deletion site set to form a sub-element deletion vector, and the two are merged to obtain a common chemical reference structure. In the perfect lattice composition constraint mode, the element-wise integer atomic number of the perfect reference lattice is first determined and elements are allocated on all reference sites. Then, the sub-element deletion vector is calculated from the dislocation loop deletion site set.

[0013] Furthermore, the initial state of the vacancy cluster includes spherical vacancy clusters, tetrahedral vacancy clusters, planar vacancy sheets, ellipsoidal vacancy clusters, cylindrical vacancy clusters, multilayered sheet-like vacancy clusters, or vacancy clusters determined by a spatial evaluation function; for any initial state and any element, atoms to be deleted are selected from the candidate atom set corresponding to that element in the common chemical reference structure, and the number of atoms of that element deleted is equal to the number of elements deleted from the dislocation loop deletion position set.

[0014] Furthermore, the method for verifying the final state of a dislocation loop includes: extracting a dislocation line network; grouping dislocation line segments with shared endpoints or endpoint periodic distances less than a connection threshold into connected components; determining whether the target connected component is closed, whether its Burgers vector belongs to family a<100>, and whether the closure error is less than a set threshold; and determining whether the target connected component corresponds to a vacancy-type defect by at least one of reference site occupancy analysis, missing lattice position counting, and atomic volume deficiency.

[0015] Furthermore, the topological anchor point is an atom with the same reference site identifier and the same element type in the initial and final states; when there is no corresponding atom or the element type is inconsistent in the initial and final states for the same reference site, no topological anchor point is established, and the relevant atom is included in the set of non-shared atoms of the same element for global matching.

[0016] This invention also provides a computational system based on the above-mentioned method for calculating dislocation loops in BCC-based metal and alloy vacancy clusters, comprising: The parameter receiving module is used to read material system parameters, crystal structure parameters, defect parameters, chemical random seeds, endpoint relaxation parameters, dislocation topological criteria, and elastic band calculation parameters. Reference lattice and chemical partitioning module, used to generate multi-component BCC reference structures with reference site identifiers; The discrete topology search module is used to search for the set of dislocation loop deletion positions where the actual number of deletion positions equals the target number of empty positions; The initial state construction module is used to construct chemically consistent initial states of vacancy clusters based on the element-wise deletion vector of the set of dislocation loop deletion positions. The endpoint relaxation and dislocation topology verification module is used to relax endpoints and filter valid dislocation loop final states based on closed connectivity, Burgs vector, and vacancy properties. The Atom Mapping module is used to maintain topological anchor points and perform periodic global one-to-one matching on other atoms of the same element; The path task generation module is used to unify the atom number, determine the number of path images, and generate and verify the elastic band path images as input for ordinary NEB or CI-NEB path optimization. The results extraction and classification module is used to perform or call ordinary NEB and CI-NEB path optimization, and output diagnostic paths, NEB path peak or convergence saddle point energy barriers. The verification and parallel scheduling module is used to store hash values, mapping tables, logs, and task array information.

[0017] The present invention also provides an electronic device, including a memory and a processor, wherein the memory is used to store a program that supports the processor in executing the above-described calculation method for translocation dislocation loops of vacancy clusters in BCC-based metals and alloys, and the processor is configured to execute the program stored in the memory.

[0018] The present invention also provides a storage medium storing a computer program, which, when run by a processor, executes the steps of the above-described method for calculating dislocation loops in BCC-based metal and alloy vacancy clusters.

[0019] The beneficial effects of this invention are as follows: This invention ensures strict consistency between the actual number of constructed vacancies and the target number of vacancies by using discrete topological search rather than estimation based solely on continuous geometric radii; it constrains all initial states by using element-wise deletion vectors of the dislocation loop deletion position set to ensure consistency between the total number of atoms and element-wise counts in the initial and final states, avoiding artificial alteration of the alloy's chemical composition; it avoids mismapping of dissimilar elements, non-one-to-one mapping, and pseudo-long-distance movement across periodic boundaries by using topological anchor points of reference sites and periodic global optimal matching of the same elements; and it automatically eliminates collapses, splits, openings, or incorrect types by verifying the relaxed closed connected components, Burgers vectors, and vacancy properties. Dislocation loop final state; by adaptive path image number, interpolation quality check and preprocessing, the probability of atomic overlap, excessive atomic force and path numerical divergence is reduced; by the hierarchical rule of "diagnostic path - NEB path peak - convergence saddle point energy barrier", the convergence of ordinary NEB path and CI-NEB saddle point convergence are clearly distinguished, avoiding the representation of path peaks that have not converged numerically or have not been confirmed by climbing images as accurate saddle point energy barriers; by structured configuration, hash verification, atomic mapping table and batch parallel scheduling, the repeatability, traceability and batch processing efficiency of calculations for different material systems, number of vacancies and random seeds are improved. Attached Figure Description

