Dislocation loop migration energy barrier calculation method and system

Abstract

The application discloses a dislocation loop migration energy barrier calculation method and system, and belongs to the technical field of computational materials science and atomic scale simulation; the method comprises the following steps: constructing a reference crystal with unique atomic identity and element type; dividing atomic strings according to Burgers direction and forming a dislocation loop; generating multiple translation candidate endpoints through physical atomic relay mapping, so that the identity and element type are transmitted with physical atoms; relaxing the candidate endpoints, screening equivalent initial and final states according to loop center displacement, defect cluster connectivity and dislocation topology; generating intermediate images with consistent identity and meeting minimum spacing, and performing elastic band calculation; performing high-precision single-point energy back calculation on the final image to obtain the migration energy barrier; the application can avoid atomic mismatch, element transposition and incorrect endpoints, and improve the physical correctness, reproducibility and automation degree of dislocation loop energy barrier calculation of pure metals and multicomponent alloys.

Description

Technical Field

[0001] This invention belongs to the fields of computational materials science, atomic-scale simulation and high-performance computing technology, and relates to a method and system for calculating the migration barrier of dislocation loops. Background Technology

[0002] Dislocation loops are important defect structures in irradiation damage, quenching defects, and plastic deformation. The migration energy barrier of dislocation loops determines their thermally activated migration ability, and further affects defect aggregation, void formation, irradiation hardening, and microstructure evolution. Molecular dynamics is suitable for observing dynamic processes under high temperature or high stress, but for rare low-temperature events, it is usually necessary to use the elastic band method or the climbing elastic band method to find the lowest energy path between the initial and final states.

[0003] Elastic band calculations require all mirror images to have the same number of atoms and a strictly corresponding atomic order. For diffusion of single vacancy or single interstitial atoms, it is usually easy to establish an atomic correspondence between the initial and final states; however, the overall migration of dislocation loops involves cooperative or sequential relay motion on multiple atomic strings. If only the final state geometry is translated as a whole, or only the nearest lattice position is renumbered, it is common to see the same identifier corresponding to different physical atoms, intersecting atomic trajectories, excessively short atomic spacing, and abnormally high-energy intermediate mirror images.

[0004] For multi-element alloys, the above problems are even more pronounced. Element type represents the chemical identity of physical atoms. If element type is redistributed according to the final state lattice position, it is equivalent to exchanging alloying elements without basis in the reaction path, which will mix chemical transposition energy into the dislocation loop migration energy barrier; if only the number of coordinates is guaranteed to be the same without checking the identity and type sequence, the calculation program can run, but the obtained energy barrier does not correspond to the target physical process.

[0005] Existing automated calculations typically focus on linear interpolation of general atomic diffusion or surface reactions, lacking identity-preserving mapping for multi-atom relay processes in dislocation loops, as well as integrated control of endpoint translation periods, dislocation topology, defect cluster connectivity, and high-precision back-calculation of the final mirror image. Therefore, a general technical solution is needed that allows for interchangeable crystal structures, alloy compositions, dislocation loop sizes, and interaction models. Summary of the Invention

[0006] The technical solution of this invention is used to solve the problems of unclear physical atomic correspondence between the initial and final states, non-physical transposition of alloy element types, entry of incorrect endpoints into the calculation, atomic collisions in the path, and insufficient energy output accuracy in the calculation of the overall migration elastic band of dislocation loops.

[0007] The present invention solves the above-mentioned technical problems through the following technical solutions: This invention provides a method for calculating the migration barrier of dislocation loops, comprising the following steps: Obtain the various parameters of the target material to construct a reference crystal, and assign a unique atomic identity and element type to each physical atom in the reference crystal; Based on the toroidal normal and Burgers vector direction, the lattice position of the reference crystal is divided into multiple atomic strings, and insertion positions are selected within the target toroidal region to construct the initial dislocation loop; For multiple preset translation amounts, a relay mapping is established in each atom string participating in the migration to the adjacent lattice position, so that the unique atom identity and element type are passed with the corresponding physical atom, generating multiple candidate endpoints with the same total number of atoms, identity set and element type sequence. Multiple candidate endpoints are relaxed separately, and the dislocation topology and defect atom clusters of the relaxed candidate endpoints are extracted. Candidate endpoints are then selected based on the displacement of the ring center along the Burgers vector, the connectivity of the defect atom clusters, and the allowable set of the dislocation topology. From the selected candidate endpoints, determine the initial and final states that are topologically equivalent and separated by one Burgers translation cycle. While maintaining the consistency of the atomic identity set and element type sequence of each mirror image, generate multiple intermediate mirror images and perform elastic band calculations on the initial state, final state, and intermediate mirror images. Read the final mirror configuration at the end of the elastic band calculation, perform single-point energy calculations on each final mirror configuration, and determine the migration energy barrier of the dislocation loop by the maximum value of each single-point energy relative to the initial state energy.

