Method for calculating vacancy-helium-hydrogen complex forming energy and defect binding energy

Abstract

The invention belongs to the technical field of nuclear material irradiation damage simulation, and particularly discloses a vacancy-helium-hydrogen complex forming energy and defect binding energy calculation method, which comprises the following steps: S1, randomly distributing a given number of helium atoms and hydrogen atoms around a vacancy cluster, and obtaining a stable cluster configuration and energy information thereof; s2, calculating binding energy of hydrogen atoms, helium atoms, vacancies, self-interstitial atoms and the vacancy-helium-hydrogen complex; and S3, analyzing binding energy of the hydrogen atoms, the helium atoms, the vacancies, the self-interstitial atoms and the vacancy-helium-hydrogen complex, introducing reduced variables based on the occupation characteristics of the helium atoms and / or the hydrogen atoms in the cavity, uniformly mapping the binding energy of the point defects-clusters in different sizes to the same characteristic curved surface, and constructing an equal-interval numerical network model through curved surface fitting. According to the calculation method, the calculation amount is reduced, the calculation precision is improved, the efficient prediction of the large cluster defect formation energy is realized, and the method has the advantages of rapidness, high efficiency and universality.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of nuclear material irradiation simulation, and particularly relates to a calculation method for vacancy-helium-hydrogen complex formation energy and defect energy combination. BACKGROUND

[0002] In a fusion reactor, neutron irradiation of ferritic / martensitic steel structural materials not only produces off-site damage, but also generates hydrogen and helium atoms through transmutation reactions. Among them, the complex defects (denoted as V p1 He p2 H p3 , where p1, p2 and p3 represent the number of single V, He and H in the cluster, respectively) play a key role in the swelling phenomenon induced by irradiation. In order to carry out multi-scale simulation research, it is necessary to accurately obtain the basic property parameters of such complex defects, including formation energy and vacancy, helium, hydrogen and self-interstitial atom (SIA) binding energy with the cluster. However, due to the large range of p1, p2 and p3 values, and the high complexity of the cluster configuration space, the comprehensive calculation of the defect properties of all possible configurations faces a huge challenge in computational cost.

[0003] The current calculation of complex formation energy and defect binding energy is mainly based on a progressive strategy. Specifically, starting from a smaller defect cluster configuration, a larger cluster configuration is constructed by gradually adding point defects, for example, adding helium (He) and hydrogen (H) atoms to a smaller V p1 He p2 H p3 cluster, and trying and relaxing at all possible positions, resulting in a huge amount of calculation and time consumption. In addition, for the interaction of defects with clusters of different sizes (such as binding energy), a physical model with a clear mathematical expression needs to be established. Although there are mature interaction models for simple pure vacancy clusters or vacancy-hydrogen clusters, for V p1 He p2 H p3 Such complex complexes, due to the high-dimensional nature of their interaction energy surface, it is still difficult to establish an accurate analytical model. SUMMARY

[0004] Therefore, the primary purpose of the present application is to provide a method for calculating vacancy-helium-hydrogen complex formation energy and defect binding energy, by randomly distributing a given number of helium (He) and hydrogen (H) atoms around a vacancy cluster (V) to obtain stable cluster configurations and their energy information; and innovatively introducing a reduced variable to describe the defect characteristics, mapping the point defect-cluster binding energy of different sizes to the same characteristic surface, and constructing an equidistant numerical network model through surface fitting. p1 He p2 H p3 The method for calculating defect configuration binding energy is used to quickly determine the V p1 He p2 H p3 defect configuration and its binding energy.

[0005] In order to achieve the above purpose, the following technical solutions are adopted in the present application: One aspect of the present application discloses a method for calculating vacancy-helium-hydrogen complex formation energy and defect binding energy, comprising the following steps: S1, randomly distributing a given number of helium atoms and hydrogen atoms around a vacancy cluster, and obtaining stable cluster configurations and their energy information; S2, calculating the binding energy of hydrogen atoms, helium atoms, vacancies, interstitial atoms, and vacancy-helium-hydrogen complexes; S3, analyzing the binding energy of hydrogen atoms, helium atoms, vacancies, interstitial atoms, and vacancy-helium-hydrogen complexes, introducing a reduced variable based on the occupation characteristics of helium atoms and / or hydrogen atoms in the cavity, mapping the point defect-cluster binding energy of different sizes to the same characteristic surface, and constructing an equidistant numerical network model through surface fitting.

[0006] In the present application, a certain concentration of He and H atoms is randomly distributed around the vacancy (V), and the capture position of He / H is simulated and determined; based on the occupation characteristics of He / H in the cavity, a reduced variable parameter is introduced, the point defect-cluster binding energy of different sizes is mapped to the same characteristic surface, an equidistant numerical grid model is constructed through surface fitting, efficient prediction of large cluster defect formation energy is realized; at the same time, the reduced variable parameter and the equidistant gridding method are used to avoid the construction difficulty of complex analytical model, which is suitable for three-dimensional modeling of high-dimensional complex cluster system, and significantly improves the calculation speed and universality.

[0007] In some examples, in step S1, the initial configuration of a given number of helium atoms and hydrogen atoms is randomly generated around the vacancy cluster using random sampling (different from the method of enumerating all positions commonly used in the art).

[0008] In some examples, the obtaining of the stable cluster configuration comprises the following steps: Molecular dynamics (MD) simulation is performed at a suitable temperature to diffuse helium atoms and / or hydrogen atoms to the vicinity of stable positions; Full relaxation of the configuration is achieved by molecular static (MS) calculation to obtain a stable cluster configuration.