[0020] Figure 1 This is a flowchart illustrating the overall calculation method of the present invention. Figure 2 Flowchart for topology verification and feedback screening of dislocation loops after relaxation; Figure 3 A diagram showing the atomic structure and dislocation line characterization of the relaxed V-Ta-Ti vacancy type a<100> dislocation loop; Figure 4 Flowchart for maintaining periodic global matching of topological anchors with the same elements; Figure 5 A flowchart for path image generation and result classification based on matching displacement; Figure 6 A representative NEB energy path diagram for the transformation from a tetrahedral (Tetra) configuration to a vacant a<100> dislocation loop; Figure 7 This is a block diagram showing the structural composition of the computing system of the present invention. Detailed Implementation

[0021] 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.

[0022] Example 1 like Figure 1 As shown, this embodiment provides a method for calculating dislocation loops in BCC-based metals and alloys with vacancy clusters. Without departing from the technical concept of this invention, the element types, potential function forms, cell sizes, vacancy cluster shapes, dislocation extraction algorithms, matching solvers, elastic band solvers, and computing platforms can all be equivalently replaced. The technical solution of this invention is also applicable to elemental metals. Specifically, it includes the following steps: S01, Parameter Reading The system reads material system parameters, crystal structure parameters, defect parameters, chemical random seed, endpoint relaxation parameters, dislocation topological criteria, and elastic band calculation parameters. The material system parameters include element symbols, atomic masses, target composition weights, and interatomic interaction models. The crystal structure parameters include the unit cell matrix H and the number of BCC regular unit cell repetitions in three directions. , , Defect parameters include the target number of vacancy numbers. The parameters include: dislocation loop normal, loop center, candidate radius range, and number of deleted lattice layers. A chemical random seed is used to control the random allocation of alloying elements at reference lattice sites to achieve statistical sampling of different local chemical arrangements. Endpoint relaxation parameters include force convergence tolerance, energy convergence tolerance, and maximum number of iterations. Dislocation topology criteria include connectivity threshold, closure error threshold, and Burgers vector decision tolerance. Elastic band calculation parameters include the number of path images, spring constant, optimization algorithm, and convergence criteria.

[0023] S02, BCC reference lattice construction Based on the cell matrix H and the conventional cell repeating number of BCC in the three directions. , , Establish a reference lattice. For a reference lattice structure composed of repeating BCC conventional unit cells, the perfect reference lattice has the following number of atoms: Each ideal lattice location is assigned a unique reference site identifier that remains unchanged throughout the endpoint construction, atom mapping, and result tracing. This identifier is not equivalent to the consecutive atom numbers in subsequent elastic band calculations, but rather is used to identify lattice locations that originate from the same source in the initial and final states, ensuring that the original reference lattice site corresponding to each atom can be traced before and after relaxation.

[0024] Optionally, before constructing the defect structure, zero-pressure cell relaxation is performed on the perfect reference lattice, and the equilibrium lattice parameters are updated according to the relaxed cell matrix to eliminate the deviation between the initial lattice constant and the equilibrium lattice constant of the interatomic interaction model.

[0025] S03, Discrete Topology Search and Candidate Selection Based on the target number of empty spaces The discrete lattice topology of candidate dislocation loops is constructed by considering the dislocation loop normal, loop center, candidate radius, number of deleted lattice layers, and displacement field parameters. The discrete lattice topology of the candidate dislocation loops is then searched using the following method: within a preset discrete candidate parameter space, at least one of the following is changed: the dislocation loop radius, the offset of the loop center relative to the lattice plane, and the number of deleted lattice layers. For each candidate dislocation loop, the set of actual deletion positions is calculated. and its cardinality, only those that satisfy Discrete lattice topology of candidate dislocation loops as target vacancy number Acceptable candidates.

