Optimization method of vacancy defect structure at interface

Abstract

The present invention discloses a method for optimizing vacancy-type defect structures at interfaces. The main steps include: obtaining the lattice position and affected region with minimum vacancy formation energy, deleting atoms in the region that may be affected by vacancy occupation; dividing the affected region after the atoms are deleted into a grid; inserting atoms into the divided grid; optimizing the occupied positions of the inserted atoms on the grid; and relaxing the optimized occupied positions to obtain the vacancy ground-state atomic structure. This optimization method does not restrict the atomic lattice position and can search for vacancy structures at all positions in a certain spatial region. It can effectively access the potential energy surface characteristics near the interface and obtain the ground-state structure of the vacancy.

Description

Technical Field

[0001] The present invention belongs to the technical field of nuclear material radiation damage simulation, and in particular relates to an optimization method for a quasi-full real space vacancy defect structure at an interface. Background Art

[0002] Radiation damage to nuclear materials refers to the process in which high-energy particles irradiate the material, producing a series of defects. Radiation damage to nuclear materials is one of the key issues affecting the safety and stability of nuclear energy devices. Since it is difficult to carry out a large number of irradiation experiments to evaluate the damage mechanism of nuclear materials, relevant theoretical simulations are crucial.

[0003] When materials are irradiated with high-energy particles, vacancy-type defects are generated. Therefore, obtaining their ground-state structure is crucial for understanding the microstructural evolution of radiation damage. Generally speaking, vacancies in bulk materials often occupy normal lattice positions (after static relaxation, only small strains are generated). These lattice positions are ideal approximations of their potential locations during structural optimization. However, at interfaces, due to the complex strain field, the ground-state position of vacancies often deviates significantly from the normal lattice position, meaning that atoms near the defect rearrange themselves. Furthermore, due to the anisotropy of the spatial structure at the interface, the potential energy surface often exhibits numerous energy minima, resulting in a significant energy barrier between the normal lattice position and the ground-state position. Therefore, structural optimization is necessary to obtain the ground-state structure.

[0004] Currently, when people use static calculations for structural optimization, they usually generate an initial structure with vacancies according to the lattice position. Since static calculations cannot automatically overcome energy barriers, they can only search for vacancy structures at a spatially characteristic atomic lattice position, making it difficult to optimize to the true ground state structure. Summary of the Invention

[0005] In light of this, the present invention provides a method for optimizing vacancy-type defect structures at interfaces. This method removes atoms from the region near the introduced defect, discretizes the interface space, and reoptimizes the positions of these atoms, taking into account certain lattice symmetries. This optimization method is not restricted by atomic lattice positions and can search for vacancy structures at all locations within a given spatial region. This method effectively accesses the potential energy surface features near the interface and obtains the ground-state structure of the vacancy.

[0006] In order to achieve the above object, the present invention adopts the following technical solutions:

[0007] The present invention provides a method for optimizing a vacancy-type defect structure at an interface, comprising the following steps:

[0008] S1. Obtain the lattice position [x0, y0, z0] and the affected region with the minimum vacancy formation energy. The affected region is the region with the lattice position [x0, y0, z0] as the center and the influence radius of each direction of its three-dimensional coordinates rx, ry, and rz respectively; at the same time, delete the regions in the affected region with coordinates satisfying |x-x0|<rx, |y-y0|<ry, |z-z0|<rz atoms[x, y, z];

[0009] S2, dividing the affected area after the atoms are deleted in step S1 into a grid, wherein the grid point coordinates are within the boundary range of the affected area;

[0010] S3, inserting atoms with a number of atoms nA1 into the grid divided in step S2, wherein nA1=nA-nV, nA is the number of atoms deleted in step S1, and nV is the number of vacancies to be generated in the affected area after deleting the atoms;

[0011] S4, optimizing the occupied positions of the inserted atoms in step S3 on the grid;

[0012] S5. Relax the occupied positions optimized in step S4 to obtain the vacancy ground state atomic structure.

[0013] In a further solution, in step S1, the lattice position of the minimum vacancy formation energy is obtained by selecting lattice points within 1 nm from the grain boundary with the crystal interface as the center, and then placing a vacancy at each position, and then relaxing the system using a static calculation method, and comparing the vacancy formation energy at each lattice point after relaxation, thereby obtaining the lattice position of the minimum vacancy formation energy.