[0009] In the present application, a certain number of He and H atoms are randomly distributed around the vacancy by random sampling, and the low diffusion coefficient of helium and hydrogen atoms is fully utilized. MD simulation is performed at a suitable temperature to diffuse the atoms to the vicinity of stable positions; then full relaxation of the configuration is achieved by MS calculation, which can significantly reduce the calculation amount of position search, realize efficient prediction of large cluster defect formation energy, and ensure the reliability of the results.

[0010] In a further scheme, in step S2, the calculation of the binding energy of hydrogen atoms, helium atoms, vacancies, self-interstitial atoms, and vacancy-helium-hydrogen complexes is divided into the following three cases: (1) When p3=0, the cluster complex is V p1 He p2 ; the formation energy is fitted in the p1 and p2 directions, respectively, and then the binding energy of He, V and V p1 He p2 is calculated; (2) When p2=0, the cluster complex is V p1 H p3 ; the formation energy is fitted in the p1 and p3 directions, respectively, and then the binding energy of H, V and V p1 H p3 is calculated; (3) When p2≠0 and p3≠0, the cluster complex is V p1 He p2 H p3 , the formation energy is fitted in the p1, p2 and p3 directions, respectively, and then the binding energy of He, H, V and V p1 He p2 H p3 is calculated; Wherein, V, He, H represent vacancies, helium atoms, hydrogen atoms, respectively, V p1 He p2 , V p1 H p3 , V p1 He p2 H p3 represent vacancy-helium complex, vacancy-hydrogen complex, vacancy-helium-hydrogen complex, respectively, p1, p2, p3 represent the number of single V, He, H in the cluster.

[0011] Specifically, the prior art is generally a method of directly calculating the formation energy of all possible configurations to obtain the numerical formation energy, which is suitable for relatively simple defect systems, but has obvious deficiencies in dealing with the more complex system of vacancy-helium-hydrogen: first, the calculation amount is too large, and second, it is difficult to find stable configurations due to the complexity of the configuration, resulting in a large error in the calculation result of the formation energy, and the error is more significant if the interaction energy is directly calculated. In contrast, in the method proposed in the present application, the formation energy surface is uniformly processed and smoothed by fitting a limited number of calculation points, which not only significantly reduces the calculation amount, but also effectively improves the calculation accuracy.

[0012] In some specific examples, obtaining the fitted formation energy includes the following steps: loading the formation energy Ef(p1, p2) or Ef(p1, p3) or Ef(p1, p2, p3) obtained in step S1; fitting along the p1 direction, taking the minimum and maximum values of p2 as p2min and p2max, and recording each p2 in the range [p2min, p2max] as p2i, for a given p2i, selecting a subset of formation energies Ef1(p1, p2=p2i) from Ef(p1, p2) that satisfy p2=p2i, and fitting y-x with x and y being the independent variable p1 and the dependent variable Ef1 in Ef1(p1, p2=p2i), respectively; fitting in the p2 and p3 directions, referring to the same method as described above; The fitting formula is shown in formulas (1)-(3): , , , For V p1 He p2 , the fitting formula in the p1 and p2 directions is formula (1); For V p1 H p3 , the fitting formula in the p1 direction is formula (2), and the fitting formula in the p3 direction is formula (3); For V p1 He p2 H p3 , the fitting formula in the p1 direction is formula (1), the fitting formula in the p2 direction is formula (3), and the fitting formula in the p3 direction is formula (3); where β1, β2, β3, β4, and β5 are fitting parameters.

[0013] Further, according to the fitted formation energy, the binding energy is calculated, wherein the calculation of the binding energy can be performed according to the formula known in the art.

[0014] In some examples, for V p1 He p2 , V and V p1 He p2 binding energy EbV_V p1 He p2 , self-interstitial atom and V p1 He p2 binding energy EbSIA_V p1 He p2 , He and V p1 He p2 binding energy EbHe_V p1 He p2 are calculated according to formulas (4)-(6): EbV_V p1 He p2 (p1,p2)= Ef_fitp1(p1+1,p2)- Ef_fitp1(p1,p2) EbSIA_V p1 He p2 (p1,p2)= + - EbV_V p1 He p2 (p1,p2), EbHe_V p1 He p2 (p1,p2)= Ef_fitp2(p1,p2+1)- Ef_fitp2(p1,p2) ; for V p1 H p3 , V and V p1 H p3 binding energy EbV_V p1 H p3 , self-interstitial atom and V p1 H p3 binding energy EbSIA_V p1 H p3 , H and V p1 H p3 binding energy EbH_V p1 H p3 are calculated according to formulas (7)-(9): EbV_V p1 H p3 (p1,p3)= Ef_fitp1(p1+1,p3)- Ef_fitp1(p1,p3) EbSIA_V p1H p3 (p1,p3)= + - EbV_V p1 H p3 (p1,p3), EbH_V p1 H p3 (p1,p3)= Ef_fitp3(p1,p3+1)- Ef_fitp3(p1,p3) ; For V p1 He p2 H p3 , V with V p1 He p2 H p3 binding energy EbV_V p1 He p2 H p3 , self-interstitial with V p1 He p2 H p3 binding energy EbSIA_V p1 He p2 H p3 , He with V p1 He p2 H p3 binding energy EbHe_V p1 He p2 H p3 , H with V p1 He p2 H p3 binding energy EbH_V p1 He p2 H p3 are calculated according to formulas (10)-(13): EbV_V p1 He p2 H p3 (p1,p2,p3)= Ef_fitp1(p1+1,p2,p3)- Ef_fitp1(p1,p2,p3) , EbSIA_V p1 He p2 H p3 (p1,p2,p3)= + - EbV_V p1 He p2 Hp3 (p1,p2,p3), ; EbHe_V p1 He p2 H p3 (p1,p2,p3)= Ef_fitp2(p1,p2+1,p3)- Ef_fitp2(p1,p2,p3) （12）， EbH_V p1 He p2 H p3 (p1,p2,p3)= Ef_fitp3(p1,p2,p3+1)- Ef_fitp3(p1,p2,p3) Among them, Ef_fitp1, Ef_fitp2, and Ef_fitp3 are the formation energies obtained after fitting along the directions of p1, p2, and p3, respectively. 、 are the formation energies of a single vacancy and a self-interstitial atom in the bulk region, respectively.