[0008] Furthermore, the parameters of the target material include crystal structure parameters, chemical composition, interatomic interaction model, dislocation loop parameters, and calculation parameters; the dislocation loop parameters include the number of interstitial atoms, loop radius or loop region threshold, loop center, loop plane normal, direction and sign of the Burgers vector.

[0009] Furthermore, the plurality of preset translation amounts include at least three of 0b, 0.5b, 1b and 2b, where b is the Burgers vector; by comparing the loop center displacement and topological equivalence of the candidate endpoints 0b, 1b and 2b, it is verified whether the candidate endpoint 1b constitutes a complete migration process, and the candidate endpoint 0.5b is used to evaluate the path mid-configuration.

[0010] Furthermore, the relay mapping method is as follows: Establish an ordered lattice position sequence along the atomic string; Position the inserted atom and its adjacent parent atoms; For the translation reaction coordinate λ, the inserted atom and at least one parent atom in front of it are mapped from their respective starting positions to the interpolated positions in the direction of the next lattice position. When the translation reaction coordinate λ changes from 0 to 1, the inserted atom occupies the next lattice position, and the corresponding parent atom occupies the next lattice position in turn, while the identity and element type of each physical atom remain unchanged.

[0011] Furthermore, the elastic band calculation includes a non-climbing stage and a climbing stage, and convergence is determined based on the maximum mirror force, the continuity of adjacent mirror energy, and the topological integrity of dislocations; when the maximum mirror force does not reach the threshold, the climbing stage continues from the saved final path.

[0012] Furthermore, the method for calculating the single-point energy is as follows: read each final mirror configuration that is forcibly output at the end of the elastic band calculation, perform a unified back calculation with a higher energy output accuracy than the elastic band log, and output the forward energy barrier, reverse energy barrier, reaction energy, highest energy mirror number, maximum mirror force, and topology check results.

[0013] Furthermore, the intermediate image generation method adopts a cooperative path generation method or a zipper path generation method; the cooperative path generation method enables the atom strings participating in the migration to advance along the same reaction coordinates; the zipper path generation method triggers the relay mapping of different atom strings sequentially according to the circumferential order of the dislocation loop.

[0014] The present invention also provides a dislocation loop migration barrier calculation system, comprising: a reference crystal construction module, an initial dislocation loop construction module, a candidate endpoint generation module, a screening module, an elastic band calculation module, and a barrier determination module; The reference crystal construction module is used to acquire various parameters of the target material to construct a reference crystal, and to assign a unique atomic identifier and element type to each physical atom in the reference crystal. The initial dislocation loop construction module is used to divide the lattice position of the reference crystal into multiple atomic strings according to the toroidal normal and the Burgers vector direction, select the insertion position in the target toroidal region, and construct the initial dislocation loop; The candidate endpoint generation module is used to establish a relay mapping of physical atoms to adjacent lattice positions in each atom string participating in the migration for multiple preset translation amounts, so that the unique atom identity and element type are passed with the corresponding physical atom, and generate multiple candidate endpoints with the same total number of atoms, identity set and element type sequence. The filtering module is used to relax the multiple candidate endpoints respectively, extract the dislocation topology and defect atom clusters of the relaxed candidate endpoints, and filter the candidate endpoints according to the displacement of the ring center along the Burgers vector, the connectivity of the defect atom clusters and the allowable set of the dislocation topology. The elastic band calculation module is used to determine the initial and final states that are topologically equivalent and separated by one Burgers translation cycle from the candidate endpoints that have passed the screening. Under the condition of keeping the atomic identity set and element type sequence of each mirror consistent, multiple intermediate mirrors are generated, and elastic band calculation is performed on the initial state, final state and intermediate mirrors. The energy barrier determination module is used to read the final mirror configuration at the end of the elastic band calculation, perform single-point energy calculations on each final mirror configuration, and determine the migration energy barrier of the dislocation loop by the maximum value of each single-point energy relative to the initial state energy.

[0015] 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 dislocation loop migration barrier calculation method, and the processor is configured to execute the program stored in the memory.

[0016] 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 the dislocation loop migration barrier.

[0017] The beneficial effects of this invention are as follows: This invention explicitly preserves the physical atom identification, ensuring that the multi-atom relay migration of dislocation loops corresponds to continuous physical atom trajectories, avoiding atom mismatches and trajectory intersections, and guaranteeing the physical rationality of the path. For random or ordered alloys, element types are bound to physical atoms, prohibiting the reallocation of element types based on lattice positions throughout the entire calculation process. This avoids introducing non-physical element transpositions between initial and final states, thus accurately distinguishing between chemical environment effects and intrinsic migration processes of dislocation loops, allowing this invention to be directly extended to multi-component alloy systems. Through multi-translation endpoint scanning and joint verification of dislocation topology-defect clusters, invalid endpoints such as loop collapse, erroneous periods, topological transformations, or multiple defect clusters can be identified before high-cost elastic band calculations, ensuring that the initial and final states entering the elastic band calculation have correct physical meaning and saving computational resources. Cooperative paths and zipper paths can adapt to different sizes and migration mechanisms, and geometric quality checks reduce atomic collisions and anomalous high-energy mirrors, ensuring the convergence of elastic band calculations. The final configuration can be uniformly back-calculated at a single point, reducing energy barrier errors caused by output truncation, and can resolve energy barrier differences at the millielectronvolt level, meeting the requirements of high-precision simulations. Task dependency and continuation control reduce repetitive input and human intervention, making it easy to reproduce in batches on high-performance computing platforms. It is applicable to general calculations with different crystal structures, alloy compositions, dislocation loop sizes and interaction models. Attached Figure Description