[0026] The search uses the actual number of deletion positions as a hard constraint, rather than replacing the actual number of vacancies with an estimated value of the continuous geometric radius. When multiple exact matching candidate structures exist, i.e., multiple candidate structures that meet the target number of vacancies constraint are obtained, the candidates are sorted based on at least one of the following: the normal dispersion of the deletion positions relative to the target torus, the in-plane radial dispersion, the offset of the center of the deletion set relative to the center of the target torus, and the topological stability after relaxation. A candidate score is constructed, and the set of deletion positions of the target dislocation ring is selected without changing the hard constraint of the target number of vacancies. When no exact match exists, the candidate parameter space is expanded or a hint is output indicating that the target number of vacancies cannot be achieved in the current parameter space, rather than replacing the target number of vacancies with an approximate number of vacancies.

[0027] S04, Chemical Partition and Element Deletion Vectors The number of elements removed from the set of dislocation loop removal locations is counted. Element type allocation adopts either the defect-post composition constraint mode or the perfect lattice composition constraint mode.

[0028] In the post-defect composition constraint mode, the geometric positions of the dislocation loop deletion site set are first determined. The remaining reference sites are then allocated to integers according to the target composition ratio to obtain the target element-wise atomic number of the defect structure. Finally, elements are allocated to the dislocation loop deletion site set to form an element-wise deletion vector. ,in, , Let m be the number of elements to be deleted, m be the total number of elements, and i be the counting factor. The sum of all components equals the target number of empty spaces. .

[0029] Under the perfect lattice composition constraint mode, the number of integer atoms per element in the perfect reference lattice is first determined and elements are assigned to all reference sites. Then, the element-wise deletion vector is calculated from the set of dislocation loop deletion positions. As a chemical constraint for the subsequent construction of all vacancy cluster initial states, it ensures that any initial state has the same total number of remaining atoms and the same element-wise atom count as the dislocation loop final state.

[0030] S05, Initial state of constructing vacancy clusters For spherical, tetrahedral, planar vacancy sheets, or user-defined spatial evaluation functions, select and delete element-specific vectors in the common chemical reference structure according to element type. A corresponding number of atoms to be deleted form at least one initial state of vacancy clusters, thereby ensuring that any initial state has the same total number of remaining atoms and the same element-by-element atom count as the final state of the dislocation loop, while maintaining the original elemental identity in the random alloy. The initial states of vacancy clusters include spherical vacancy clusters, tetrahedral vacancy clusters, planar vacancy plates, ellipsoidal vacancy clusters, cylindrical vacancy clusters, multilayered plate-like vacancy clusters, or vacancy clusters determined by a spatial evaluation function. For any initial state and any element, atoms to be deleted are selected from the candidate atom set corresponding to that element in the common chemical reference structure, and the number of atoms of that element deleted is equal to the number of atoms of that element deleted from the dislocation loop deletion position set.

[0031] S06, Endpoint Relaxation Relax the initial states of all vacancy clusters and the final states of dislocation loops under the same periodic boundary conditions and the same interatomic interaction model. The interaction model used should cover all target elements and be able to provide the energy and atomic forces for bulk phase, vacancies, dislocation cores, and high-strain configurations. The interaction model can be an embedded atom potential, a modified embedded atom potential, a bond-level potential, a machine learning potential, or other applicable models.

[0032] During relaxation, the energy of the atomic positions is minimized until the atomic force is less than the preset convergence tolerance, or the maximum number of iterations is reached. After the endpoints are relaxed, the total energy, atomic positions, and cell parameters of each endpoint are recorded.

[0033] S07, Topological Verification of Dislocation Loops After Relaxation like Figure 2 As shown, the topology verification and feedback screening process for relaxed dislocation loops includes the following steps: First, the dislocation line network of the final state of the relaxed dislocation loop is extracted; then, dislocation line segments with shared endpoints or endpoint periodic distances less than the connection threshold are grouped into connected components; then, it is determined whether the target connected component is closed, whether its Burgers vector belongs to family a<100>, and whether the closure error is less than the set threshold. The target connected component is also determined to correspond to a vacancy-type defect by at least one of the following methods: reference site occupancy analysis, missing lattice position counting, and atomic volume deficiency. When the final state of the dislocation loop fails the verification, the type of the failure criterion is recorded, and at least one of the following is replaced: chemical random seed, dislocation loop center, candidate radius, number of deleted lattice layers, displacement field parameter and endpoint relaxation parameter. The element allocation, dislocation loop construction, endpoint relaxation and dislocation loop verification are re-executed until a preset number of valid final states are obtained or a preset termination condition is reached.

[0034] Figure 3 An example of the atomic structure and dislocation line characterization of a relaxed V-Ta-Ti vacancy-type a<100> dislocation loop is given. The left side shows the non-BCC atomic structure near the dislocation core, and the right side shows the extracted closed dislocation line. The relaxed structure retains the target number of atoms, and the dislocation extraction result forms a closed a<100> dislocation connectivity component with Burgs vector lattice components of [1,0,0]. The closure error satisfies the set topological criterion.