[0015] Further solution, step S3 is specifically: If p1<p1*, the binding energy value obtained in step S2 is used directly; where p1 is the size of the vacancy cluster (i.e., the number of vacancies contained in the cluster. p1* represents a critical value, and the p1* value is determined based on the maximum vacancy cluster size that can be calculated with available computing resources. For example, for a pure vacancy cluster V p1 , can be 15-120; for vacancy-helium or vacancy-hydrogen clusters, it is 30-60; for vacancy-helium-hydrogen clusters, it is 15-30. That is, the more complex the cluster, the smaller the value. However, considering that smaller clusters have greater discreteness (i.e., after introducing reduced variables, the interaction energy cannot be well unified on a unified plane, and subsequent fitting fails), p1* has a minimum value, such as 15.

[0016] If p1≥p1*, the reduced variables are introduced, the He occupation ratio in the cavity is p2 / p1, and the H coverage ratio on the cavity surface is p3 / p1. 2 / 3 : For V p1 He p2 , EbV_V obtained in step S2 p1 He p2 (p1,p2),EbHe_V p1 He p2 (p1,p2), converted to EbV_V p1 He p2 (p2 / p1), EbHe_V p1 He p2(p2 / p1); let x = p2 / p1, fit the relation between binding energy and x according to formula (14): y = A2 + (A1 - A2) / (1 + e^(-B1x)) )（14） , wherein A1, A2, x0, dx are fitting parameters respectively.

[0017] For V p1 H p3 , let x = p2 / p1, fit the relation between binding energy and x according to formula (14): p1 H p3 , EbH_V p1 H p3 (p1, p3), convert EbV_V p1 H p3 (p1, p3 2 / 3 ), EbH_V p1 H p3 (p1, p3 2 / 3 ); let x = p3 / p1 2 / 3 , for EbV_V p1 H p3 (p3 / p1 2 / 3 ), fit the relation between binding energy and x according to formula (14); for EbH_V p1 H p3 (p3 / p1 2 / 3 ), fit the relation between binding energy and x according to formula (15): y = Intercept + B1x + B2x 2 +B3x 3 （15） , wherein Intercept, B1, B2, B3 are fitting parameters respectively.

[0018] For V p1 He p2 H p3 , let x1 = p2 / p1, x2 = p3 / p1 2 / 3 , convert the binding energy of V, He, H and V p1 He p2 H p3 (p1, p2, p3) into the relation of x1, x2; divide the uniform line in x2 direction, let its interval be dH, the minimum and maximum x2 in x2 direction are 0 and maxx2 respectively, then the grid nodes in x2 direction are 0:dH:maxx2, for a certain node x2i in it, find the data subset falling in the node x2i by abs(x2-x2i)<0.5dH, let it be Eb1_V p1 He p2 Hp3 (x1,x2i), and then subset Eb1_V p1 He p2 H p3 The data in (x1,x2i) is fitted to x1, and the fitting function is ; Then bring in the homogenized x1 variable x1g to generate Eb1_V p1 He p2 H p3 (x1g,x2i), traversing the above x2 will eventually generate V, He, H, SIA and V p1 He p2 H p3 Table of equally spaced binding energies.

[0019] Another aspect of the present application discloses a computer device / equipment / system, comprising a memory, a processor, and a computer program stored in the memory, wherein the processor executes the computer program to implement the steps of the computing method described above.

[0020] Another aspect of the present application discloses a computer-readable storage medium having a computer program / instruction stored thereon, which implements the steps of the aforementioned calculation method when the computer program / instruction is executed by a processor.

[0021] Another aspect of the present application discloses a computer program product, including a computer program / instruction, characterized in that the computer program / instruction implements the steps of the above-mentioned calculation method when executed by a processor.

[0022] Beneficial effects of this application: This application simulates and determines the He / H capture location by placing a certain concentration of He and H atoms near a vacancy (V). Based on the He / H occupancy characteristics in the cavity, a reduced variable parameter is introduced to uniformly map point defect-cluster binding energies of different sizes to the same characteristic surface. An equidistant numerical grid model is constructed through surface fitting. Compared with existing technologies, this application breaks through the traditional calculation model that relies on the gradual extrapolation of small cluster configurations and achieves efficient prediction of defect formation energies for large clusters. The proposed reduced variable parameter and equidistant gridding method avoids the difficulty of constructing complex analytical models and is particularly suitable for three-dimensional modeling of high-dimensional complex cluster systems. The characteristic surface is used to uniformly describe defect binding energies at different scales, significantly improving calculation speed and universality. BRIEF DESCRIPTION OF THE DRAWINGS

[0023] Figure 1 Flowchart of the calculation method of this application.