[0018] Figure 1 This is a flowchart illustrating the overall process of calculating the dislocation loop migration barrier according to the present invention. Figure 2A schematic diagram illustrating how the physical atom identifiers on the same atom string remain unchanged during relay motion; Figure 3 A schematic diagram illustrating the scanning and automatic filtering of candidate endpoints for 0b, 0.5b, 1b, and 2b. Figure 4 This is a schematic diagram of collaborative paths and zipper paths; Figure 5 A schematic diagram showing the calculated elastic band of a dislocation loop consisting of 7 interstitial atoms in body-centered cubic Fe; Figure 6 A schematic diagram showing the calculated elastic band of a dislocation loop consisting of 19 interstitial atoms in body-centered cubic Fe; Figure 7 A schematic diagram of the calculated elastic band of a dislocation loop consisting of 37 interstitial atoms in body-centered cubic Fe; Figure 8 This is a schematic diagram of the module of the dislocation loop migration barrier calculation system of the present invention. Detailed Implementation

[0019] 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.

[0020] The technical solution of the present invention will be further described below with reference to the accompanying drawings and specific embodiments: Example 1 like Figure 1 As shown, this embodiment provides a method for calculating the migration barrier of dislocation loops, including the following steps: Step S1: Read configuration parameters.

[0021] Read configuration files in JSON, YAML, or other machine-readable formats. Configuration parameters are categorized as follows: (1) System parameters: including lattice type (e.g., body-centered cubic), lattice constant, supercell size (number of cell repetitions along the three crystal axes), and periodic boundary condition markers.

[0022] (2) Chemical composition parameters: including a list of element types, the atomic fraction or number of atoms of each element, and a random seed. For pure metals, the element type is a single element, and the atomic fraction is 1.

[0023] (3) Interatomic interaction parameters: including potential function file path, potential function type, element order, mapping from atom type to element symbol, and neighbor cutoff radius. When constructing the example, the potential function file is copied to the example directory and the file's checksum is recorded to avoid the results becoming unreproducible due to subsequent changes to the external file.

[0024] (4) Geometric parameters of dislocation loop: including the center coordinates of the dislocation loop (fractional coordinates or Cartesian coordinates in the supercell), the unit vector of the toroidal normal, the direction and sign of the Burgers vector, the number of target interstitial atoms or the loop radius, and the toroidal region screening threshold.

[0025] (5) Elastic band calculation control parameters: including total number of mirror images, elastic constant (spring force constant), convergence force threshold, maximum number of iteration steps, optimization algorithm type, and hill-climbing stage triggering conditions.

[0026] (6) Scheduling parameters: including task dependencies, maximum number of parallel tasks, restart policy, and log output level.

[0027] Each parameter is provided by an independent configuration file, which decouples physical parameters such as material system and dislocation loop size from the execution script, facilitating batch calculations and parameter scanning.

[0028] Step S2: Construct a reference crystal and assign identity identifiers and element types to the atoms.

[0029] A periodic reference crystal is constructed based on the lattice type, lattice constant, and supercell size. The reference crystal is a defect-free, complete lattice in which atoms occupy all lattice positions.

[0030] Each physical atom is assigned a globally unique atomic identifier (ID) and element type (type). Specifically, the parent atom can be numbered sequentially as 1, 2, 3, ..., N according to its order in the atom list. host , where N host This represents the total number of atoms in the parent dataset. Each atom ID remains constant throughout the entire calculation process.

[0031] For element type allocation: If the target material is a pure metal, all atoms have the same element type, which is equal to the element symbol of that metal.

[0032] If the target material is an alloy containing at least two elements, the element types are randomly assigned to each lattice position of the reference crystal according to a preset atomic fraction and a fixed random seed. The fixed random seed ensures consistent results across multiple runs of the same configuration. The specific atomic number of each element after actual assignment is written into the parsed configuration file for easy verification.

[0033] For alloys, the element types of all atoms are determined once during the construction of the reference crystal. Throughout the subsequent processes of candidate endpoint generation, mirror configuration generation, and elastic band calculation, it is prohibited to reallocate or modify the element types of any atoms based on their lattice occupancy. Element type, as an inherent chemical property of physical atoms, is transmitted along with the atom's identity identifier.

