A method and system for calculating dislocation loop reaction path and energy barrier of body-centered cubic materials

Abstract

A body-centered cubic material dislocation loop reaction path and energy barrier calculation method and system belong to the technical field of computational materials science, and the present application establishes a periodic atomic model and obtains a reference path with a topological anchor point; after the anchor point is relaxed, the dislocation topology is identified and screened; in the alloy system, the fixed mapping of atomic identification and element type is established and applied to all images; adjacent anchor points are divided into reaction segments, the intermediate image is resampled according to the periodic minimum mirror displacement, and the anchor point coordinate correction amount is propagated to the intermediate image; the intermediate image is pre-relaxed by gradually weakening the constraint strength, and the quality is checked, and then the elastic band transition path calculation is performed; when the energy is combined, only the target point is selected from the synchronous checkpoint which simultaneously has energy record and all atomic structure output, the energy zero point of each segment is unified and combined, the overall energy barrier and reaction energy are determined; it is suitable for atomic scale energy barrier calculation of dislocation loop approach, merging and type conversion in body-centered cubic materials.

Description

Technical Field

[0001] This invention belongs to the fields of computational materials science, irradiation damage simulation, atomic-scale defect dynamics, and transition path calculation technology, and relates to a method and system for calculating dislocation loop reaction paths and energy barriers in body-centered cubic materials. Background Technology

[0002] Body-centered cubic materials such as iron, tungsten, vanadium, chromium, molybdenum, niobium, and tantalum generate vacancies, interstitial atoms, and their clusters when used in nuclear energy, fusion devices, high-energy particle irradiation, and high-temperature, high-stress environments. The aggregation of interstitial atoms can form interstitial dislocation loops, among which the common Burgers vector family includes 1 / 2 <111> and <100> The migration, collision, node formation, and type transformation of dislocation loops can affect defect networks, radiation hardening, embrittlement, and dimensional stability.

[0003] Dislocation ring reactions typically do not involve the rigid movement of several atoms initially labeled as interstitial atoms, or their removal from their original situ followed by direct recombination. For 1 / 2 <111> In interstitial dislocation loops, dislocation slip at the atomic scale can be manifested as the cooperative pushing of close-packed atomic clusters and the propagation of atomic identity along these clusters. During the reaction, atoms that were originally in interstitial positions may return to their normal lattice positions, and lattice atoms may transform into new interstitial atoms. Therefore, a physically continuous reaction path must simultaneously maintain the topological evolution of dislocations and the continuity of atomic identity.

[0004] The elastic band method and climbing image elastic band method can be used to determine the minimum potential energy path of an atomic system. However, when only linear coordinate interpolation is performed on the initial and final states of the reaction, problems such as periodic boundary jumps, atoms being too close together, different atoms exchanging identities, a few atoms migrating too far, interstitial atoms directly recombining, and topological disappearance of intermediate dislocations can easily occur. Even if a continuous energy curve is obtained, the curve may not correspond to the expected dislocation slip and node formation mechanism.

[0005] For random or multi-principal-element alloys, a fixed geometry can lead to different local stresses and dislocation core stability under random element occupancy. Some chemical random seeds can cause initial dislocation loops to come into contact prematurely before the formal calculation, or cause instability in nodal, closed, and final states. If anchor point failures are only discovered after all intermediate image construction and long-term elastic band calculations are completed, a large amount of invalid computation will result.

[0006] Multi-stage dislocation loop reactions also face challenges related to high-dimensional path tangency and energy splicing. Single-segment elastic band calculations require numerous copies and struggle to simultaneously resolve local processes such as approach, contact, node generation, closure, and growth. Segmented calculations, on the other hand, require addressing issues such as segment endpoint consistency, energy zero-point unification, duplicate anchor point deletion, energy recording synchronization with atomic structure, refinement of local anomalous segments, and final dislocation topology verification.

[0007] Therefore, a computational method is needed for the motion mechanism of real body-centered cubic dislocation loops, which can enable reaction paths to migrate from existing reliable trajectories and can also be generated independently from perfect lattices, dislocation slip templates, and candidate node structures. At the same time, it can maintain the identity of atoms and alloy elements across images, use topological anchors to constrain the reaction mechanism, and automatically complete path quality checks, abnormal segment encryption, segmented energy merging, and dislocation topology final checks. Summary of the Invention

[0008] The technical solution of this invention is used to solve the following technical problems: First, conventional linear interpolation of initial and final states is difficult to maintain the layer-by-layer atomic pushing and atomic identity propagation of dislocation loops, and is prone to generating non-physical paths; Second, topological anchors and local chemical environments in random alloys are prone to instability; Third, it is difficult to balance computational efficiency, path continuity and local accuracy in multi-stage reaction paths; Fourth, existing energy barrier extraction may lack complete atomic structure and dislocation topological evidence corresponding to energy records.

[0009] The present invention solves the above-mentioned technical problems through the following technical solutions: This invention provides a method for calculating the dislocation loop reaction pathway and energy barrier of body-centered cubic materials, including: Establish a periodic atomic model of body-centered cubic materials, obtain reference reaction paths that preserve atomic identity, and set topological anchor points in the reference reaction paths; Atomic relaxation and dislocation topology identification are performed on the topological anchor points respectively, and only the topological anchor points that satisfy the expected dislocation topology are retained; For alloy systems, a fixed mapping between atomic identifiers and element types is established, and this fixed mapping is applied to all topological anchors and intermediate images; The adjacent topological anchor points are divided into reaction segments. The intermediate image is resampled along the reference reaction path according to the periodic minimum mirror displacement, and the coordinate correction of the relaxed topological anchor points relative to the corresponding reference structure is propagated to the intermediate image. The intermediate images are pre-relaxed with gradually decreasing constraint strength, and path quality checks are performed. Perform elastic band transition path calculations on each reaction segment that passes the inspection; Select the target checkpoint from only the synchronous checkpoints that simultaneously have the energy records of each image and the output of the atomic structure of all copies, unify the energy zero points of each reaction segment and merge each reaction segment, and determine at least one of the overall forward energy barrier, reverse energy barrier and reaction energy. Perform dislocation topology final inspection on the merged reaction path and output the atomic reaction trajectory and energy results.