[0024] Figure 2 The potential occupied positions of He and H in and near the vacancy V are shown in Figure 2, where NcandiH 、N candiHe are the number of potential locations of nearby H and He respectively.

[0025] Figure 3 The calculation method for this application is defective and V p1 He p2 H p3 Binding energy is p2 / p1, p3 / p1 2 / 3 Schematic diagram of the two-dimensional equally spaced grid formed in space.

[0026] Figure 4 V is calculated using the calculation method of this application in the application example p1 He p2 ( Figure 4 (a)), V p1 H p3 ( Figure 4 (b)), and V p1 He p2 H p3 Formation energy ( Figure 4 (c) and Figure 5 (d) corresponds to the cases of vacancy cluster sizes V39 and V65, respectively).

[0027] Figure 5 V / He / H / SIA and V calculated using the calculation method of this application in the application example p1 H p3 ( Figure 5 Center left), V p1 He p2 Binding energy ( Figure 6 center right) and an illustration of an equidistant numerical grid.

[0028] Figure 6 V / He / H / SIA and V calculated using the calculation method of this application in the application example p1 He p2 H p3 Binding energy ( Figure 6 The middle left is the case of p1<30, Figure 1 p1 in the middle right 30 results). DETAILED DESCRIPTION

[0029] The present application will be further illustrated below with reference to specific embodiments. It should be noted that the following specific embodiments are only for illustrative purposes and do not limit the scope of the present application in any way.

[0030] Unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this application belongs. The terminology used in the description herein is for the purpose of describing particular embodiments only and is not intended to be limiting of the application.

[0031] In addition, unless otherwise specified, the method of which the conditions or steps are not specifically recorded is a conventional method.

[0032] Embodiment The embodiment discloses a method for calculating vacancy-helium-hydrogen complex formation energy and defect binding energy, and specifically comprises the following steps (for specific flow, please refer to Figure 2 ): S1, V p1 He p2 H p3 Random occupation of configuration and acquisition of stable defect configuration and energy information thereof.

[0033] First, p2 He atoms and p3 H atoms are randomly generated around p1 vacancies (V) in a random sampling manner, EbV_V The potential occupation position of He and H near and in the vacancy V is shown in the middle; then, molecular dynamics (MD) simulation is performed at an appropriate temperature to diffuse the atoms to the vicinity of the stable position; finally, complete relaxation of the configuration is realized through molecular static (MS) calculation; and the stable defect configuration and energy information (i.e., formation energy) are obtained.

[0034] S2, H / He / V / SIA and V p1 He p2 H p3 Binding energy calculation method.

[0035] According to the different defect configurations, the calculation method of the defect binding energy mainly includes three cases: (1) When p3=0, the cluster degenerates into V p1 He p2 , respectively, in the p1 and p2 directions, and then the binding energy of He, V and V p1 He p2 is calculated, and the specific steps are as follows: Load the V p1 He p2 formation energy obtained in step S1, and set it as Ef(p1, p2).

[0036] Fit along p1 direction. Let p2min and p2max be the minimum and maximum value of p2, and p2i for each p2 in the range of [p2min, p2max]. For a given p2i, select the subset of formation energies from Ef(p1, p2) that satisfy p2 = p2i, denoted as Ef1(p1, p2 = p2i), and fit y - x, where x and y are the independent variable p1 and dependent variable Ef1 in Ef1(p1, p2 = p2i), respectively, and the fitting formula is: , The fitted formation energy is denoted as Ef_fitp1(p1, p2). Calculate V and V p1 He p2 The binding energy is EbV_V p1 He p2 , and V p1 He p2 The binding energy is EbSIA_V p1 He p2 (p1, p2), and the calculation formulas are as follows: He p1 (p1,p2)= Ef_fitp1(p1+1,p2)- Ef_fitp1(p1,p2) p2 EbSIA_V , He p1 (p1,p2)= p2 - EbV_V + He p1 (p1,p2), p2 EbHe_V where, , are the formation energies of a single vacancy and self-interstitial atom in the bulk region, respectively.

[0037] Fit along p2 direction. Let p1min and p1max be the minimum and maximum value of p1, and p1i for each p1 in the range of [p1min, p1max]. For a given p1i, select the subset of formation energies from Ef(p1, p2) that satisfy p1 = p1i, denoted as Ef1(p1 = p1i, p2), and fit y - x, where x and y are the independent variable p2 and dependent variable Ef1 in Ef1(p1 = p1i, p2), respectively, and the fitting formula is: , The formation energy obtained after fitting is denoted as Ef_fitp2(p1, p2); According to the formation energy after fitting, He and V p1 He p2 The binding energy EbHe_V p1 He p2 The formula is as follows: He p1 (p1,p2)= Ef_fitp2(p1,p2+1)- Ef_fitp2(p1,p2) p2 EbV_V .

[0038] (2) When p2=0, the cluster degenerates into V p1 H p3 In this case, first fit the formation energy in the p1 and p3 directions respectively, and then calculate the binding energy of H, V and V p1 H p3 , the specific steps are as follows: First, load V p1 H p3 The formation energy is denoted as Ef(p1, p3).