[0035] S08, Topological Anchors and Global Matching like Figure 4 As shown, the process of maintaining topological anchor points and periodic global matching of the same element includes the following steps: First, identify common reference sites between the initial and final states; then, directly retain the correspondence between atoms with the same reference site identifier and element type as topological anchor points; and finally, establish sets of non-common atom sources according to element type for the remaining non-common atoms. Non-common target atom set and verify .

[0036] The topological anchor point is an atom with the same reference site identifier and element type in both the initial and final states. When there is no corresponding atom or the element type is inconsistent in both the initial and final states for the same reference site, no topological anchor point is established, and the relevant atom is included in the set of non-shared atoms of the same element for global matching.

[0037] For source atom p and target atom q of the same element type, respectively, use fractional coordinates... and This indicates the positions of the two elements within the same periodic unit cell, and defines the fractional coordinate difference. The integer periodic translation vector is searched using the unit cell matrix H to find the periodic image that minimizes the Cartesian displacement. The corresponding periodic shortest displacement is Where p is the source atom index in the initial state; q is the target atom index of the same element in the final state; Let p be the three-dimensional fractional coordinate vector of the source atom p; Let be the three-dimensional fractional coordinate vector of the target atom q; This represents the fractional coordinate difference between the target atom and the source atom. is a 3×3 unit cell matrix composed of three unit cell basis vectors, used to convert fractional coordinate displacements into Cartesian coordinate displacements; n is a three-dimensional integer periodic translation vector; Represents a three-dimensional set of integer vectors; The L2 norm of the Cartesian displacement after a given periodic translation vector n; Let represent the independent variable that minimizes this norm. Geometric displacement cost is defined as... ,in, The weights of the geometric displacements, The weight of the local element environment. The weight of the local adjacency relationship. The L1 norm of the periodic shortest displacement. A measure of the difference in the local elemental environment of two atoms. This measures the difference in local adjacency or topological environment between two atoms. For orthogonal units or units satisfying the nearest integer minimum mirror condition, the optimal integer periodic translation vector can be obtained by... Each component is obtained by taking the nearest integer.

[0038] In addition to the geometric displacement cost, the total matching cost also includes at least one of the following: local element environment difference term, adjacency relationship difference term, maximum allowable displacement constraint term, and prohibited pairing constraint term. Pairing between different element types is set as infeasible, and the maximum allowable displacement constraint is used to limit the maximum periodic displacement after global matching.

[0039] For each element Non-public atomic source set Non-common target atom set ,exist Given the conditions, find the bijective mapping that minimizes the total matching cost, i.e. ,in, Index for element type, and These represent the number of atoms in the two sets, respectively. for arrive The set of all feasible bijective mappings; for Any candidate bijective mapping in the dataset; for The source atom in; For mapping Below and source atoms The corresponding target atom; For source atoms With target atom The total cost of matching.

[0040] Global one-to-one matching employs the Hungarian algorithm, minimum cost maximum flow algorithm, auction algorithm, or bipartite graph optimal matching algorithm. The matching results of non-shared atoms of each element are merged with the topological anchor mapping, and output in a unified order continuous atom numbers, initial state structure, final state structure, and a mapping table containing new numbers, initial state numbers, final state numbers, reference site identifiers, and element types.

[0041] S09, Path Image Generation and Verification like Figure 5 As shown, the process of generating and classifying path images based on matching displacement includes the following steps: First, the total number of path images is determined based on the maximum periodic displacement after matching. Then, each path image is generated by interpolation between the initial and final states according to the shortest periodic displacement. Next, the quality of the interpolated path images is checked. If the check fails, preprocessing measures are performed. Finally, path optimization is performed and the results are output in a graded manner.

[0042] Let M be the total number of elastic band path images, including the initial and final states. To achieve the maximum periodic displacement of each atom after atomic matching, To predetermine the maximum allowed initial displacement between adjacent images, the total number of path images satisfies... ,in, The function is the floor function; each path image is generated by interpolation between the initial and final states according to the shortest periodic displacement, as shown in the formula. ,in, To represent the coordinates of the i-th atom in the k-th path image, To represent the coordinates of the i-th atom in the initial state, To represent the interpolation parameters corresponding to the k-th path image, Let M be the shortest periodic displacement vector of the i-th atom from the initial state to the final state after atomic mapping; M represents the total number of path images including the initial and final states; k=0,...,M-1 represents the path image number. As the path image number gradually changes from 0 corresponding to the initial state to 1 corresponding to the final state, a continuous initial path image of the elastic band is generated between the initial and final states based on the periodic shortest displacement.