[0010] Furthermore, the method for obtaining the reference reaction path is as follows: resampling from a verified elastic band path, or extracting from a molecular dynamics trajectory and aligning it according to atomic identifiers, or generating multiple dislocation loop states from a perfect body-centered cubic lattice and connecting them through a dislocation slip template, or applying local cooperative displacement to the reaction core region and performing restricted relaxation, or splicing multiple candidate node structures after topological screening.

[0011] Furthermore, the topological anchor point is configured with at least: the Burgers vector family of the expected dislocations, the number of dislocations, the closed or open state, and the dislocation segment connection relationship.

[0012] Furthermore, the method for dislocation topology identification is as follows: the identified dislocation segments are grouped according to the Burgers vector family of the expected dislocation, the closed state, and the connection relationship of the dislocation nodes, and the grouping results are compared with the configuration of the corresponding topological anchor points.

[0013] Furthermore, the method for establishing a fixed mapping between atom identifiers and element types is as follows: generate an element type sequence according to the target number of atoms of each element, and then shuffle the element type sequence using a chemical random seed to correspond it one-to-one with the atom identifier.

[0014] Furthermore, the pre-relaxation includes at least two constraint stages, where the in-situ constraint strength of the later constraint stage is less than that of the earlier constraint stage, and the maximum single-step atomic displacement allowed in the later constraint stage is not less than that allowed in the earlier constraint stage; the endpoint image uses the relaxed topological anchor point.

[0015] Furthermore, the path quality check includes: the minimum atomic spacing of each image is not less than a preset distance threshold; the root mean square of atomic displacement of adjacent images is not greater than a preset root mean square threshold; the maximum single atomic displacement of adjacent images is not greater than a preset displacement threshold; the atomic identifier set, element type array and periodic simulation box of each image are consistent; and the dislocation topology of the preset topological anchor point meets the configuration requirements.

[0016] Furthermore, the method for performing elastic band transition path calculation on each reaction segment that has passed the inspection is as follows: each reaction segment is configured with a number of replicas, elastic band spring constant, force tolerance, number of iteration steps, atomic structure output interval, and climbing image parameters, and is run in parallel on a parallel computing platform or sequentially according to anchor point dependencies.

[0017] Furthermore, the target checkpoint satisfies the following conditions: the checkpoint step number is aligned with the atomic structure output interval, all replicas have corresponding atomic structure outputs, and the checkpoint data fields are complete; among the candidate checkpoints that meet the aforementioned conditions, the target checkpoint is selected based on at least one of the following: maximum replica force, maximum atomic force, energy change rate, and dislocation topological stability.

[0018] This invention also provides a system for calculating dislocation loop reaction pathways and energy barriers in body-centered cubic materials, comprising: The atomic model and reference path generation module is used to build a periodic atomic model of a body-centered cubic material, obtain reference reaction paths that preserve atomic identity, and set topological anchor points in the reference reaction paths. The Atom Identifier and Composition Mapping Module is used to establish a fixed mapping between atom identifiers and element types in the alloy system, and to apply the fixed mapping to all topological anchors and intermediate images; The topology anchor point setting and verification module is used to perform atomic relaxation and dislocation topology identification on topology anchor points respectively, and retain only the topology anchor points that meet the expected dislocation topology. The minimum mirror resampling module is used to divide the area between adjacent topological anchors into reaction segments, resample the intermediate image along the reference reaction path according to the periodic minimum mirror displacement, and propagate the coordinate correction of the relaxed topological anchors relative to the corresponding reference structure to the intermediate image. The intermediate image pre-relaxation module is used to pre-relax the intermediate image by gradually reducing the constraint strength, and to perform path quality checks. The segmented elastic band calculation module is used to perform elastic band transition path calculations on each reaction segment that has passed the inspection. The synchronous checkpoint selection and energy merging module is used to select target checkpoints only from synchronous checkpoints that simultaneously have energy records for each image and outputs of all copied atomic structures, unify the energy zeros of each reaction segment, and merge each reaction segment to determine at least one of the overall forward energy barrier, reverse energy barrier, and reaction energy; and... The dislocation topology final inspection and result output module is used to perform dislocation topology final inspection on the merged reaction path and output the atomic reaction trajectory and energy results.

[0019] The beneficial effects of this invention are as follows: Compared to schemes that only use initial-final state linear interpolation, this invention reduces atomic identity swapping, periodic boundary jumps, and non-physical long migrations of a few atoms by preserving atom identifiers across images, mapping cluster atom strings, and minimizing mirror resampling. This invention explicitly writes the dislocation Burgers vector, quantity, closure, and node connectivity relationships into topological anchors and repeatedly verifies them in the preprocessing and post-processing stages, establishing a verifiable structural correspondence between energy paths and expected dislocation reaction mechanisms. This invention can migrate verified physical reference trajectories and can also independently generate reference paths from perfect body-centered cubic lattices, single-ring slip templates, double-ring proximity sequences, and candidate node structures, reducing dependence on a single existing configuration file. Through random seed anchor pre-screening and local component exchange while maintaining global counts, this invention can compare the effects of different global components, local components, and chemically random environments on dislocation reaction energy barriers under conditions of reaction geometric consistency. This invention reduces atomic overlap and reaction channel deviation by employing multi-stage restricted pre-relaxation, path quality gating, and adaptive encryption of anomalous sections. It also reduces the risk of single-segment high-dimensional path corner cutting by segmented elastic band calculation. Furthermore, this invention selects results only from checkpoints that are synchronously stored in the energy record and all copies of the atomic structure, enabling the reported energy barrier to be reconstructed image by image from the corresponding atomic structure. Finally, it further improves the repeatability of the results through dislocation topology final inspection and defect conservation. Attached Figure Description