[0039] Fit along the p1 direction. Let p3min and p3max be the minimum and maximum values of p3 respectively. For each p3 in the range [p3min, p3max], denoted as p3i; for a given p3i, select a subset of formation energies Ef1(p1, p3=p3i) from Ef(p1, p3) that satisfy p3=p3i; let x and y be the independent variable p1 and dependent variable Ef1 in Ef1(p1, p3=p3i) respectively, and fit y-x, where the fitting formula is: , The formation energy obtained after fitting is denoted as Ef_fitp1(p1, p3); According to the formation energy after fitting, V and V p1 H p3 The binding energy EbV_V p1 H p3 The self-interstitial and V p1 H p3 The binding energy is EbSIA_V p1 H p3 (p1, p3), and the calculation formula is as follows: (p1,p3)= Ef_fitp1(p1+1,p3)- Ef_fitp1(p1,p3) p1 H p3 EbSIA_V (p1,p3)= p1 H p3- EbV_V + (p1,p3), p1 H p3 EbH_V wherein, , are the formation energies of a single vacancy and a self-interstitial atom in the bulk region, respectively.

[0040] Fit along the p3 direction. Let the minimum and maximum values of p1 be p1min and p1max, respectively. For each p1 in the range [p1min, p1max], denote it as p1i. For a given p1i, select a subset of formation energies from Ef(p1, p3) that satisfy p1 = p1i, denoted as Ef1(p1 = p1i, p3). Let x and y be the independent variable p3 and the dependent variable Ef1 in Ef1(p1 = p1i, p3), respectively. Fit y - x, where the fitting formula is: , The formation energy obtained after fitting is denoted as Ef_fitp3(p1, p3). Calculate H and V p1 H p3 from the fitted formation energy. p1 H p3 The calculation formula is as follows: (p1,p3)= Ef_fitp3(p1,p3+1)- Ef_fitp3(p1,p3) p1 H p3 EbV_V

[0041] (3) When p2 ≠ 0 and p3 ≠ 0, for V p1 He p2 H p3 , first fit the formation energy in the p1, p2, and p3 directions, respectively, and then calculate the binding energy of He, H, and V p1 Hep2Hp3. The specific steps are as follows: First, load the V p1 He p2 H p3 formation energy calculated in S1, denoted as Ef(p1, p2, p3).

[0042] Fitting along p1 direction. Let p2min and p2max be the minimum and maximum values of p2, and p2i be each p2 in the range of [p2min, p2max]; let p3min and p3max be the minimum and maximum values of p3, and p3j be each p3 in the range of [p3min, p3max]. For given p2i and p3j, filter the formation energy subset Ef1(p1, p2=p2i, p3=p3j) from Ef(p1, p2, p3) that satisfies p2=p2i and p3=p3j, and let x and y be the independent variable p1 and dependent variable Ef1 in Ef1(p1, p2=p2i, p3=p3j) respectively, and fit y-x, where the fitting formula is: , The formation energy obtained after fitting is denoted as Ef_fitp1(p1, p2, p3); According to the fitted formation energy, calculate V and V p1 He p2 H p3 The binding energy EbV_V p1 He p2 H p3 , and V p1 He p2 H p3 The binding energy is EbSIA_V p1 He p2 H p3 (p1, p2, p3), and the calculation formula is as follows: He p1 (p1,p2,p3)= Ef_fitp1(p1+1,p2,p3)- Ef_fitp1(p1,p2,p3) p2 H p3 EbSIA_V He p1 (p1,p2,p3)= p2 H p3 - EbV_V + He p1 (p1,p2,p3), p2 H p3 EbHe_V wherein, , are the formation energies of a single vacancy and a self-interstitial atom in the bulk region respectively.

[0043] Fitting along p2 direction. Let p1min and p1max be the minimum and maximum values of p1, and p1i be each p1 in the range of [p1min, p1max]; let p3min and p3max be the minimum and maximum values of p3, and p3j be each p3 in the range of [p3min, p3max]; for given p1i and p3j, then filter the formation energy subset Ef1(p1=p1i, p2, p3=p3j) from Ef(p1, p2, p3) that satisfies p1=p1i and p3=p3j, let x and y be the independent variable p2 and dependent variable Ef1 in Ef1(p1=p1i, p2, p3=p3j) respectively, and fit y-x, wherein the fitting formula is: , The formation energy obtained after fitting is denoted as Ef_fitp2(p1, p2, p3); According to the fitted formation energy, calculate He and V p1 He p2 H p3 Binding energy EbHe_V p1 He p2 H p3 , and the calculation formula is as follows: He p1 ​ p2 H p3 (p1,p2,p3) = Ef_fitp2(p1,p2+1,p3) - Ef_fitp2(p1,p2,p3) .

[0044] Fitting along p3 direction. Let p1min and p1max be the minimum and maximum values of p1, and p1i be each p1 in the range of [p1min, p1max]; let p2min and p2max be the minimum and maximum values of p2, and p2j be each p2 in the range of [p2min, p2max]; for given p1i and p2j, then filter the formation energy subset Ef1(p1=p1i, p2=p2j, p3) from Ef(p1, p2, p3) that satisfies p1=p1i and p2=p2j, let x and y be the independent variable p3 and dependent variable Ef1 in Ef1(p1=p1i, p2=p2j, p3) respectively, and fit y-x, wherein the fitting formula is: , The formation energy obtained after fitting is denoted as Ef_fitp3(p1, p2, p3); Then according to the fitted formation energy, calculate H and V p1 He p2 H p3 Binding energy EbH_Vp1 He p2 H p3 , the calculation formula is as follows: EbH_V p1 He p2 H p3 (p1,p2,p3) = Ef_fitp3(p1,p2,p3+1) - Ef_fitp3(p1,p2,p3).