[0014] In a further solution, in step S1, the values ​​of the impact radii rx, ry, and rz are determined so that the number of deleted atoms nA is on the order of 100.

[0015] In a further embodiment, in step S1, the typical value of the influence radius rx, ry, and rz is 5Å.

[0016] In a further solution, in step S2, the grid intervals in each direction within the affected area are dx, dy, and dz, respectively, and the boundary values ​​in each direction of the area are [lx, hx], [ly, hy], and [lz, hz], respectively. Then, the grid point coordinates of the divided grid are [lx+i×dx, ly+j×dy, lz+k×dz], where i, j, and k are integers whose values ​​are taken so that the grid point coordinates are within the boundary range of the affected area.

[0017] In a further solution, in step S3, if nV<0, it indicates that the inserted defect is an interstitial atom defect.

[0018] In a further solution, in step S4, a differential evolution method is used to optimize the occupied positions of the inserted atoms on the grid. The optimization problem is to find nA1 positions in the grid divided in step S2 so that the system energy is minimized.

[0019] In a further solution, the specific operation of step S5 is: inserting atoms according to the nA1 atomic positions optimized in step S4, and then statically optimizing the system architecture using the conjugate gradient method.

[0020] The beneficial effects of the present invention are:

[0021] By removing atoms surrounding vacancies at the interface, taking into account certain lattice symmetries, and then discretizing the interface space, and then re-optimizing the positions of these atoms, it is possible to find the ground state of the structure that is severely distorted after the introduction of the vacancy. Compared with existing simulation methods that use lattice positions as the initial occupation position of the vacancy, this method takes into account the significant positional rearrangement of atoms around the vacancy, and can find configurations with lower defect energy. BRIEF DESCRIPTION OF THE DRAWINGS

[0022] Figure 1 This is a flow chart of the main steps of a method for optimizing vacancy-type defect structures at interfaces in a preferred embodiment of the present invention;

[0023] Figure 2 This is a flow chart of an optimization algorithm for vacancy-type defect structures at interfaces in a preferred embodiment of the present invention;

[0024] Figure 3 To adopt Figure 2 The single vacancy and divacancy ground state structures at the iron Ʃ5(310) /

[001] grain boundary obtained by the algorithm and the point structures of single vacancy and divacancy obtained by the general static calculation method, among which, Figure 3 The black circles in the middle represent the divided grid positions, the gray squares represent the inserted atomic positions, and the other small balls represent atoms. DETAILED DESCRIPTION

[0025] The embodiments of the present invention are described in detail below. The embodiments described below with reference to the accompanying drawings are exemplary and are only used to explain the present invention, and should not be understood as limiting the present invention.

[0026] Unless otherwise defined, all technical and scientific terms used herein have the same meaning as those commonly understood by those skilled in the art of the present invention. The terms used in the specification of the present invention herein are only for the purpose of describing specific embodiments and are not intended to limit the present invention.

[0027] In a preferred embodiment of the present invention, a method for optimizing the vacancy defect structure at the interface is disclosed. The specific process can be combined with Figure 1 As shown in , the following steps are included:

[0028] S1. Delete atoms in the region potentially affected by vacancy occupation. The specific deletion steps are as follows: First, determine the affected region based on the possible vacancy occupation positions, and define a range of distances from the center as the affected region. Specifically, the lattice position with the minimum vacancy formation energy is initially determined based on the MS results of the vacancy formation energy, with its coordinates labeled [x0, y0, z0]. The lattice position with the minimum vacancy formation energy is obtained using the molecular statics (MS) method. Specifically, with the crystal interface as the center, select lattice points within 1 nm of the grain boundary. Then, place a vacancy at each position (i.e., remove the corresponding atom at that lattice point). The system is then relaxed using the MS method. The vacancy formation energies at each lattice point after relaxation are compared to obtain the lattice position with the minimum vacancy formation energy. The affected region is then determined with the lattice position [x0, y0, z0] as the center. Specifically, the affected region is the region centered at the lattice position [x0, y0, z0] with the influence radius rx, ry, and rz in each direction of the three-dimensional coordinates, respectively. Finally, delete the atoms near the lattice position [x0, y0, z0]. The coordinates of the deleted atoms are marked as [x, y, z]. When the atomic coordinates meet |x-x0|<rx, |y-y0|<ry, |z-z0|<rz , then delete. In this step, the total number of atoms deleted is recorded as nA.