[0034] Step S3: Divide the atomic string and construct the initial dislocation loop.

[0035] Let the unit vector e_b = b / |b| be the longitudinal axis of the Burgers direction, where b is the Burgers vector. For each lattice position r in the reference crystal, calculate the longitudinal coordinate u = r·e_b and the transverse coordinate q = ru·e_b.

[0036] Lattice positions with equal lateral coordinate q within the tolerance range are grouped into the same atomic string. The atomic string extends along the Burgers direction, and each atomic string contains a series of lattice positions arranged along that direction.

[0037] For an atom string with a horizontal coordinate q located within the target annular region, an additional atom (i.e., a self-interstitial atom) is constructed by selecting a representative position within one Burgers period thickness of the atom string. Thus, the number of self-interstitial atoms can be directly specified by the target quantity, or it can be obtained by filtering based on the ring radius and horizontal position.

[0038] To reduce the extremely short interatomic spacing in the initial configuration, a symmetrical splitting method is used to insert atoms: the original lattice atoms and the inserted atoms are slightly displaced in opposite directions along the Burgers vector. Specifically, the original lattice atoms are displaced by δ / 2 along the +Burgers direction, and the inserted atoms are displaced by δ / 2 along the -Burgers direction, where δ is a preset splitting distance (usually a small proportion of the Burgers vector length, such as 5%-15%). Symmetrical splitting homogenizes the interatomic spacing and avoids excessive atomic repulsion in the initial configuration.

[0039] Step S4: Establish a relay mapping table and generate candidate endpoints.

[0040] For each string of atoms that needs to be translated, an ordered list of lattice positions is constructed. This list is arranged in ascending order of the vertical coordinates along the Burgers direction. The starting lattice position index and the next adjacent lattice position index (i.e., the target position) of the inserted atom in this list are determined.

[0041] Establish a relay mapping table, which should record at least the following information: Atomic string numbering; Initial lattice position coordinates; Target lattice position coordinates; A list of IDs of the physical atoms involved in the migration; The element type corresponding to each ID; The period offset that each atom needs to cross (if it crosses a period boundary). The propagation range of each atom on the reaction coordinate λ.

[0042] For continuous reaction coordinates λ ranging from 0 to 1, the coordinate advancement rule for relay mapping is as follows: The inserted atom X is progressively moved from its initial lattice position r0 to the next lattice position r1. Simultaneously, the parent atom H1, originally located at r1, is moved from r1 to the next lattice position r2, and the parent atom H2, originally located at r2, is moved from r2 to r3, and so on. This coordinate progression can be represented as: r i (λ)=r i (0)+s i (λ)·b Where r i (0) represents the starting position of the i-th physical atom, s i (λ) is the piecewise continuous propagation function for the i-th physical atom. i (λ) changes monotonically between 0 and 1, and all s are equal when λ = 0. i =0, when λ=1 all s i =1.

[0043] Throughout the entire coordinate progression, the atomic identification ID and element type of each physical atom remain consistent with their initial assignment and are not exchanged or changed due to changes in the lattice position they occupy. Figure 2 This process is illustrated: X (inserted atom), H1 and H2 represent the additional atom and the parent atom, respectively, the arrows indicate the direction of coordinate advancement for each atom, and the atom labels (ID and type) do not change with the placeholder position.

[0044] For multiple preset fractional translations (such as 0b, 0.5b, 1b, and 2b), the above relay mapping is applied to generate candidate endpoint configurations respectively. After generating each candidate endpoint, the atom list is output in sorted order by ID; if the IDs are not consecutive, the ID set changes, the type of the same ID changes, or the total number of atoms changes, the generation is immediately determined to have failed, and the reason for failure is recorded.

[0045] The minimum image convention or unpacking coordinates are used to process the periodic boundaries to ensure that atomic displacements do not cross the boundaries and generate long-distance pseudo-displacements.

[0046] Step S5: Relax candidate endpoints and perform topology verification.

[0047] The candidate endpoints 0b, 0.5b, 1b, and 2b are each subjected to energy minimization relaxation. The relaxation is performed using the conjugate gradient method or a fast inertial relaxation engine, with the convergence condition being that the atomic force is below a preset threshold.

[0048] Analyze the structure of each candidate endpoint after relaxation: (1) Dislocation Extraction Analysis: Dislocation extraction algorithms (such as the DXA algorithm) are used to identify dislocation segments and their Burgers vectors in the crystal. For a body-centered cubic a / 2 <111> A prism dislocation cycle requires the existence of a single closed a / 2 <111> The dislocation loop has a size that deviates from the preset loop radius within an acceptable range.

[0049] (2) Defect cluster identification: Using common nearest neighbor analysis or Wigner-Seitz defect analysis, defect atoms that deviate from the reference lattice position are identified, and spatially adjacent defect atoms are clustered into defect clusters. The defect clusters are required to be single connected clusters (rather than multiple dispersed clusters), and the geometric center of the defect cluster is consistent with the preset ring center.