[0045] S3, H / He / V / SIA and V p1 He p2 H p3 The binding energy analytical expression and the numerical grid modeling method are combined.

[0046] (1) For V p1 He p2 , when p1 * (For example, p1 * = 60), directly use the binding energy value calculated in step S2. When p1 p1 * , introduce the reduced variable: the occupation ratio of He in the cavity (p2 / p1), and convert EbV_V p1 He p2 (p1, p2), EbHe_V p1 He p2 (p1, p2) into EbV_V p1 He p2 (p2 / p1), EbHe_V p1 He p2 (p2 / p1); let x = p2 / p1, then fit the relationship between the binding energy and x, and the function relationship selected for fitting is: y = A2 + (A1 - A2) / (1 + ), where A1, A2, x0, dx are fitting parameters.

[0047] (2) For V p1 H p3 , when p1 * (For example, p1 * = 60), directly use the binding energy value calculated in step S2. When p1 p1 * , introduce the reduced variable: the occupation ratio of H on the surface of the cavity (p3 / p1 2 / 3 ), and convert EbV_V p1 H p3 (p1, p3), EbH_V p1 H p3 (p1, p3) into EbV_Vp1 H p3 (p3 / p1 2 / 3 )、EbH_V p1 H p3 (p3 / p1 2 / 3 ); let x = p3 / p1 2 / 3 , and then fit the relationship between binding energy and x.

[0048] For EbV_V p1 H p3 (p3 / p1 2 / 3 ), the fitting function relationship is selected: y=A2 + (A1 - A2) / (1 + ), where A1, A2, x0, and dx are fitting parameters.

[0049] For EbH_V p1 H p3 (p3 / p1 2 / 3 ), the fitting function relationship is selected: y= Intercept+B1x+B2x 2 +B3x 3 , where Intercept, B1, B2, and B3 are fitting parameters.

[0050] (3) For V p1 He p2 H p3 , when p1 <p1 * (such as p1 * =30), directly use the binding energy value calculated in step S2. p1 * When the reduced variables are introduced: the occupation ratio of He in the cavity (p2 / p1), the coverage ratio of H on the cavity surface (p3 / p1 2 / 3 ), let x1=p2 / p1, x2= p3 / p1 2 / 3 , V, He, H and V p1 He p2 H p3 The binding energy of (p1, p2, p3) is converted to the relationship between x1 and x2. Next, in order to quickly call the binding energy data, we further generate a binding energy value table with equal spacing (the grid spacing in the x1 and x2 directions is equal) (such as Figure 3The uniform line is first divided in the x2 direction, and the interval is set as dH. The minimum and maximum x2 in the x2 direction are 0 and maxx2, respectively. The nodes of the grid in the x2 direction are 0:dH:maxx2. For a given node x2i, the data subset falling on the x2i node is found by abs(x2-x2i)<0.5dH, and is set as Eb1_V p1 He p2 H p3 (x1,x2i), and then the subset Eb1_V p1 He p2 H p3 (x1,x2i) is fitted with respect to the data pair x1, and the fitting function is: .

[0051] Then the uniform x1 variable x1g is brought in to generate Eb1_V p1 He p2 H p3 (x1g,x2i). The above x2 is traversed to finally generate the equidistant binding energy table of V, He, H, SIA and V p1 He p2 H p3 .

[0052] Application Example Taking the base iron material of the ferrite / martensite steel used as the nuclear structural material of the fusion reactor as an example, the crystal structure thereof is body-centered cubic, and the lattice constant is 2.8553 Å. The potential functions used in the calculation of MD and MS are as follows: the potential functions developed in the literature Phys. Rev. B 79 (2009) 174101 and J. Phys.: Condens. Matter 16 (2004) 2629-42 are used to describe the iron-hydrogen and hydrogen-hydrogen interactions, respectively; and the potential functions developed in J. Nucl. Mater. 382 (2008) 143-6, J. Phys.: Condens. Matter 24 (2012) 265402 and Mol. Phys. 14 (1968) 311-5 are used to describe the iron-helium, helium-hydrogen and helium-helium interactions, respectively.

[0053] The formation energy of the vacancy-helium-hydrogen complex and the defect binding energy are calculated by using the calculation method disclosed in the embodiment, and the results are shown in Figures 4-6 As can be seen from the results in Figures 4-6 , by using the calculation method of the present application, the formation energy and defect interaction energy of a large-scale defect system can be calculated and modeled and quickly accessed. For V p1 He p2 , V p1 H p3The system successfully constructs a cluster formation energy curve surface with a vacancy cluster size of up to 120 vacancies; in comparison, existing literature reports are generally limited to a size of less than 10 vacancies. For vacancy-helium-hydrogen clusters, existing studies are mostly limited to the combination of a single vacancy and limited helium-hydrogen; and the calculation method of the present application first obtains the formation energy results of vacancy-helium-hydrogen clusters containing up to 65 vacancies Figure 4 ).