[0020] Figure 1 This is a flowchart illustrating the overall process of calculating the dislocation loop reaction pathway and energy barrier in body-centered cubic materials according to the present invention. Figure 2 A schematic diagram illustrating cross-image atomic identifier preservation and periodic minimum mirror displacement; Figure 3 A schematic diagram for unifying segmented energy zero points, merging paths, and determining the overall energy barrier; Figure 4 For two 1 / 2 <111> Dislocation loop <100> A schematic diagram of the topological anchor points and reaction segments in the transformation of dislocation loops; Figure 5 A schematic diagram illustrating the local composition adjustment of the reaction core region to maintain a constant global element count; Figure 6 Figure showing the dislocation extraction analysis results of three key frames for the independent construction path of the iron system; Figure 7 Energy path diagram of a regular-NEB example for an independent case study of an iron system; Figure 8 This is a schematic diagram of the structural composition of the body-centered cubic material dislocation loop reaction path and energy barrier calculation 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] The technical solution of the present invention will be further described below with reference to the accompanying drawings and specific embodiments: Example 1 1. Overall Technical Solution like Figure 1 As shown, this embodiment provides a method for calculating the dislocation loop reaction path and energy barrier of a body-centered cubic material. This method can be automatically executed by a computer program and specifically includes steps S01 to S15.

[0023] S01. Establish a periodic atomic model for body-centered cubic materials. The elemental composition, lattice constant, simulation box, boundary conditions, total number of atoms, potential function or interatomic interaction model, and net number of interstitial atoms in reaction defects of the body-centered cubic (BCC) material are determined. All reaction images to be compared use the same periodic simulation box, the same total number of atoms, and the same set of atom identifiers. The atom identifiers range from 1 to the total number of atoms, and all atomic structures are ordered according to the atom identifiers. The element type allocation, coordinate sorting, format conversion, and file reading / writing of the BCC material do not change the correspondence between atom identifiers and physical atoms.

[0024] The dislocation loop reaction includes the approach, slippage, contact, node formation, closure, merging, type transformation, or growth of two or more interstitial dislocation loops.

[0025] The body-centered cubic material includes at least one of iron, tungsten, vanadium, chromium, molybdenum, niobium, tantalum, and their alloys.

[0026] S02, Reference reaction pathway for obtaining atomic identity preservation Atomic identity preservation means that throughout the entire reaction pathway, the same atomic identifier always represents the same physical atom; for alloy systems, the same atomic identifier also always corresponds to the same element. Atoms can undergo large cooperative displacements in the crystal lattice, but these cannot be replaced by renumbering or reassigning identifiers according to spatial nearest neighbors to replace the actual atomic motion.

[0027] Reference reaction paths are used to provide the direction, sequence, and local topological changes of atomic cooperative motions. They can be obtained from existing trajectories or through the independent path generation process of this invention. Reference paths can be reused across components, but when the number, size, orientation, or reaction mechanism of dislocation loops changes, a new reference path corresponding to the target mechanism should be generated.

[0028] The reference reaction path is obtained through one or more of the following methods: resampling from a validated elastic band path; extracting from molecular dynamics trajectories and aligning them according to atomic identifiers; generating multiple dislocation loop states from a perfect body-centered cubic lattice and connecting them through a dislocation slip template; applying local cooperative displacement to the reaction core region and performing confined relaxation; and splicing together multiple candidate node structures after topological screening.

[0029] Furthermore, the generation of multiple dislocation loop states from a perfect body-centered cubic lattice includes: generating at least two interstitial dislocation loops with a first Burgers vector family and at least one product dislocation loop with a second Burgers vector family in the same periodic simulation box; the sum of the net number of interstitial atoms contained in the interstitial dislocation loops of the first Burgers vector family is equal to the net number of interstitial atoms contained in the product dislocation loop.

[0030] Furthermore, the dislocation slip template is used to: identify cluster atom strings that are parallel or approximately parallel to the dislocation loop slip direction; expand and sort the atom coordinates along the atom string direction; enumerate and cyclically permutate the atom identifiers within the atom string; construct a mapping score based on the total square displacement, the maximum single atom displacement, and the number of atoms exceeding the displacement threshold; retain candidate mappings whose mapping scores meet preset conditions; and select mappings that maintain atomic identity continuity and dislocation topological continuity through short-path pre-relaxation or short-step elastic band calculation.

[0031] S03, Set topology anchor points Topological anchors are placed at locations where there are discriminative changes in dislocation type, number of dislocations, closure state, or dislocation segment connectivity. Topological anchors refer to atomic structures that are significant in determining the reaction mechanism; not all topological anchors are necessarily local energy minima.

[0032] Each topological anchor point should be configured with at least the following: the Burgers vector family of the expected dislocations, the number of dislocations, the closed or open state, and the dislocation segment connection relationship. It can be further configured with: source structure number, dislocation line length range, defect atom number range, and Burgers vector identification tolerance.

[0033] Preferably, the Burgers vector family includes: 1 / 2 <111> , <100> and <110> At least one of them.

[0034] S04, Calibrate the lattice constant of the target material A body-centered cubic phase model was established for the target alloy composition. The zero-pressure lattice constant was obtained through joint relaxation of atomic coordinates and the simulation cell, and the reference reaction path was scaled according to the zero-pressure lattice constant. For different alloy compositions, the lattice constant was calibrated separately to reduce the average strain between the fixed reference geometry and the target composition.

[0035] S05. Establish a fixed mapping between atom identifiers and element types. For alloy systems, an element type sequence is generated according to the target number of atoms for each element. After the element type sequence is shuffled using a chemical random seed, it is mapped one-to-one with the atom identifier. All reference structures, topological anchors, and intermediate images share the same mapping, and element types must not be reallocated during cross-image file conversions.

[0036] For multiple candidate chemical random seeds, only relaxation of topological anchor points and dislocation topology identification are performed. Candidate chemical random seeds whose topological anchor points all satisfy the expected dislocation topology are determined as chemical random seeds used for formal reaction path calculation.

[0037] S06. Adjusting the local elemental concentration in the reaction core region (optional step) While keeping the global number of atoms of each element constant, the local element concentration in the reaction core region is adjusted; the reaction core region is determined based on at least one of the following: the maximum periodic minimum mirror displacement of the atom in the complete reference reaction path, the local structural disorder, or the distance from the atom to the dislocation line, wherein the local structural disorder is characterized by at least one of the following: centrosymmetry parameter, common nearest neighbor analysis results, coordination number deviation, or non-body-centered cubic atom label; by exchanging element types between atoms in the reaction core region and far-field atoms, the core region achieves the preset local composition.