[0050] (3) Calculation of ring center displacement: The ring center c is estimated by the weighted average of the defect atom coordinates or dislocation line node coordinates, and the displacement of the ring center along the Burgers direction is calculated as follows: Δ=(c-c0)·b / |b| 2 , where c0 is the ring center of the initial configuration.

[0051] The filtering criteria for candidate endpoints include: For endpoint 0b: Δ should be within the range of 0 ± ε0, and a closed loop a / 2 exists. <111> Dislocation loops, defect clusters are single connected clusters; For endpoint 0.5b: Δ should be within the range of 0.5 ± ε0.5, and the topology may differ from the initial state (as a reference for intermediate configurations along the path). For endpoint 1b: Δ should be within the range of 1 ± ε1, and the topology should be the same as that of endpoint 0b (both are closed a / 2). <111> Dislocation loops), and defect clusters are single connected clusters; For endpoint 2b: Δ should be within the range of 2±ε2, and the topology is the same as that of endpoint 0b.

[0052] ε0, ε0.5, ε1, and ε2 are preset tolerance thresholds, typically taken as 5%–10% of the Burgers vector length.

[0053] Figure 3 The process of scanning and automatically filtering candidate endpoints 0b, 0.5b, 1b, and 2b is illustrated schematically, where the 1b endpoint is verified as an equivalent endpoint to the 0b endpoint that differs from the 0b endpoint by one full migration cycle.

[0054] Step S6: Generate intermediate mirror configuration.

[0055] From the selected candidate endpoints, endpoints 0b and 1b are chosen as the initial and final states for the elastic band calculation, respectively. A preset number of intermediate mirror configurations are generated between the initial and final states.

[0056] like Figure 4 As shown, this invention provides two path generation modes: (1) Cooperative path generation mode: All atomic strings participating in the migration adopt the same global reaction coordinate λ value (λ is uniformly distributed from 0 to 1), and the relay mapping on each atomic string is synchronously advanced. This mode is suitable for small dislocation loops that are approximately synchronously advanced, where the migration of each part of the loop has good consistency.

[0057] (2) Zipper-style path generation mode: The atomic strings are sorted according to the polar angle of each atomic string in the direction of the dislocation loop or the preset migration priority, and each atomic string is assigned a staggered local reaction coordinate λ. j Define λ j =clip((λ-τ j ) / w,0,1), where τ j For the starting phase based on circumferential sorting, w is the propulsion width, clip((λ-τ) j The function () / w,0,1) is used to restrict a value to a specified interval, that is: if (λ-τ) j If ) / w is less than 0, then clip((λ-τ) j The function () / w,0,1) takes the value of 0; if (λ-τ) j If ) / w is greater than 1, then clip((λ-τ) j The function () / w,0,1) takes the value 1; if (λ-τ) j If ) / w is greater than or equal to 0 and less than or equal to 1, then clip((λ-τ) j The function takes the value (λ-τ) / w,0,1. j This mode enables relay mapping of different atomic strings to be triggered sequentially along the circumferential direction, and is suitable for observing large-sized dislocation loops that nucleate and propagate locally around the circumference.

[0058] In both modes, a quality check is performed after each intermediate mirror configuration is generated: Check whether the total number of atoms, ID set, and element type sequence in the mirror image are completely consistent with the initial state; Check whether the maximum displacement of each physical atom between adjacent mirror configurations is reasonable (it should usually be less than the Burgers vector length). Check whether the minimum spacing between any two atoms in the same mirror configuration is higher than a preset safety threshold (usually a certain percentage of the lattice constant, such as 20%–30%).

[0059] If any check fails, adjust the interpolation step size or regenerate the path.

[0060] Step S7: Perform elastic band calculation.

[0061] First, a non-climbing elastic band relaxation phase is performed: all mirror images (initial and final states are fixed) minimize energy under the coupling of spring force, so that the path moves towards the lowest energy path.

[0062] Then, the climbing elastic zone relaxation phase is carried out: the current image with the highest energy is applied to the climbing force along the path tangent direction, so that it is further close to the saddle point configuration.

[0063] Convergence criteria include: The maximum force on each atom in each mirror configuration is lower than the preset force convergence threshold (e.g., 0.01 eV / Å). The energy between adjacent mirror configurations exhibits a continuous single-peak distribution along the reaction coordinates; The dislocation topology of the first-to-last mirror configuration is consistent with that of the initial reference crystal.

[0064] If the maximum number of iterations is reached but the maximum atomic force does not decrease below the force convergence threshold, the coordinates and energies of all current mirror configurations are saved. Based on the saved path state, a continuation task is automatically initiated to continue executing the climbing elastic band relaxation phase until convergence.

[0065] If anomalies such as mirrored atom overlap or the disappearance of the target dislocation loop structure occur during the calculation process, the process will revert to the path generation step, automatically switch the path generation mode (such as from cooperative path to zipper path), and then try again.