[0043] Before performing path optimization, the interpolated path image is checked for at least one of the following: minimum atomic spacing, local strain, single image energy anomaly, and continuity of displacement between adjacent images. If the check fails, at least one of the following processing methods is adopted: increasing the number of path images, implementing constrained pre-relaxation, image correlation potential preprocessing, tightening the upper limit of matching displacement, or re-finding atomic matching.

[0044] S10, Path Optimization and Result Classification Perform standard NEB path optimization, and, when necessary, perform CI-NEB path optimization based on standard NEB. Let the path image energy be Ek, k=0,…,M 1. The forward path peak, reverse path peak, and endpoint energy difference satisfy the following conditions: , , When the maximum path residual force or image continuity of the ordinary NEB does not meet the set threshold, the result is marked as a diagnostic path; when the ordinary NEB meets the convergence threshold but the CI-NEB does not obtain a converged climbing image, the forward path peak and the reverse path peak are marked as NEB path peaks and output; when the CI-NEB climbing image meets the convergence threshold, the corresponding peak is marked as the convergence saddle point energy barrier and output.

[0045] Figure 6 Representative NEB energy paths for the transformation from a tetrahedral (Tetra) configuration to a vacant a<100> dislocation loop are presented. For direct transformation paths that do not satisfy the residual force convergence criterion, the peak values ​​in the figure are interpreted only as diagnostic paths.

[0046] S11, Data Tracing and Parallel Scheduling When generating path computation tasks, the system simultaneously records the hash checksum of the inter-atom interaction model or machine learning model file, cell information, total number of atoms, element-wise count, atom numbering continuity, endpoint topology verification results, atom mapping statistics, number of path images, and parallel task description. After computation, the system summarizes path classification, endpoint energy difference, maximum path residual force, and statistical dispersion according to the chemical random seed and initial state type.

[0047] Example 1: Construction of 37 vacancy dislocation loop paths in equiatomic V-Ta-Ti alloys The effectiveness of the method of the present invention was verified by using V-Ta-Ti BCC random alloys with equal atomic ratios. Referring to Table 1 below, the initial lattice constant is 3.2156 Å, the supercell consists of 17×17×17 BCC conventional unit cells, the perfect reference lattice contains 9826 atoms, the target vacancy number is 37, and the defect structure contains 9789 atoms.

[0048] Table 1. Main parameters of the V-Ta-Ti example.

[0049] Candidate dislocation loops with 37 reference lattice sites actually deleted were obtained through discrete topological search. For random seed 20260716, the number of V, Ta, and Ti atoms at the dislocation loop deletion sites were 13, 12, and 12, respectively. Spherical, tetrahedral, and planar vacancy sheet initial states were constructed using this deletion vector, such that the number of V, Ta, and Ti atoms deleted in each initial state was also 13, 12, and 12, respectively; therefore, all endpoints retained 3263 V atoms, 3263 Ta atoms, and 3263 Ti atoms.

[0050] After atom matching is completed, the initial and final state files for the three types of paths—spherical, tetrahedral, and planar vacancy plate—each contain 9789 consecutively numbered atoms, with each element counted as 3263 / 3263 / 3263, and retain a mapping table from the unified numbering to the reference site identifier. Three valid random seeds and three initial state types can automatically generate independent and traceable path computation tasks.

[0051] The relaxed structure contains 9789 atoms, and the dislocation extraction results in a closed a<100> dislocation connectivity component; the total length of the dislocation line is 26.4853 Å, the Burgers vector lattice components are [1,0,0], and the closure error is 1.3943 × 10⁻⁶. 8 Å satisfies the topological criterion set in this example.

[0052] Example 2: NEB path results for V-Ta-Ti alloy V-Ta-Ti structures with different local chemical arrangements but identical target vacancies and element-wise defect counts were constructed using different chemical random seeds. For each random seed, ordinary NEB paths were calculated for the final states of spherical vacancy clusters, tetrahedral vacancy clusters, and planar vacancy sheet-oriented common dislocation loops. Eight path images were used for each path, with the energy set to zero at its respective initial state.