[0054] Further, the reduced variable method is used to combine the binding energies of different sizes of more than 60 vacancies into a curve Figure 5 ), it can be seen that different results are not on the same curve when the cluster size is small, so the present application directly calls the numerical results for less than 60, and for more than 60, the results are divided into a uniform and equidistant table, and the relevant numerical table is called in large-scale simulation; especially for vacancy-helium-hydrogen clusters Figure 6 ), the calculation method of the present application first obtains the interaction energy curve surface of vacancy-helium-hydrogen-self-interstitial atoms and clusters at different cluster sizes and different helium-hydrogen contents, thereby enabling efficient prediction of the formation energy of large-size defect clusters, and significantly improving the calculation speed and universality.

[0055] It should be noted that the present application is not limited to the above embodiments. The above embodiments are only examples, and embodiments having the same technical idea and playing the same role within the scope of the technical solutions of the present application are all included in the technical scope of the present application. In addition, within the scope of the main idea of the present application, various modifications of the embodiments that can be thought of by those skilled in the art, and other ways constructed by combining part of the constituent elements of the embodiments are also included in the scope of the present application.

Claims

1. A method for calculating the formation energy and defect binding energy of a vacancy-helium-hydrogen complex, characterized in that: The following steps are involved: S1. Randomly distribute a given number of helium atoms and hydrogen atoms around the vacancy cluster and obtain the stable cluster configuration and its energy information; S2. Calculate the binding energies of hydrogen atoms, helium atoms, vacancies, self-interstitial atoms, and vacancy-helium-hydrogen complexes; S3. Analyze the binding energies of hydrogen atoms, helium atoms, vacancies, self-interstitial atoms, and vacancy-helium-hydrogen complexes. Based on the occupancy characteristics of helium atoms and / or hydrogen atoms in the cavity, introduce reduced variables, uniformly map the point defect-cluster binding energies of different sizes to the same characteristic surface, and construct an equidistant numerical network model through surface fitting.

2. The calculation method according to claim 1, wherein: In step S1, an initial configuration of a given number of helium atoms and hydrogen atoms is randomly generated around the vacancy cluster by random sampling.

3. The calculation method according to claim 1, wherein: In step S1, obtaining the stable cluster configuration includes the following steps: Perform molecular dynamics simulations at a suitable temperature to allow helium atoms and / or hydrogen atoms to diffuse to the vicinity of stable positions; Through molecular static calculations, complete relaxation of the configuration is achieved to obtain a stable cluster configuration.

4. The calculation method according to claim 1, wherein: In step S2, the calculation of the binding energies of hydrogen atoms, helium atoms, vacancies, self-interstitial atoms, and vacancy-helium-hydrogen complexes is divided into the following three cases: (1) When p3=0, the cluster complex is V p1 He p2 ; Fit the formation energy in the p1 and p2 directions respectively, and then calculate He, V and V p1 He p2 The binding energy of (2) When p2=0, the cluster complex is V p1 H p3 ; Fit the formation energy in the p1 and p3 directions respectively, and then calculate H, V and V p1 H p3 The binding energy of (3) When p2≠0 and p3≠0, the cluster complex is V p1 He p2 H p3 , respectively fit the formation energy in the p1, p2, and p3 directions, and then calculate He, H, V and V p1 Binding energy of Hep2Hp3; Among them, V, He, and H represent vacancies, helium atoms, and hydrogen atoms, respectively. p1 He p2 、V p1 H p3 、V p1 He p2 H p3 represent vacancy-helium complex, vacancy-hydrogen complex, and vacancy-helium-hydrogen complex, respectively. p1, p2, and p3 represent the number of single V, He, and H in the cluster, respectively.

5. The calculation method according to claim 4, wherein: The acquisition of the fitted formation energy includes the following steps: The formation energy Ef(p1, p2) or Ef(p1, p3) or Ef(p1, p2, p3) obtained in step S1 is loaded; Fit along the direction of p1, take the minimum and maximum values ​​of p2 as p2min and p2max respectively, and record each p2 in the range [p2min, p2max] as p2i; for a given p2i, select the formation energy subset Ef1 (p1, p2=p2i) that satisfies p2=p2i from Ef (p1, p2); let x and y be the independent variable p1 and the dependent variable Ef1 in Ef1 (p1, p2=p2i), respectively, and fit yx; Fitting in the p2 and p3 directions follows the same method as above; The fitting formula is shown in formulas (1) to (3): ， ， ， For V p1 He p2 , the fitting formulas for p1 and p2 directions are both formula (1); For V p1 H p3 , the fitting formula in the p1 direction is formula (2), and the fitting formula in the p3 direction is formula (3); For V p1 He p2 H p3 , the fitting formula in the p1 direction is formula (1), the fitting formula in the p2 direction is formula (3), and the fitting formula in the p3 direction is formula (3); Among them, β1, β2, β3, β4, and β5 are fitting parameters respectively.