[0066] Step S8: High-precision single-point energy return calculation and result output.

[0067] After the elastic band calculation converges or reaches the maximum number of steps, the complete atomic coordinate file for each mirror configuration is forcibly saved. Each final mirror configuration is read, and the total system energy for each final mirror configuration is recalculated using the same interatomic interaction model, periodic boundary conditions, and neighbor truncation parameters as in the elastic band relaxation calculation, with a numerical precision higher than that in the elastic band relaxation calculation process log output (e.g., retaining more than ten decimal places).

[0068] The energy values ​​in the elastic band relaxation calculation log are replaced with the recalculated single-point energy values. The relative energies of each mirror configuration are calculated based on the initial state energy, and the maximum relative energy is taken as the forward migration energy barrier. The reverse migration energy barrier and reaction energy are also calculated.

[0069] The output includes: forward migration barrier, backward migration barrier, reaction energy, the number and reaction coordinates of the highest-energy mirror; convergence status flag (converged / not converged); and an energy-reaction coordinate data table for each mirror. Let the energy of the i-th mirror be E. i The initial state is E0, and the final state is E n Then the forward migration energy barrier E a + =max(E i -E0, reverse migration energy barrier E a - =max(E i )-E n The reaction energy ΔE = E n -E0.

[0070] The initial state, the mirror image near the peak, and the final state are subjected to topological analysis again to generate a machine-readable report containing the hash value of the input parameters, the program version number, the potential file check value, the convergence index, and the anomaly flag, which facilitates batch system comparison and result traceability.

[0071] Example: a / 2 in body-centered cubic pure Fe <111> Calculation of dislocation loop migration barrier This embodiment uses body-centered cubic pure Fe as the verification system to explain in detail the implementation process and effects of the method of the present invention.

[0072] (1) System setup: Body-centered cubic Fe was used, with a lattice constant a = 2.855 Å. A supercell with a size of 20a × 20a × 20a was constructed, containing approximately 16,000 atoms. The interactions between Fe atoms were described using embedded atomic potentials.

[0073] Construct a / 2 containing 7, 19, and 37 additional self-interstitial atoms, respectively. <111> Prismatic dislocation loop. Burgers vector b = a / 2

[111] , vector length ‖b‖ = ≈ 2.472 Å. A complete migration is defined as the center of the dislocation loop moving 1b along the signed Burgers vector.

[0074] (2) Endpoint generation and filtering: Candidate endpoints 0b, 0.5b, 1b, and 2b are constructed. Taking a dislocation loop with 37 interstitial atoms as an example, relay mapping is used to generate each candidate endpoint, ensuring that the atom ID and element type (Fe in this case) remain consistent across all endpoints.

[0075] Each candidate endpoint was relaxed separately. After relaxation, the DXA dislocation extraction algorithm was used to identify the dislocation structure. The dislocation extraction results of endpoint 0b showed the existence of a single closed a / 2

[111] dislocation loop with a loop radius of about 25 Å. Endpoint 1b showed the same topology, with the loop center moving about 2.47 Å along the

[111] direction, verifying that 1b corresponds to a complete migration cycle. Endpoint 2b showed that the loop center moved further by about 2.47 Å, and the topology remained intact. Although the defect cluster at endpoint 0.5b was still connected, the geometry of the dislocation loop was significantly deformed, indicating that the half-cycle position corresponds to a high-energy transition state region in the path.

[0076] (3) Path generation and elastic band calculation: Thirty-one mirror images (including initial and final states) are used. For small rings with seven interstitial atoms, a cooperative path generation mode is adopted, with all atom strings advancing synchronously. For large rings with 19 and 37 interstitial atoms, a zipper-style path generation mode is adopted, triggering the migration of each atom string sequentially according to the polar angle of the ring circumference.

[0077] In the elastic band calculation, the spring constant is 1.0 eV / Ų, and the convergence threshold is 0.01 eV / Å. The maximum number of iterations is set to 2000. The non-climbing phase consists of 500 iterations, after which the climbing phase begins.

[0078] (4) Single-point back-calculation is possible: After the elastic band calculation converges, a high-precision single-point energy back-calculation is performed on all 31 final mirror configurations. When performing single-point energy calculations for each configuration, twelve decimal places are retained.

[0079] The calculation results are as follows: Seven self-interstitial atomic rings: the forward migration energy barrier is about 0.016 eV, and the highest energy mirror is located in the range of λ≈0.4-0.6; 19 self-interstitial atomic rings: forward migration barrier approximately 0.0312 eV; 37 self-interstitial atomic rings: the forward migration barrier is about 0.053 eV, and the highest energy mirror is located near λ≈0.5.

[0080] Figures 5 to 7 The calculation results of elastic bands for dislocation loops composed of 7, 19, and 37 interstitial atoms are presented respectively.