[0029] Among them, the values ​​of the influencing radii rx, ry, and rz can be adjusted according to the optimization performance and optimization requirements of the subsequent method. For example, if the differential evolution method is subsequently adopted, on the one hand, rx, ry, and rz are too large, which will lead to nA being too large, exceeding the optimization ability of differential evolution. On the other hand, if rx, ry, and rz are too small, the atoms around the vacancy cannot be fully optimized. Therefore, in some specific embodiments of the present invention, in view of the performance of the subsequent differential evolution method, the values ​​of the influencing radii rx, ry, and rz are such that nA is on the order of 100. More specifically, in some specific embodiments of the present invention, the typical value of the influencing radii rx, ry, and rz is 5Å.

[0030] S2. Divide the affected region after the atoms are deleted in step S1 into a grid. The grid coordinates of the grid points are within the boundary range of the affected region. Specifically, assuming that the grid intervals in each direction of the affected region are dx, dy, and dz respectively, and the boundary values ​​of each direction of the affected region are [lx, hx], [ly, hy], and [lz, hz] respectively, then the grid coordinates of the divided grid points are [lx+i×dx, ly+j×dy, lz+k×dz], where i, j, and k are integers whose values ​​are selected so that the grid coordinates of the grid points are within the boundary range of the affected region.

[0031] The number of grid points in this step is denoted as N. Based on the subsequent optimized structure, the grid spacing in this step is set to a series of discrete values, such as 0.25, 0.5, and 1.0 Å; and the boundary range is gradually increased, so that the vacancy structure converges to the ground state.

[0032] S3. Inserting nA1 atoms into the grid created in step S2, where nA1 = nA - nV, nA is the number of atoms deleted in step S1, and nV is the number of vacancies to be created in the affected region after the atoms are deleted. Specifically, when nV < 0, it indicates that interstitial defects are being inserted.

[0033] S4. Optimize the positions of the atoms inserted in step S3 on the grid. Specifically, in some specific embodiments of the present invention, this step calls a differential evolution method to optimize the positions of the nA1 atoms inserted in step S3 on the grid, and sets the optimization problem to find nA1 positions from the above N grid positions so that the system energy is minimized.

[0034] S5. Relax the occupied positions optimized in step S4 to obtain the vacant ground state atomic structure. Specifically, based on the optimized nA1 atomic positions, atoms are inserted, and then the system architecture is statically optimized using the conjugate gradient method to obtain the vacant ground state atomic structure.

[0035] Figure 2 Shown in Figure 1 The algorithm flow chart of the calculation method described in a preferred embodiment is as follows:

[0036] S100, read in the crystal configuration coordinates, the number of vacancies (nV), delete the atomic influence region radius rx, ry, rz and grid spacing dx, dy, dz parameters;

[0037] S200, delete the coordinate position in the affected area that meets |x-x0|<rx, |y-y0|<ry, |z-z0|<rz nA atoms;

[0038] S300, divide the grid and insert nA1=nA-nV atoms into the grid;

[0039] S400, calling the differential evolution method to optimize the grid positions of nA1 inserted atoms;

[0040] S500, determining whether the vacancy defect structure energy changes with changes in the grid spacing and the radius of the affected area; if it does not change, indicating that the result has converged, then proceeding to step S600; if it changes, indicating that the result has not converged, then going to step S100, modifying the parameters such as the grid spacing and the radius of the affected area;

[0041] S600, after the iteration is completed, nA1 atoms are inserted at the grid positions of the obtained nA1 atoms, and the system is optimized using a static calculation method to obtain the atomic structure of the corresponding defect;

[0042] S700, end.

[0043] The present invention is described below by means of specific examples. It should be noted that the following specific examples are only for illustrative purposes and do not limit the scope of the present invention in any way. In addition, unless otherwise specified, methods without specific conditions or steps are conventional methods.