[0038] like Figure 2 As shown, for the coordinate difference of atom i in reference frame k and reference frame k+1, the periodic minimum mirror displacement can be expressed as:

[0039] in, Let be the periodic minimum mirror displacement component of atom i from reference frame k to reference frame k+1 in the α direction. and Let be the coordinates of atom i in the α direction at reference frame k and reference frame k+1, respectively. Let be the period length of the simulation box in the α direction. This means taking the nearest integer from each of the dimensionless numbers within the parentheses. The three coordinate components together form the periodic minimum mirror displacement vector of atom i. The aforementioned periodic minimum mirror displacement component can clearly handle periodic reversals and avoid apparent excessive displacements when atoms cross periodic boundaries.

[0040] The reaction core region can be defined by the maximum periodic minimum mirror displacement of atoms in the complete reference trajectory:

[0041] in, Let i be the set of atom numbers in the core reaction region; i is the atom number. This represents the total number of atoms in the system. A set of reference frame indexes for the complete reference reaction path; Let be the periodic minimum mirror displacement vector of atom i from the initial reference frame 0 to the reference frame k, and let be determined according to the minimum mirror rule described above. and calculate; This represents the Euclidean second norm, i.e., the magnitude of the displacement vector; The preset core displacement threshold, and >0. If the displacement magnitude of an atom in any reference frame reaches or exceeds 0. Then the atom is assigned to the reaction core region. The threshold can be determined based on the nearest neighbor distance, the inflection point of the complete path displacement distribution, or a preset statistical quantile. When comparing different material compositions, local components, or chemical random seeds, it is preferable to use a consistent threshold determination rule to reduce the impact of differences in core area division on the comparison results.

[0042] S07, Relax and Filter Topological Anchor Points Atomic coordinate relaxation is performed on each topological anchor point, and the Burgers vector, quantity, closure, node, and line length of the dislocation are obtained using dislocation decimation or equivalent topological identification methods. For random alloys, topological anchor point relaxation can be performed on multiple candidate chemical random seeds first, eliminating seeds with any unstable topological anchor point.

[0043] S08. Divide the reaction into stages. The complete reaction is divided into at least one reaction segment based on the topological anchor points. Each reaction segment is configured with start and end anchor points, reference structure range, number of replicas, and calculation parameters.

[0044] S09. Perform periodic minimum mirror resampling along the reference reaction path. For adjacent reference structures, such as when generating a resampled image between reference structure k and reference structure k+1, first perform periodic minimum mirror correction on the coordinate difference with the same atom identifier, and then interpolate the corrected coordinate difference according to the local path score; the number of target replicas may be different from the number of reference structures, and may be based on the non-uniform distribution of cumulative atom displacement or local path curvature.

[0045] S10, Propagation Topology Anchor Point Correction The periodic minimum mirror coordinate corrections of the relaxed starting and ending topological anchors relative to the corresponding reference structures are calculated respectively. The coordinate corrections are then continuously propagated according to the path fraction of the intermediate image in the reaction segment, so that the segment endpoints are strictly equal to the relaxed topological anchors, while reducing coordinate abrupt changes near the endpoints.

[0046] S11. Implement restricted pre-relaxation on a per-image basis. For non-endpoint images, in-situ constraints from strong to weak and maximum single-step displacement from small to large are applied sequentially for multi-stage relaxation. Abnormal short distances and high-energy contacts are eliminated first, and then the local structural degrees of freedom are gradually released to maintain the target response channel.

[0047] Pre-relaxation includes at least two constraint stages, where the in-situ constraint strength of the later constraint stage is less than that of the earlier constraint stage, and the maximum single-step atomic displacement allowed in the later constraint stage is not less than that allowed in the earlier constraint stage; the endpoint image uses the relaxed topological anchor point.

[0048] S12, Execution Path Quality Check The path quality check includes: the minimum atomic spacing of each image is not less than a preset distance threshold; the root mean square of atomic displacements of adjacent images is not greater than a preset root mean square threshold; the maximum single atomic displacement of adjacent images is not greater than a preset displacement threshold; the atomic identifier set, element type array, and periodic simulation box of each image are consistent; and the dislocation topology of the preset topological anchor point meets the configuration requirements. When any indicator fails to meet the requirements, an intermediate image is added to the corresponding segment, the pre-relaxation step size is reduced, the single cooperative displacement is reduced, the atomic identity mapping is modified, or a new topological anchor point is inserted.

[0049] S13, Perform segmented elastic band calculation For each reaction segment that passes the inspection, the elastic band transition path calculation is performed. The number of replicas, elastic band spring constant, force tolerance, number of iteration steps, atomic structure output interval and climbing image parameters can be set for each reaction segment. The calculation is performed in parallel on a parallel computing platform or sequentially according to the anchor point dependency.

[0050] S14. Select a recoverable checkpoint and merge the energy. The target checkpoint is selected only from checkpoints where both the energy records of each image and the atomic structure output of all copies exist simultaneously; the energy zero points of each reaction segment are unified and the reaction segments are merged, the energy difference between the segment endpoints is accumulated, and duplicate anchor points of adjacent segments are deleted to obtain the complete energy path, forward energy barrier, reverse energy barrier, and reaction energy. Figure 3As shown, the energy of the starting topological anchor point of the first reaction segment is taken as the unified energy zero point. The energy bias of each reaction segment is accumulated according to the energy correspondence between the ending topological anchor point of the previous reaction segment and the starting topological anchor point of the next reaction segment, and the duplicate topological anchor points of adjacent reaction segments are deleted. The overall forward energy barrier is the difference between the maximum value of the merged energy path and the initial state energy, the reverse energy barrier is the difference between the maximum value and the final state energy, and the reaction energy is the difference between the final state energy and the initial state energy.

[0051] The target checkpoint satisfies the following conditions: the checkpoint step number is aligned with the atomic structure output interval, all replicas have corresponding atomic structure outputs, and the checkpoint data fields are complete. Among the candidate checkpoints that meet the aforementioned conditions, the target checkpoint is selected based on at least one of the following: maximum replica force, maximum atomic force, energy change rate, and dislocation topological stability.