[0081] The above values ​​illustrate that the method of this invention can resolve energy barrier differences much smaller than the total energy level of the system (tens of thousands of electron volts). Replacing Fe with W, V, Ta, Cr, or multi-principal-element body-centered cubic alloys (such as FeCrNi, FeCrMnNi, etc.) only requires changing the lattice constant, element type mapping, composition, random seed, and interaction model path in the configuration file; the core logic of atom ID relay mapping, candidate endpoint screening, and path generation remains unchanged.

[0082] Example 2 like Figure 8 As shown, this embodiment provides an automatic calculation system for the energy barrier of dislocation loop migration, including: a reference crystal construction module, an initial dislocation loop construction module, a candidate endpoint generation module, a screening module, an elastic band calculation module, and an energy barrier determination module; The reference crystal construction module is used to acquire various parameters of the target material to construct a reference crystal, and to assign a unique atomic identity and element type to each physical atom in the reference crystal. The initial dislocation loop construction module is used to divide the lattice position of the reference crystal into multiple atomic strings according to the toroidal normal and the Burgers vector direction, select the insertion position in the target toroidal region, and construct the initial dislocation loop; The candidate endpoint generation module is used to establish a relay mapping of physical atoms to adjacent lattice positions in each atom string participating in the migration for multiple preset translation amounts, so that the unique atom identity and element type are passed with the corresponding physical atom, and multiple candidate endpoints with the same total number of atoms, identity set and element type sequence are generated. The filtering module is used to relax the multiple candidate endpoints respectively, extract the dislocation topology and defect atom clusters of the relaxed candidate endpoints, and filter candidate endpoints based on the displacement of the ring center along the Burgers vector, the connectivity of the defect atom clusters, and the allowable set of the dislocation topology. The elastic band calculation module is used to determine the initial state and the final state that are topologically equivalent and separated by one Burgers translation cycle from the candidate endpoints that have passed the screening. Under the condition of keeping the atomic identity set and element type sequence of each mirror consistent, multiple intermediate mirrors are generated, and elastic band calculation is performed on the initial state, the final state and the intermediate mirrors. The energy barrier determination module is used to read the final mirror configuration at the end of the elastic band calculation, perform single-point energy calculation on each final mirror configuration, and determine the migration energy barrier of the dislocation loop by the maximum value of each single-point energy relative to the initial state energy.

[0083] The modules exchange data through structure files, configuration files, and task status files, forming a complete automated computation chain from parameter input to energy barrier output. Each module can be implemented by a single program on the same computing node, or it can be distributed across login nodes, computing nodes, and post-processing nodes.

[0084] On the high-performance computing platform, the entire process is encapsulated into a single entry command. After reading the configuration, the entry command creates a test case directory and sequentially generates tasks for endpoint relaxation, endpoint analysis, path generation, trial run, formal elastic band, post-processing, image-by-image single-point energy, and final topology check. The task scheduler uses prior success dependencies, and the endpoint analysis script only returns a success status when the center displacement and topology conditions are met.

[0085] The trial run is used to check parallel partitioning, potential function loading, number of atoms, image files, and initial maximum force. If the formal calculation reaches the maximum number of steps but the maximum image force fails to converge, the system reads the forcibly written final image and establishes a continuation calculation; after the continuation calculation is completed, energy back-calculation and topology checking are re-executed. The final summary simultaneously provides the result values, convergence Boolean values, and rejection reasons, facilitating comparison of batch systems.

[0086] Those skilled in the art can replace the elastic band solver with an improved tangential elastic band, climbing elastic band, string method, or other multi-mirror minimum energy path solver without changing the core idea of ​​this invention. They can also replace the structural analysis tool with a tool capable of identifying equivalent dislocation topology and defect clusters. All such substitutions should fall within the protection scope of this invention.

[0087] Example 3 This embodiment provides an electronic device, including a memory and a processor.

[0088] The memory is used to store a computer program that supports the processor in executing the dislocation loop migration barrier calculation method 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 device, 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.

[0089] 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 dislocation loop migration barrier 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.

[0090] 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 the migration energy barrier of dislocation loops, characterized in that, Includes the following steps: Obtain the various parameters of the target material to construct a reference crystal, and assign a unique atomic identity and element type to each physical atom in the reference crystal; Based on the toroidal normal and Burgers vector direction, the lattice position of the reference crystal is divided into multiple atomic strings, and insertion positions are selected within the target toroidal region to construct the initial dislocation loop; For multiple preset translation amounts, a relay mapping is established in each atom string participating in the migration to advance physical atoms to adjacent lattice positions, so that the unique atom identity and element type are passed with the corresponding physical atom, generating multiple candidate endpoints with the same total number of atoms, identity set and element type sequence. Multiple candidate endpoints are relaxed separately, and the dislocation topology and defect atom clusters of the relaxed candidate endpoints are extracted. Candidate endpoints are then selected based on the displacement of the ring center along the Burgers vector, the connectivity of the defect atom clusters, and the allowable set of the dislocation topology. From the selected candidate endpoints, determine the initial and final states that are topologically equivalent and separated by one Burgers translation cycle. While maintaining the consistency of the atomic identity set and element type sequence of each mirror image, generate multiple intermediate mirror images and perform elastic band calculations on the initial state, final state, and intermediate mirror images. Read the final mirror configuration at the end of the elastic band calculation, perform single-point energy calculations on each final mirror configuration, and determine the migration energy barrier of the dislocation loop by the maximum value of each single-point energy relative to the initial state energy.

