Methods, systems, and computer storage media of determining the size distribution and number density of radiation-induced re-defect clusters in mo-re alloys under strain conditions

Abstract

Embodiments of the present application relate to the technical field of computer material science, in particular to a method, system and computer storage medium for determining size distribution and number density of Re-defect clusters generated by irradiation of Mo-Re alloy under strain condition. The method provided by the present application can apply strain to a pure molybdenum crystal supercell, and the strain can reflect stress, so as to determine the vacancy (V) formation energy, interstitial atom (SIA) formation energy of the pure molybdenum crystal supercell after being subjected to stress, and the Re atom solubility, Re-V binding energy and Re-SIA binding energy after being doped with Re, and on this basis, the diffusion barrier of defects of the pure molybdenum crystal supercell after being subjected to stress is combined to quantify the influence of stress on the diffusion energy barrier, so as to accurately simulate the structure evolution process of the Re-defect clusters generated by irradiation of the Mo-Re alloy under the strain condition, and make the determined size distribution and number density of the Re-defect clusters more consistent with the actual situation.

Description

Technical Field

[0001] The embodiments of this application relate to the field of computer materials science and technology, specifically to a method, system, and computer storage medium for determining the size distribution and number density of Re-defect clusters generated by irradiation of Mo-Re alloys under strain conditions. Background Technology

[0002] The statements herein are provided only as background information in connection with this application and do not necessarily constitute prior art.

[0003] Mo-Re alloys are widely used as structural materials for high-power new mass reactors due to their high melting point, low coefficient of thermal expansion, low density, low ductile-brittle transition temperature, and excellent high-temperature mechanical properties and creep resistance. However, Mo-Re alloys in the reactor core face a complex service environment of neutron irradiation and strain-coupled damage. As solute atoms, Re atoms in the alloy are prone to combine with irradiation-induced defects to form Re-defect clusters (such as Re-V complexes and Re-SIA complexes), which affect the mechanical properties of Mo-Re alloys and reduce the service life of structural materials made from them.

[0004] Therefore, in order to conduct long-term service evaluation of Mo-Re alloy structural materials, it is necessary to simulate the structural evolution process of Re-defect clusters generated by irradiation under strain conditions, so as to predict the performance changes of the alloy during actual reactor service. Summary of the Invention

[0005] A brief overview of this application is provided below to offer a basic understanding of certain aspects thereof. It should be understood that this overview is not an exhaustive summary of the application. It is not intended to identify key or essential parts of the application, nor is it intended to limit its scope. Its purpose is merely to present certain concepts in a simplified form as a prelude to the more detailed description that follows.

[0006] In a first aspect, embodiments of this application provide a method for determining the size distribution and number density of Re-defects generated by irradiation of a Mo-Re alloy under strain conditions, comprising the following steps: S10: determining the defects of a pure molybdenum crystal supercell; S20: determining, based on the defects of the pure molybdenum crystal supercell, the vacancy (V) formation energy, the interstitial atom (SIA) formation energy of the pure molybdenum crystal supercell, and the Re atom dissolution energy, Re-V binding energy, and Re-SIA binding energy after Re doping; S30: applying strain to the pure molybdenum crystal supercell and determining the strain; S40: determining, based on the strain, the vacancy (V) formation energy and the interstitial atom (SIA) formation energy of the pure molybdenum crystal supercell after the change. And the Re atom dissolution energy, Re-V binding energy, and Re-SIA binding energy after Re doping; S50: Determine the diffusion barrier of defects based on the defects in the pure molybdenum crystal supercell; S60: Apply strain to the pure molybdenum crystal supercell and determine the strain; determine the diffusion barrier of the changed defects based on the strain and the diffusion barrier of defects; S70: Determine the size distribution and number density of Re-defect clusters based on the vacancy (V) formation energy and interstitial atom (SIA) formation energy of the pure molybdenum crystal supercell determined in step S40, as well as the Re atom dissolution energy, Re-V binding energy, Re-SIA binding energy after Re doping, and the diffusion barrier of the changed defects determined in step S60.