[0053] The maximum path residual force for the direct transformation paths of spherical and tetrahedral vacancy clusters ranges from 0.843451 to 3.531438 eV / Å. However, subsequent climbing image calculations show numerical divergence; therefore, the corresponding path peak values ​​in Table 2 are only used as numerical information to diagnose the difficulty of direct path rearrangement and not as convergence saddle point energy barriers. The maximum path residual force for planar vacancy sheet paths is 1.6474 × 10⁻⁶ eV / Å. 5~5.0567×10 3 eV / Å can be used as the peak value of the convergence path of ordinary NEB.

[0054] Table 2 Peak Path Statistics for Ordinary NEB Paths

[0055] The peak values ​​of the ordinary NEB path for the planar vacancy sheet with the three random seeds are 0.466483 eV, 0.023208 eV, and 0.620085 eV, respectively, with an average of 0.369926 eV and a sample standard deviation of 0.309932 eV. Within the range of the three chemical random seeds in this example, this dispersion indicates that the peak value of the ordinary NEB path is relatively sensitive to local chemical configuration, suggesting that the local chemical environment may affect the path energy characteristics of the transformation of the planar vacancy sheet to the a<100> dislocation loop.

[0056] Example 3: Changing the target number of empty spaces Keeping the material system unchanged, the target number of vacancies is modified to Nv′. The system automatically calculates the number of defect structure atoms N′=N0. For Nv′, redetermine the target integer number of each element, search for discrete topologies where the actual number of deletion positions equals Nv′, calculate the new element deletion vector, and construct a chemically consistent initial state. Subsequent endpoint relaxation, topology verification, atom mapping, and path generation do not require modification of the algorithm source code.

[0057] As Nv′ increases, the supercell size can be increased to reduce the interaction between dislocation loops and periodic mirror images. When the existing candidate radius, center offset, and number of loop layers cannot generate the discrete topology corresponding to Nv′, the system outputs the search range, the set of realized empty bits, and the reason for failure, for adjusting the topology parameters.

[0058] Example 4: Changing the multi-component BCC material system Replace the element set, mass, composition weights, cell parameters, and interatomic interaction model in the configuration with another BCC unary, binary, ternary, quaternary, or pentaneous alloy system. The program automatically generates a mass table, integer composition, element deletion vectors, and interaction model parameters based on the new element set, and performs the same discrete topology search, chemically consistent endpoint construction, topology verification, and atom mapping as in Example 1. The interaction model used should cover all target elements and be able to provide the energy and atomic forces for bulk phases, vacancies, dislocation cores, and high-strain configurations. The interaction model can be an embedded atom potential, a modified embedded atom potential, a bond-level potential, a machine learning potential, or other applicable models.

[0059] Example 2 This embodiment provides a computational system based on the BCC-based metal and alloy vacancy cluster dislocation loop calculation method of Embodiment 1. Its modules include: parameter receiving module, reference lattice and chemical allocation module, discrete topology search module, initial state construction module, endpoint relaxation and dislocation topology verification module, atom mapping module, path task generation module, result extraction and classification module, and verification traceability and parallel scheduling module. The parameter receiving module is used to read material system parameters, crystal structure parameters, defect parameters, chemical random seeds, endpoint relaxation parameters, dislocation topological criteria, and elastic band calculation parameters. The reference lattice and chemical partitioning module is used to generate a multi-component BCC reference structure with reference site identifiers. The discrete topology search module is used to search for the set of dislocation loop deletion positions where the actual number of deletion positions is equal to the target number of empty positions; The initial state construction module is used to construct a chemically consistent initial state of a vacancy cluster based on the element-wise deletion vector of the set of dislocation loop deletion positions. The endpoint relaxation and dislocation topology verification module is used to relax endpoints and filter valid dislocation loop final states based on closed connectivity, Burgers vector and vacancy attributes. The atom mapping module is used to maintain the topological anchor point and perform periodic global one-to-one matching on the remaining atoms of the same element; The path task generation module is used to unify the atom number, determine the number of path images, and generate and verify the elastic band path image as input for ordinary NEB or CI-NEB path optimization. The result extraction and classification module is used to perform or call ordinary NEB and CI-NEB path optimization, and output diagnostic paths, NEB path peaks or convergence saddle point energy barriers.

[0060] The verification traceability and parallel scheduling module is used to store hash values, mapping tables, logs, and task array information.

[0061] like Figure 7 As shown, the main flow of the computing system in this embodiment is connected by solid lines, while traceability information such as hash values, mapping tables, logs, and task arrays are associated by dashed lines.