2. The method for calculating the migration energy barrier of dislocation loops according to claim 1, characterized in that, The parameters of the target material include crystal structure parameters, chemical composition, interatomic interaction model, dislocation loop parameters, and calculation parameters; the dislocation loop parameters include the number of interstitial atoms, loop radius or loop region threshold, loop center, loop plane normal, direction and sign of the Burgers vector.

3. The method for calculating the migration barrier of dislocation loops according to claim 1, characterized in that, The plurality of preset translation amounts include at least three of 0b, 0.5b, 1b and 2b, where b is the Burgers vector; By comparing the loop center displacement and topological equivalence of candidate endpoints 0b, 1b, and 2b, we verify whether candidate endpoint 1b constitutes a complete migration process, and evaluate the path mid-configuration using candidate endpoint 0.5b.

4. The method for calculating the migration energy barrier of dislocation loops according to claim 1, characterized in that, The relay mapping method is as follows: Establish an ordered lattice position sequence along the atomic string; Position the inserted atom and its adjacent parent atoms; For the translation reaction coordinate λ, the inserted atom and at least one parent atom in front of it are mapped from their respective starting positions to the interpolated positions in the direction of the next lattice position. When the translation reaction coordinate λ changes from 0 to 1, the inserted atom occupies the next lattice position, and the corresponding parent atom occupies the next lattice position in turn, while the identity and element type of each physical atom remain unchanged.

5. The method for calculating the migration barrier of dislocation loops according to claim 1, characterized in that, The elastic band calculation includes a non-climbing stage and a climbing stage, and convergence is determined based on the maximum mirror force, the continuity of adjacent mirror energy, and the topological integrity of dislocations. When the maximum mirror force does not reach the threshold, the climbing stage continues from the saved final path.

6. The method for calculating the migration energy barrier of dislocation loops according to claim 1, characterized in that, The method for calculating the single-point energy is as follows: read each final mirror configuration that is forcibly output at the end of the elastic band calculation, use a higher energy output accuracy than the elastic band log for unified back calculation, and output the forward energy barrier, reverse energy barrier, reaction energy, highest energy mirror number, maximum mirror force and topology check results.

7. The method for calculating the migration barrier of dislocation loops according to claim 1, characterized in that, The intermediate image generation method adopts either a cooperative path generation method or a zipper path generation method; the cooperative path generation method enables the atom strings participating in the migration to advance along the same reaction coordinates; the zipper path generation method triggers the relay mapping of different atom strings sequentially according to the circumferential order of the dislocation loop.

8. A system for calculating the migration barrier of dislocation loops, characterized in that, include: The reference crystal construction module is used to acquire various parameters of the target material to construct a reference crystal, and to assign a unique atomic identifier and element type to each physical atom in the reference crystal. The initial dislocation loop construction module is used to divide the lattice position of the reference crystal into multiple atomic strings according to the toroidal normal and the Burgers vector direction, select the insertion position in the target toroidal region, and construct the initial dislocation loop; The candidate endpoint generation module is used to establish a relay mapping of physical atoms to adjacent lattice positions in each atom string participating in the migration for multiple preset translation amounts, so that the unique atom identity and element type are passed with the corresponding physical atom, and generate multiple candidate endpoints with the same total number of atoms, identity set and element type sequence. The filtering module is used to relax the multiple candidate endpoints respectively, extract the dislocation topology and defect atom clusters of the relaxed candidate endpoints, and filter the candidate endpoints according to the displacement of the ring center along the Burgers vector, the connectivity of the defect atom clusters and the allowable set of the dislocation topology. The elastic band calculation module is used to determine the initial and final states that are topologically equivalent and separated by one Burgers translation cycle from the candidate endpoints that have passed the screening. Under the condition of keeping the atomic identity set and element type sequence of each mirror consistent, multiple intermediate mirrors are generated, and elastic band calculation is performed on the initial state, final state and intermediate mirrors. The energy barrier determination module is used to read the final mirror configuration at the end of the elastic band calculation, perform single-point energy calculations on each final mirror configuration, and determine the migration energy barrier of the dislocation loop by the maximum value of each single-point energy relative to the initial state energy.

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 dislocation loop migration barrier calculation method 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, The computer program is executed by the processor to perform the steps of the dislocation loop migration barrier calculation method according to any one of claims 1 to 7.

Images