[0052] S15. Perform dislocation topology final check and output results. Dislocation topology identification and defect counting are performed on the initial state, node state, closed state, final state, local energy peak and other key images in the merging path; when the results meet the expected topology and defect conservation requirements, the complete atomic trajectory, image-by-image energy, path force, energy barrier, reaction energy, key frame and verification report are output.

[0053] 2. General process of the present invention Users implement this invention using structural data files, configuration files, and automated programs. The configuration file includes the system name, atomic model, reference path source, lattice parameters, element symbols and precise atom counts, interatomic interaction model, topological anchor points, reaction segmentation, pre-relaxation parameters, path mass thresholds, elastic band parameters, parallel computing parameters, and output fields.

[0054] After reading all atomic structures, the program sorts them by atomic identifier and checks the total number of atoms, identifier set, periodicity simulation box, and element type array for each structure. If any structure has missing identifiers, duplicate identifiers, discontinuous identifiers, element type drift, or inconsistent simulation boxes, the program stops further calculations and outputs the error location.

[0055] For alloy systems, the program can first perform lattice constant calibration on multiple chemical random seeds in a smaller bulk model to obtain the average zero-pressure lattice constant; alternatively, it can directly calibrate the formal-sized bulk model. The reference path coordinates are scaled according to the lattice constant ratio, while maintaining the atomic identifiers and topological anchor indexes.

[0056] After minimizing the energy at each topological anchor point, a dislocation extraction algorithm is used to identify dislocation segments. For body-centered cubic lattices, the identified Burgers vectors can be classified as 1 / 2. <111> , <100> and <110> The anchor point is classified into groups, and its closure is determined based on whether the first and last nodes of the dislocation segment coincide. If there are unconfigured additional dislocation segments, the expected number of dislocations is incorrect, the line length exceeds the allowable range, or the node connection relationship is incorrect, the anchor point is marked as invalid.

[0057] Resampling is performed on the reference structure intervals between effective anchor points. Resampling locations can be uniformly set according to the reference structure sequence number, or non-uniformly set according to cumulative atomic displacement, local path curvature, maximum single-atom displacement, or topological change density. The replica count is increased in regions of intense reaction and decreased in regions of gradual structural change.

[0058] The intermediate image pre-relaxation can employ three in-situ constraint stages: high, medium, and low. For example, the constraint strength can be selected successively at the order of 50, 10, and 2 eV / Ų, and the maximum single-step atomic displacement can be selected successively at the order of 0.002, 0.005, and 0.010 Å. The above values ​​are merely examples and can be adjusted according to the material potential function stiffness, the total number of atoms, and the size of the dislocation loops.

[0059] Before the formal elastic band calculation, the program calculates the minimum atomic spacing, RMS displacement of adjacent images, maximum single-atom displacement, and energy mutation for each image, and verifies the atom identifiers, element type arrays, simulation boxes, and topological anchors. When anomalies are detected, the program prioritizes modifying local paths, adding copies, or changing identity mappings, rather than simply increasing the elastic band iteration steps.

[0060] Each reaction segment can run independently on a parallel computing platform. Each replica uses one or more computing processes, and the reaction segments can be executed in parallel or sequentially according to the start and end anchor point dependencies. The atomic structure of all replicas is synchronously saved every preset number of steps, and the maximum replica force, maximum atomic force, segment forward and reverse energy barriers, reaction coordinates, and energy of each replica are recorded in the log.

[0061] 3. Independent Reference Path Generation Method When no directly usable parent path exists, reaction paths can be independently generated from a perfect body-centered cubic lattice. First, the initial reaction state, candidate nodal states, and final reaction state are generated under the same simulation box and the same net defect number. All states are relaxed under no permanent constraints and filtered by dislocation topology and defect counting.

[0062] For a single 1 / 2 <111> For interstitial dislocation loops, the two endpoints of the loop, when moved one lattice period along the Burgers vector direction, should be generated from the same perfect lattice, rather than rigidly translating the entire set of initially added interstitial atom identifiers. The program identifies cluster atom strings parallel to the Burgers vector, expands and sorts the atoms along the atom string direction, enumerates ordered cyclic identity permutations, and selects candidate identity mappings based on mapping scores.

[0063] For each candidate identity mapping, a short path is generated, and geometric checks, restricted pre-relaxation, and short-step elastic band smoke calculations are performed sequentially. Candidates are selected based on the following conditions: continuous atomic identifiers, controlled maximum single-atom displacement, dislocation loop center moving along the target direction, identical initial and final dislocation topologies, and no unexpected dislocation vanishing or additional defects appearing in the intermediate images. This yields a reusable single-loop migration template.

[0064] During the weak interaction phase of the two-ring system, two single-ring migration templates can be applied alternately or simultaneously to bring the two rings closer together cycle by cycle along their respective slip directions. After each migration cycle, unconstrained relaxation, dislocation topology identification, defect counting, minimum dislocation line distance between the two rings, and interaction energy calculation are performed.

[0065] When the minimum distance between dislocation lines is lower than the threshold, non-body-centered cubic core regions begin to overlap, defect clusters begin to merge, or the single-loop template cannot maintain two independent closed dislocation loops, the single-loop template is stopped, the two dislocation cores are merged into the same active region, and the generation of strongly coupled paths begins.

[0066] Strongly coupled paths can generate candidate branches such as synchronous propulsion, first dislocation loop priority, second dislocation loop priority, and alternating crowdion propulsion; the propulsion amount adopts the fractional reaction coordinates and atomic displacement fields in the single-loop migration template, rather than directly applying fractional Burgers vector rigid translation to the dislocation loop atom set.

[0067] For candidate node states, the program generates the next target structure through local cooperative displacement, local shearing, atomic string propagation, and hierarchical spring constraints. For each target structure, a new constraint reference position is established, and strong, medium, and weak constraint relaxations are performed sequentially, ultimately releasing the constraints. For the structure after constraint release, dislocation topology identification is performed, retaining only segments with expected open dislocations. <100> Candidates for embryonic or closed product rings.