[0062] In one parallel implementation, three chemical random seeds and three initial state types form nine task units, each containing multiple elastic band path images. Before submission and at the computation nodes, the potential function or machine learning model hash value, cell matrix, number of atoms, element-wise count, endpoint topology, atom numbering, atom mapping statistics, and path image integrity are checked. After computation, the path classification results are summarized according to the random seed and initial state type.

[0063] The V-Ta-Ti system, 37 vacancies, 17×17×17 supercell, specific chemical random seed, number of path images, and specific values ​​in the above embodiments are only used to illustrate the feasibility of the present invention and do not constitute a limitation on the material system, number of vacancies, supercell size, defect shape, dislocation extraction algorithm, shortest period displacement solution method, matching solver, path optimization program, or computing platform.

[0064] Example 3 This embodiment provides an electronic device, including a memory and a processor. The memory stores a computer program that supports the processor in executing the calculation method for BCC-based metal and alloy vacancy cluster dislocation loops as described in Embodiment 1. The memory can be a high-speed random access memory or a non-volatile memory, such as a disk storage device, flash memory, or other solid-state storage device. The processor is configured to execute the program stored in the memory. The processor can be a general-purpose central processing unit, a dedicated processor, a microprocessor, or a digital signal processor. The electronic device may also include a communication interface for exchanging data with other computing nodes or storage devices. The communication interface can be a wired interface (such as an Ethernet interface) or a wireless interface. The electronic device may also include input / output interfaces for connecting peripheral devices such as a monitor, keyboard, and mouse, so that the user can view the computing status and input control commands.

[0065] Example 4 This embodiment provides a storage medium on which a computer program is stored. The storage medium can be any medium capable of storing program code, including but not limited to: USB flash drive, portable hard drive, read-only memory, random access memory, magnetic disk, optical disk, flash memory card, etc. When the computer program is run by a processor, it executes the steps of the BCC-based metal and alloy vacancy cluster dislocation loop calculation method as described in Embodiment 1. The storage medium can be located on a single computing device or distributed across multiple computing devices, such as in a distributed storage system. The program can be loaded onto a single processor for execution or loaded onto multiple processors for parallel execution.

[0066] The above embodiments are only used to illustrate the technical solutions of the present invention, and are not intended to limit it. 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 of the technical features. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for calculating dislocation loops in BCC-based metal and alloy vacancy clusters, characterized in that, include: Establish a BCC reference lattice with periodic cell information, element type, and reference lattice site identifier; Based on the target number of vacancies, dislocation loop orientation, loop center, and geometric parameters, the discrete lattice topology of candidate dislocation loops is searched to obtain the set of dislocation loop deletion positions where the actual number of deletion positions is strictly equal to the target number of vacancies. The number of element deletions in the set of dislocation loop deletion positions is counted, and the initial state of vacancy clusters is constructed on the reference structure with the same number of element deletions, so that the initial state of vacancy clusters is consistent with the total number of remaining atoms and the number of atoms of each element in the final state of dislocation loops. The initial and final states of the dislocation loop were relaxed under the same periodic boundary conditions and the same interatomic interaction model. The final state of the dislocation loop was verified based on the closed connectivity, Burgers vector and vacancy properties of the relaxed dislocation line network. Atoms with the same reference site identifier and element type in the initial and final states are used as topological anchor points to directly establish a correspondence. For the remaining atoms, global one-to-one matching based on the periodic shortest displacement is performed according to element type. Based on the topological anchor points and global one-to-one matching to unify the initial and final state atom identities and atom numbers, generate and verify the elastic band path image, perform ordinary NEB path optimization, and perform CI-NEB path optimization on the basis of ordinary NEB when necessary; Based on path residual force, image continuity, and climbing image convergence status, the diagnostic path, NEB path peak, or convergence saddle point energy barrier are output.

2. The method for calculating dislocation loops in BCC-based metal and alloy vacancy clusters according to claim 1, characterized in that, The BCC reference lattice consists of BCC conventional cell repeats in three directions. , , With the unit cell matrix H determined, the number of atoms in the perfect reference lattice satisfies Each ideal lattice location is assigned a unique reference site identifier that remains unchanged throughout the process of endpoint construction, atomic mapping, and result tracing.

3. The method for calculating dislocation loops in BCC-based metal and alloy vacancy clusters according to claim 1, characterized in that, The search method for the discrete lattice topology includes: changing at least one of the following within a preset candidate parameter space: the radius of the dislocation loop, the offset of the loop center relative to the lattice plane, and the number of lattice layers to be deleted; and calculating the set of actual deletion positions for each candidate structure. and its cardinality; only those that satisfy Candidate structures as target number of vacancies Acceptable candidates; when no exact match exists, expand the candidate parameter space or output a hint that the target number of empty spaces cannot be achieved in the current parameter space.