6. The calculation method according to claim 5, wherein: For V p1 He p2 , V and V p1 He p2 Binding energy EbV_V p1 He p2 , self-interstitial atoms and V p1 He p2 Binding energy EbSIA_V p1 He p2 , He and V p1 He p2 Binding energy EbHe_V p1 He p2 According to formulas (4) to (6), we can obtain: EbV_V p1 He p2 (p1,p2)= Ef_fitp1(p1+1,p2)- Ef_fitp1(p1,p2)(4), EbSIA_V p1 He p2 (p1,p2)= + -EbV_V p1 He p2 (p1,p2)(5), EbHe_V p1 He p2 (p1,p2)= Ef_fitp2(p1,p2+1)- Ef_fitp2(p1,p2)(6) ； For V p1 H p3 , V and V p1 H p3 Binding energy EbV_V p1 H p3 , self-interstitial atoms and V p1 H p3 Binding energy EbSIA_V p1 H p3 , H and V p1 H p3 Binding energy EbH_V p1 H p3 According to formulas (7) to (9), we can obtain: EbV_V p1 H p3 (p1,p3)= Ef_fitp1(p1+1,p3)- Ef_fitp1(p1,p3)(7), EbSIA_V p1 H p3 (p1,p3)= + -EbV_V p1 H p3 (p1,p3)(8), EbH_V p1 H p3 (p1,p3)= Ef_fitp3(p1,p3+1)- Ef_fitp3(p1,p3)(9) ； For V p1 He p2 H p3 , V and V p1 He p2 H p3 Binding energy EbV_V p1 He p2 H p3 , self-clearance and V p1 He p2 H p3 Binding energy EbSIA_V p1 He p2 H p3 , He and V p1 He p2 H p3 Binding energy EbHe_V p1 He p2 H p3 , H and V p1 He p2 H p3 Binding energy EbH_V p1 He p2 H p3 According to formulas (10) to (13), we can obtain: EbV_V p1 He p2 H p3 (p1,p2,p3)=Ef_fitp1(p1+1,p2,p3)-Ef_fitp1(p1,p2,p3)(10) ， EbSIA_V p1 He p2 H p3 (p1,p2,p3)= + -EbV_V p1 He p2 H p3 (p1,p2,p3)(11) ； EbHe_V p1 He p2 H p3 (p1,p2,p3)= Ef_fitp2(p1,p2+1,p3)- Ef_fitp2(p1,p2,p3)(12), EbH_V p1 He p2 H p3 (p1,p2,p3)= Ef_fitp3(p1,p2,p3+1)- Ef_fitp3(p1,p2,p3)(13); Among them, Ef_fitp1, Ef_fitp2, and Ef_fitp3 are the formation energies obtained after fitting along the directions of p1, p2, and p3, respectively. 、 are the formation energies of a single vacancy and a self-interstitial atom in the bulk region, respectively.

7. The calculation method according to claim 1, wherein: Step S3 is specifically as follows: If p1<p1 * , then the binding energy value obtained in step S2 is directly used, and p1* is the critical value, which is determined by the maximum vacancy cluster size that can be calculated based on the available computing resources; If p1≥p1*, the reduced variables are introduced, the He occupation ratio in the cavity is p2 / p1, and the H coverage ratio on the cavity surface is p3 / p1. 2 / 3 : For V p1 He p2 , the binding energy EbV_V obtained in step S2 p1 He p2 (p1,p2),EbHe_V p1 He p2 (p1,p2), converted to EbV_V p1 He p2 (p2 / p1), EbHe_V p1 He p2 (p2 / p1); let x=p2 / p1, and fit the relationship between binding energy and x according to formula (14): y=A2 + (A1 - A2) / (1 + )（14） ， Among them, A1, A2, x0, and dx are fitting parameters respectively; For V p1 H p3 , the binding energy EbV_V obtained in step S2 p1 H p3 (p1,p3),EbH_V p1 H p3 (p1,p3), converted to EbV_V p1 H p3 (p3 / p1 2 / 3 )、EbH_V p1 H p3 (p3 / p1 2 / 3 ); Let x = p3 / p1 2 / 3 , for EbV_V p1 H p3 (p3 / p1 2 / 3 ) According to formula (14), the relationship between binding energy and x is fitted; for EbH_V p1 H p3 (p3 / p1 2 / 3 ), and the relationship between binding energy and x is fitted according to formula (15): y= Intercept+B1x+B2x 2 +B3x 3 （15） ， Among them, Intercept, B1, B2, and B3 are fitting parameters respectively; For V p1 He p2 H p3 , let x1=p2 / p1, x2= p3 / p1 2 / 3 , V, He, H and V p1 He p2 H p3 The binding energy of (p1, p2, p3) can be transformed into the relationship between x1 and x2: divide the uniform lines in the x2 direction with an interval of dH. The minimum and maximum x2 in the x2 direction are 0 and maxx2 respectively. Then the grid nodes in the x2 direction are 0:dH:maxx2. For a given node x2i, find the data subset that falls on the x2i node by abs(x2-x2i)<0.5dH, and set it as Eb1_V p1 He p2 H p3 (x1,x2i); subset Eb1_V p1 He p2 H p3 (x1,x2i) data is fitted to x1, and the fitting function is ; Then bring in the homogenized x1 variable x1g to generate Eb1_V p1 He p2 H p3 (x1g,x2i); traverse the above x2 to generate V, He, H, SIA and V p1 He p2 H p3 Table of equally spaced binding energies.

8. A computer device / equipment / system, characterized in that: The method comprises a memory, a processor and a computer program stored in the memory, wherein the processor executes the computer program to implement the steps of the computing method according to any one of claims 1 to 7.

9. A computer-readable storage medium having a computer program / instruction stored thereon, characterized in that: When the computer program / instruction is executed by a processor, the steps of the computing method according to any one of claims 1 to 7 are implemented.

10. A computer program product comprising a computer program / instructions, characterized in that When the computer program / instruction is executed by a processor, the steps of the computing method according to any one of claims 1 to 7 are implemented.

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