[0068] From nodal states to product dislocation loops, different... <100> Multiple branches are considered, including the embryonic initiation location, closure direction, and atomic layer advancement sequence. Local path scoring, short-range elastic band calculation, and topology checking are performed on each branch, and the branch with lower energy and path force and topological continuity is selected as the formal path.

[0069] Example 1: Two 1 / 2 portions of pure tungsten <111> Dislocation loop <100> Dislocation loop transformation This example uses a body-centered cubic tungsten periodic model containing 9863 atoms. A 17×17×17 body-centered cubic conventional unit cell contains 9826 lattice atoms; adding 37 net interstitial atoms results in a 9863-atom model. Two initial 1 / 2 <111> Interstitial dislocation loops contain approximately 37 self-interstitial atoms in total, ultimately <100> The dislocation loop contains approximately 37 interstitial atoms.

[0070] Complete reactions are classified into proximity or contact, junction closure, and... <100> The ring length consists of three reaction segments with replica counts of 25, 33, and 13 respectively; after removing duplicate anchor points from adjacent segments, a 69-frame merged path is obtained. For example... Figure 4 As shown, the initial anchor point contains two closed 1 / 2 <111> The ring, with its node anchor point containing two open 1 / 2 rings, <111> Dislocation segment and an open <100> Dislocation segments, closed anchor points, and final anchor points all contain a closed... <100> ring.

[0071] In a regular-NEB example calculation, the overall positive energy barrier is obtained from a low-path force synchronization checkpoint with a complete replica structure output. The synchronization checkpoint refers to an iteration step during the elastic band calculation that simultaneously saves path energy data and all replica atomic structures; iteration steps with only log energy but lacking corresponding atomic structures are not considered as final result checkpoints. This invention's method can generate and reconstruct complete energy paths and is not intended to limit the range of material properties; formal material conclusions can be determined after further climbing image force convergence and potential function cross-validation.

[0072] Example 2: Equivalent atomic ratio WTaCrV multi-component alloy The atomic identity-preserving geometric path of Example 1 is mapped to an equiatomic ratio WTaCrV multi-component alloy. The target lattice constant is approximately 3.0769455 Å, the period repetition number is 17×17×17, and the simulation box side length is approximately 52.3081 Å. Of the 9863 atoms, there are 2466 W, 2466 Ta, and 2465 V atoms.

[0073] For multiple chemical random seeds, fixed atom identifier-element mappings are generated. Independent relaxation and dislocation topology identification are performed only on four topological anchor points: initial, node, closed, and final state. The initial anchor point of the seed selected in the formal path identifies two closed 1 / 2... <111> Ring; node anchor points identified two open 1 / 2 <111> Section and an open <100> The segment; closed anchor point and final state anchor point respectively identified a closed segment. <100> ring.

[0074] The minimum interatomic spacing of the three reaction segments is greater than approximately 2.13 Å, and the maximum RMS shift between adjacent images is less than approximately 0.085 Å, indicating that no significant atomic overlap occurred after composition mapping, anchor point correction propagation, and image-by-image restricted pre-relaxation, and the path remained continuous. The method of this invention can separate local chemical environment differences under conditions of consistent reaction topology and atomic identity. The above values ​​are example results and do not limit the statistical performance of the alloy.

[0075] Dislocation decimation final inspection is performed on the selected 69 frames of atomic trajectories. Keyframe 0 maintains two independent closed 1 / 2 frames. <111> Ring; two open 1 / 2 loops appear in keyframe 24. <111> Section and an open <100> Segment; keyframes 56 and 68 both identified a closed segment. <100> The loop is used to verify that the energy path corresponds to a predetermined dislocation topological transformation.

[0076] Example 3: The Influence of Global or Local Chromium Content When studying the global chromium content, the target number of chromium atoms in the entire simulation box is changed, and the number of atoms of other elements is adjusted accordingly to keep the sum of the counts of all elements equal to the total number of atoms. Each global component undergoes zero-pressure lattice constant calibration, screening of multiple chemical random seed anchor points, and calculation of the complete segmented elastic band. Different components use the same reaction geometry, anchor point definition, segmented replica number, and synchronous checkpoint selection rules.

[0077] like Figure 5 As shown, when studying local chromium content, the global element count and basic chemical random seed are kept unchanged. The maximum and minimum mirror displacements of each atom relative to the reference initial state are calculated throughout the entire path, and atoms exceeding the threshold are defined as reaction core atoms. Different element atoms are selected from the reaction core region and the far field, and the element types are exchanged until the percentage of chromium atoms in the reaction core region reaches the target value. This pairing exchange does not change the atom identifier, coordinates, or global element count. All topological anchor relaxation and topological verification are re-performed for each local composition level to avoid local enrichment leading to premature reaction of the initial dislocation loop or ring opening in the final state. Only paired systems with consistent topology are used for comparison to distinguish between local composition effects and path topology changes.

[0078] Example 4: Constructing 18-SiA and 19-SiA bicyclic reaction pathways independently from a perfect iron lattice. This example does not rely on existing tungsten system trajectories or prefabricated parent paths, but independently constructs two 1 / 2 tungsten lattices from a perfect body-centered cubic iron lattice. <111> Interstitial dislocation circumferentially <100> The reaction pathway of interstitial dislocation loops. The first initial dislocation loop contains 18 net interstitial atoms, the second initial dislocation loop contains 19 net interstitial atoms, and the final state... <100> The dislocation loop contains 37 net interstitial atoms, satisfying the defect number conservation rule of 18+19=37.

[0079] Select the first Burgers vector b1=a0 / 2

[111] and the second Burgers vector b2=a0 / 2[1 1 1], whose vector sum is a0

[100] , is used to generate the target

[100] type product ring. This vector relationship is used to screen crystallographically permissible reaction combinations and is not directly equivalent to the reaction necessarily occurring.