4. The method for calculating dislocation loops in BCC-based metal and alloy vacancy clusters according to claim 1, characterized in that, The element type allocation adopts either a post-defect composition constraint mode or a perfect lattice composition constraint mode. Under the post-defect composition constraint mode, the geometric position of the dislocation loop deletion site set is first determined, and the remaining reference sites are allocated to integers according to the target composition ratio to obtain the target element-wise atomic number of the defect structure. Then, elements are allocated to the dislocation loop deletion site set to form a sub-element deletion vector, and the two are merged to obtain a common chemical reference structure. Under the perfect lattice composition constraint mode, the element-wise integer atomic number of the perfect reference lattice is first determined and elements are allocated on all reference sites. Then, the sub-element deletion vector is calculated from the dislocation loop deletion site set.

5. The method for calculating dislocation loops in BCC-based metal and alloy vacancy clusters according to claim 1, characterized in that, The initial state of the vacancy cluster includes spherical vacancy clusters, tetrahedral vacancy clusters, planar vacancy sheets, ellipsoidal vacancy clusters, cylindrical vacancy clusters, multilayer sheet-like vacancy clusters, or vacancy clusters determined by a spatial evaluation function. For any initial state and any element, atoms to be deleted are selected from the candidate atom set corresponding to that element in the common chemical reference structure, and the number of atoms of that element deleted is equal to the number of elements deleted from the dislocation loop deletion position set.

6. The method for calculating dislocation loops in BCC-based metal and alloy vacancy clusters according to claim 1, characterized in that, The method for verifying the final state of a dislocation loop includes: extracting a dislocation line network; grouping dislocation line segments with shared endpoints or endpoint periodic distances less than a connection threshold into connected components; determining whether the target connected component is closed, whether its Burgers vector belongs to family a<100>, and whether the closure error is less than a set threshold; and determining whether the target connected component corresponds to a vacancy-type defect by at least one of reference site occupancy analysis, missing lattice position counting, and atomic volume deficiency.

7. The method for calculating dislocation loops in BCC-based metal and alloy vacancy clusters according to claim 1, characterized in that, The topological anchor point is an atom with the same reference site identifier and the same element type in the initial and final states. When there is no corresponding atom or the element type is inconsistent in the initial and final states for the same reference site, no topological anchor point is established, and the relevant atom is included in the set of non-shared atoms of the same element for global matching.

8. A computational system based on the calculation method for dislocation loops of vacancy clusters in BCC-based metals and alloys according to any one of claims 1 to 7, characterized in that, include: The parameter receiving module is used to read material system parameters, crystal structure parameters, defect parameters, chemical random seeds, endpoint relaxation parameters, dislocation topological criteria, and elastic band calculation parameters. Reference lattice and chemical partitioning module, used to generate multi-component BCC reference structures with reference site identifiers; The discrete topology search module is used to search for the set of dislocation loop deletion positions where the actual number of deletion positions equals the target number of empty positions; The initial state construction module is used to construct chemically consistent initial states of vacancy clusters based on the element-wise deletion vector of the set of dislocation loop deletion positions. The endpoint relaxation and dislocation topology verification module is used to relax endpoints and filter valid dislocation loop final states based on closed connectivity, Burgs vector, and vacancy properties. The Atom Mapping module is used to maintain topological anchor points and perform periodic global one-to-one matching on other atoms of the same element; The path task generation module is used to unify the atom number, determine the number of path images, and generate and verify the elastic band path images as input for ordinary NEB or CI-NEB path optimization. The results extraction and classification module is used to perform or call ordinary NEB and CI-NEB path optimization, and output diagnostic paths, NEB path peak or convergence saddle point energy barriers. The verification and parallel scheduling module is used to store hash values, mapping tables, logs, and task array information.

9. An electronic device, comprising a memory and a processor, characterized in that, The memory is used to store a program that supports the processor in executing the calculation method for translocation dislocation loops of BCC-based metal and alloy vacancy clusters according to any one of claims 1 to 7, and the processor is configured to execute the program stored in the memory.

10. A storage medium storing a computer program, characterized in that, When a computer program is run by a processor, it executes the steps of the method for calculating dislocation loops of vacancy clusters in BCC-based metals and alloys as described in any one of claims 1 to 7.

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