[0044] Application Examples

[0045] Figure 3 (a) and Figure 3 (b) shows the single vacancy and double vacancy ground state structures at the iron ∑5(310) /

[001] grain boundary obtained using the algorithm described in the present invention.

[0046] At the same time, as a comparison, Figure 3 (c) and Figure 3 (d) shows the point-like structures of single and double vacancies obtained using general MS methods.

[0047] It can be seen from the figure Figure 3 (a) and Figure 3 (b) are respectively compared with Figure 3 (c) and Figure 3 The energy of (d) is 0.05 and 0.33 eV lower, and the vacancy-type defect structure obtained by the present invention (the vacancy is in the form of a vacancy-interstitial-vacancy complex) is different from the point structure obtained by the general MS method, which shows that the optimization method of the present invention can obtain the ground state of the vacancy-type defect structure with severe distortion at the grain boundary.

[0048] The technical features of the above-mentioned embodiments can be combined arbitrarily. In order to make the description concise, not all possible combinations of the technical features in the above-mentioned embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0049] The above-described embodiments merely illustrate several implementations of the present invention, and while their descriptions are relatively specific and detailed, they should not be construed as limiting the scope of the patent. It should be noted that a person skilled in the art would be able to make numerous variations and improvements without departing from the spirit of the present invention, all of which fall within the scope of protection of the present invention. Therefore, the scope of protection of the patent for this invention shall be determined by the appended claims.

Claims

1. A method for optimizing vacancy-type defect structures at interfaces, characterized in that: The following steps are involved: S1. Obtain the lattice position [x0, y0, z0] and the affected region with the minimum vacancy formation energy. The affected region is the region with the lattice position [x0, y0, z0] as the center and the influence radius of each direction of its three-dimensional coordinates rx, ry, and rz respectively; at the same time, delete the regions in the affected region with coordinates satisfying |x-x0|<rx, |y-y0|<ry, |z-z0|<rz atoms[x,y,z]; S2, dividing the affected area after the atoms are deleted in step S1 into a grid, wherein the grid point coordinates are within the boundary range of the affected area; S3, inserting atoms with a number of atoms nA1 into the grid divided in step S2, wherein nA1=nA-nV, nA is the number of atoms deleted in step S1, and nV is the number of vacancies to be generated in the affected area after deleting the atoms; S4, using the differential evolution method to optimize the positions of the inserted atoms in step S3 on the grid. The optimization problem is to find nA1 positions in the grid divided in step S2 so that the system energy is the lowest; S5. Relax the occupied positions optimized in step S4 to obtain the vacancy ground state atomic structure.

2. The method for optimizing the interface vacancy defect structure according to claim 1, wherein: In step S1, the lattice position with the minimum vacancy formation energy is obtained by selecting lattice points within 1 nm from the grain boundary with the crystal interface as the center, placing a vacancy at each position, and then relaxing the system using a static calculation method. The vacancy formation energy at each lattice point after relaxation is compared to obtain the lattice position with the minimum vacancy formation energy.

3. The method for optimizing the vacancy defect structure at the interface according to claim 1, wherein: In step S1, the values ​​of the influence radii rx, ry, and rz are determined so that the number of deleted atoms nA is on the order of 100.

4. The method for optimizing the vacancy defect structure at the interface according to claim 2, wherein: In step S1, the typical value of the influence radius rx, ry, and rz is 5 Å.

5. The method for optimizing the vacancy defect structure at the interface according to claim 1, wherein: In step S2, the grid intervals in each direction within the affected area are dx, dy, and dz, respectively, and the boundary values ​​in each direction of the area are [lx, hx], [ly, hy], and [lz, hz], respectively. The grid point coordinates of the divided grid are [lx+i×dx, ly+j×dy, lz+k×dz], where i, j, and k are integers whose values ​​are taken so that the grid point coordinates are within the boundary range of the affected area.

6. The method for optimizing the vacancy defect structure at the interface according to claim 1, wherein: In step S3, if nV<0, it means that the inserted defect is an interstitial atom type defect.

7. The method for optimizing the vacancy defect structure at the interface according to claim 1, wherein: The specific operation of step S5 is: inserting atoms according to the nA1 atomic positions optimized in step S4, and then using the conjugate gradient method to statically optimize the system architecture.

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