[0080] A perfect iron supercell was constructed using a 25×25×25 body-centered cubic unit cell, resulting in a perfect lattice atomic number of 31,250. After adding 37 net interstitial atoms, the total atomic number reached 31,287. The effect of periodic mirroring was further examined using different supercell sizes. The lattice constant, single interstitial configuration, single interstitial migration, and half-scale values ​​of 18-SIA and 19-SIA were verified for the selected potential functions. <111> Ring stability and 37-SIA <100> Ring stability.

[0081] The A and B endpoints of 18-SIA and 19-SIA single loops are generated and moved one cycle along their respective Burgers vector directions. Single loop migration paths of 11 to 15 images are constructed using the ordered cyclic identity mapping of cluster atomic strings. Short path pre-relaxation and elastic band calculations are performed on the two single loops respectively, and the atomic displacement fields under fractional reaction coordinates are extracted to form two sets of single loop migration templates.

[0082] Targeting candidate reaction centers, the initial center distance, left and right positions, lateral dislocations, and atomic layer phases of the two dislocation loops are scanned. Each candidate double-loop initial state undergoes complete unconstrained relaxation, selecting loops that retain two independent closed loops after relaxation. <111> The structure with the smallest separation distance is taken as the initial state.

[0083] During the weak interaction phase, single-ring migration templates are applied alternately to bring the 18-SIA and 19-SIA rings closer together along their respective slip directions. After each slip cycle, unconstrained relaxation, dislocation extraction, Wigner-Seitz defect counting, and calculations of the distance between the ring center and the minimum dislocation line between the two rings are performed. Two closed half-circuit templates are maintained before the initial contact. <111> The ring, net gap number 37, and the overall distance between the two rings decreased.

[0084] Once the dislocation core regions begin to overlap, strongly coupled candidate paths are generated, including synchronous propagation, 18-SIA ring priority, 19-SIA ring priority, and alternating crowding propagation. Nodal states are searched through local cooperative displacement and progressively weakened constraints, and further generated... <100> Multiple branches of embryo formation, closure, and growth. Each branch performs atomic identity consistency checks, path quality checks, frame-by-frame dislocation topology classification, and local adaptive refinement.

[0085] Elastic band calculations are performed separately for the selected approaching segments, node-forming segments, closed segments, and long segments. If necessary, regular-NEB is performed first, followed by climbing image elastic band calculations for the locally highest energy segments. Finally, the energy paths are merged, and keyframes corresponding to the control energy barriers are output to distinguish between single-loop migration, double-loop capture, node formation, and... <100> Control steps in structural transformation.

[0086] like Figure 6 As shown, initial state, reaction intermediate state, and final state keyframes can be selected from the independently constructed iron system path for dislocation extraction analysis to verify the two 1 / 2 <111> Approach, local connectivity and dislocation loops <100> The process of product structure formation. For example... Figure 7 As shown, the segmented calculation and energy merging procedure can output example energy paths for regular-NEB structures corresponding to complete atomic structures. The numerical values ​​illustrated are used to explain the calculation process and result restoration method; quantitative conclusions on materials should also be determined by combining more rigorous path force convergence, climbing image calculation, supercell size checking, and potential function cross-validation.

[0087] Example 5: Reaction networks with three or more dislocation loops When the system under study contains three or more dislocation loops, topological anchors can be set at each contact, node generation, local closure, branch competition, or merging point. For example, the initial anchors can be configured with three closed 1 / 2 loops. <111> The ring, with the first node anchor point configured with two open 1 / 2 rings. <111> Section and an open <100> The second node anchor point is further configured with a third dislocation loop and the existing one. <100> The connection relationship of the segments, and the final anchor point is configured with one or more closed product dislocation loops.

[0088] For systems where the number, size, orientation, or reaction sequence of dislocation loops are changed, a new reference path is generated. Subsequently, the same atomic identity verification, anchor relaxation, minimum image resampling, image-by-image pre-relaxation, segmented elastic band calculation, synchronous checkpoint selection, energy merging, and topology final check are performed as in the previous example.

[0089] Example 2 like Figure 8 As shown, this embodiment provides a calculation system for dislocation loop reaction paths and energy barriers in body-centered cubic materials, including: an atomic model and reference path generation module, an atomic identification and composition mapping module, a topological anchor point setting and verification module, a minimum mirror resampling module, an intermediate image pre-relaxation module, a segmented elastic band calculation module, a synchronous checkpoint selection and energy merging module, and a dislocation topology final check and result output module. The atomic model and reference path generation module is used to establish a periodic atomic model of the body-centered cubic material, obtain a reference reaction path that preserves atomic identity, and set topological anchor points in the reference reaction path. The atomic identifier and composition mapping module is used to establish a fixed mapping between atomic identifiers and element types in the alloy system, and to apply the fixed mapping to all topological anchors and intermediate images; The topology anchor setting and verification module is used to perform atomic relaxation and dislocation topology identification on the topology anchors respectively, and retain only the topology anchors that meet the expected dislocation topology. The minimum mirror resampling module is used to divide the adjacent topological anchor points into reaction segments, resample the intermediate image along the reference reaction path according to the periodic minimum mirror displacement, and propagate the coordinate correction of the relaxed topological anchor points relative to the corresponding reference structure to the intermediate image. The intermediate image pre-relaxation module is used to pre-relax the intermediate image by gradually reducing the constraint strength, and to perform path quality checks. The segmented elastic band calculation module is used to perform elastic band transition path calculation for each reaction segment that has passed the inspection. The synchronous checkpoint selection and energy merging module is used to select target checkpoints only from synchronous checkpoints that simultaneously have energy records of each image and output of all copy atomic structures, unify the energy zero points of each reaction segment and merge each reaction segment to determine at least one of the overall forward energy barrier, reverse energy barrier and reaction energy. The dislocation topology final inspection and result output module is used to perform dislocation topology final inspection on the merged reaction path and output the atomic reaction trajectory and energy results.

[0090] 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 method for calculating dislocation loop reaction paths and energy barriers in body-centered cubic materials 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 users can view the calculation status and input control commands.

[0091] 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 method for calculating dislocation loop reaction paths and energy barriers in body-centered cubic materials 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.

[0092] 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 reaction pathway and energy barrier of dislocation loops in body-centered cubic materials, characterized in that, include: Establish a periodic atomic model of body-centered cubic materials, obtain reference reaction paths that preserve atomic identity, and set topological anchor points in the reference reaction paths; Atomic relaxation and dislocation topology identification are performed on the topological anchor points respectively, and only the topological anchor points that satisfy the expected dislocation topology are retained; For alloy systems, a fixed mapping between atomic identifiers and element types is established, and this fixed mapping is applied to all topological anchors and intermediate images; The adjacent topological anchor points are divided into reaction segments. The intermediate image is resampled along the reference reaction path according to the periodic minimum mirror displacement, and the coordinate correction of the relaxed topological anchor points relative to the corresponding reference structure is propagated to the intermediate image. The intermediate images are pre-relaxed with gradually decreasing constraint strength, and path quality checks are performed. Perform elastic band transition path calculations on each reaction segment that passes the inspection; Select the target checkpoint from only the synchronous checkpoints that simultaneously have the energy records of each image and the output of the atomic structure of all copies, unify the energy zero points of each reaction segment and merge each reaction segment, and determine at least one of the overall forward energy barrier, reverse energy barrier and reaction energy. Perform dislocation topology final inspection on the merged reaction path and output the atomic reaction trajectory and energy results.

2. The method for calculating the dislocation loop reaction path and energy barrier of body-centered cubic materials according to claim 1, characterized in that, The reference reaction path is obtained by resampling from a verified elastic band path, or by extracting from a molecular dynamics trajectory and aligning it according to atomic identifiers, or by generating multiple dislocation loop states from a perfect body-centered cubic lattice and connecting them through a dislocation slip template, or by applying local cooperative displacement to the reaction core region and performing restricted relaxation, or by performing topological screening on multiple candidate node structures and then splicing them together.

3. The method for calculating the dislocation loop reaction path and energy barrier of body-centered cubic materials according to claim 1, characterized in that, The topological anchor point is configured with at least: the Burgers vector family of the expected dislocations, the number of dislocations, the closed or open state, and the connection relationship of dislocation segments.

4. The method for calculating the dislocation loop reaction path and energy barrier of body-centered cubic materials according to claim 3, characterized in that, The method for dislocation topology identification is as follows: the identified dislocation segments are grouped according to the Burgers vector family of the expected dislocation, the closed state, and the connection relationship of the dislocation nodes, and the grouping results are compared with the configuration of the corresponding topological anchor points.

5. The method for calculating the dislocation loop reaction path and energy barrier of body-centered cubic materials according to claim 1, characterized in that, The method for establishing a fixed mapping between atomic identifiers and element types is as follows: generate an element type sequence according to the target number of atoms of each element, and then shuffle the element type sequence using a chemical random seed to correspond it one-to-one with the atomic identifier.

6. The method for calculating the reaction pathway and energy barrier of dislocation loops in body-centered cubic materials according to claim 1, characterized in that, The pre-relaxation includes at least two constraint stages, where the in-situ constraint strength of the later constraint stage is less than that of the earlier constraint stage, and the maximum single-step atomic displacement allowed in the later constraint stage is not less than that allowed in the earlier constraint stage; the endpoint image uses the relaxed topological anchor point.

7. The method for calculating the dislocation loop reaction path and energy barrier of body-centered cubic materials according to claim 1, characterized in that, The path quality check includes: the minimum atomic spacing of each image is not less than a preset distance threshold; the root mean square of atomic displacement of adjacent images is not greater than a preset root mean square threshold; the maximum single atomic displacement of adjacent images is not greater than a preset displacement threshold; the atomic identifier set, element type array and periodic simulation box of each image are consistent; and the dislocation topology of the preset topological anchor point meets the configuration requirements.

8. The method for calculating the dislocation loop reaction path and energy barrier of body-centered cubic materials according to claim 1, characterized in that, The method for performing elastic band transition path calculation on each reaction segment that has passed the inspection is as follows: Each reaction segment is configured with the number of replicas, elastic band spring constant, force tolerance, number of iteration steps, atomic structure output interval, and climbing image parameters, and is run in parallel on a parallel computing platform or sequentially according to the anchor point dependency.

9. The method for calculating the dislocation loop reaction pathway and energy barrier of body-centered cubic materials according to claim 1, characterized in that, The target checkpoint satisfies the following conditions: the checkpoint step number is aligned with the atomic structure output interval, all replicas have corresponding atomic structure outputs, and the checkpoint data fields are complete. Among the candidate checkpoints that meet the aforementioned conditions, the target checkpoint is selected based on at least one of the following: maximum replica force, maximum atomic force, energy change rate, and dislocation topological stability.

10. A system for calculating dislocation loop reaction pathways and energy barriers in body-centered cubic materials, characterized in that, include: The atomic model and reference path generation module is used to build a periodic atomic model of a body-centered cubic material, obtain reference reaction paths that preserve atomic identity, and set topological anchor points in the reference reaction paths. The Atom Identifier and Composition Mapping Module is used to establish a fixed mapping between atom identifiers and element types in the alloy system, and to apply the fixed mapping to all topological anchors and intermediate images; The topology anchor point setting and verification module is used to perform atomic relaxation and dislocation topology identification on topology anchor points respectively, and retain only the topology anchor points that meet the expected dislocation topology. The minimum mirror resampling module is used to divide the area between adjacent topological anchors into reaction segments, resample the intermediate image along the reference reaction path according to the periodic minimum mirror displacement, and propagate the coordinate correction of the relaxed topological anchors relative to the corresponding reference structure to the intermediate image. The intermediate image pre-relaxation module is used to pre-relax the intermediate image by gradually reducing the constraint strength, and to perform path quality checks. The segmented elastic band calculation module is used to perform elastic band transition path calculations on each reaction segment that has passed the inspection. The synchronous checkpoint selection and energy merging module is used to select target checkpoints only from synchronous checkpoints that simultaneously have energy records for each image and outputs of all copied atomic structures, unify the energy zeros of each reaction segment, and merge each reaction segment to determine at least one of the overall forward energy barrier, reverse energy barrier, and reaction energy; and... The dislocation topology final inspection and result output module is used to perform dislocation topology final inspection on the merged reaction path and output the atomic reaction trajectory and energy results.

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