[0007] The method provided in this application for determining the size distribution and number density of Re-defects generated by irradiation of Mo-Re alloys under strain conditions involves applying strain to a pure molybdenum crystal supercell. Strain can reflect stress, and by considering the stress on the pure molybdenum crystal supercell, the method determines the vacancy (V) formation energy, interstitial atom (SIA) formation energy, Re atom dissolution energy, Re-V binding energy, and Re-SIA binding energy after Re doping. Based on this, the method incorporates the diffusion barrier of defects in the pure molybdenum crystal supercell after stress to quantify the influence of stress on the diffusion barrier. This accurately simulates the structural evolution process of Re-defect clusters generated by irradiation of Mo-Re alloys under strain conditions, making the determined size distribution and number density of Re-defect clusters more consistent with the actual situation. This improves the accuracy of predicting performance changes in Mo-Re alloys and provides accurate data support for the long-term service evaluation of Mo-Re alloy structural materials.

[0008] Secondly, embodiments of this application provide a system for determining the size distribution and number density of Re-defects generated by irradiation of a Mo-Re alloy under strain conditions, comprising: a defect determination module and a processor. The defect determination module is configured to determine defects in a pure molybdenum crystal supercell. The processor is configured to, based on the defects in the pure molybdenum crystal supercell, determine the vacancy (V) formation energy, the interstitial atom (SIA) formation energy, and the Re atom dissolution energy, Re-V binding energy, and Re-SIA binding energy of the pure molybdenum crystal supercell; apply strain to the pure molybdenum crystal supercell and determine the strain; and, based on the strain, determine the vacancy (V) formation energy, the interstitial atom (SIA) formation energy, and the Re atom dissolution energy, Re-V binding energy, and Re-SIA binding energy of the changed pure molybdenum crystal supercell. IA binding energy; determine the diffusion barrier of defects based on the defects in the pure molybdenum crystal supercell; apply strain to the pure molybdenum crystal supercell and determine the strain; determine the diffusion barrier of the modified defects based on the strain and the diffusion barrier of the defects; determine the size distribution and number density of Re-defect clusters based on the vacancy (V) formation energy and interstitial atom (SIA) formation energy of the pure molybdenum crystal supercell after modification, as well as the Re atom dissolution energy, Re-V binding energy, Re-SIA binding energy, and the diffusion barrier of the modified defects after modification.

[0009] Thirdly, embodiments of this application provide a computer storage medium having a computer program stored thereon, the computer program being executed by a processor to implement the method provided in any embodiment of the first aspect of this application. Attached Figure Description

[0010] Other objects and advantages of this application will become apparent from the following description of embodiments of this application with reference to the accompanying drawings, and will help to provide a comprehensive understanding of this application.

[0011] Figure 1 This is a graph showing the change of the diffusion barrier of defects in a pure molybdenum crystal supercell under strain conditions, determined by the method provided in the embodiments of this application. Figure 2 This is a graph showing the relationship between the binding energy of Re-defect clusters in supercells with different Re-doping concentrations and the strain applied to the supercell, determined using the method provided in the embodiments of this application.

[0012] It should be noted that the accompanying drawings are not necessarily drawn to scale, but are shown only in a schematic manner without affecting the reader's understanding. Detailed Implementation

[0013] Exemplary embodiments of this application will be described below with reference to the accompanying drawings. For clarity and brevity, not all features of actual implementations are described in the specification. However, it should be understood that many implementation-specific decisions must be made in the development of any such actual embodiment to achieve the developer's specific goals, such as complying with constraints related to the system and business, and these constraints may vary depending on the implementation. Furthermore, it should be understood that while development work can be very complex and time-consuming, such development work is merely a routine task for those skilled in the art who benefit from the content of this application.

[0014] It should also be noted that, in order to avoid obscuring this application with unnecessary details, only the equipment structure and / or processing steps closely related to the solution according to this application are shown in the accompanying drawings, while other details that are not closely related to this application are omitted.

[0015] When Mo-Re alloys are in operation within a reactor, neutron irradiation induces atomic displacement and defect evolution, forming Re-defect clusters. This causes volume expansion and contraction of the Mo-Re alloy, generating irradiation-induced internal strain. Simultaneously, vacancies and interstitial atoms generated by irradiation interact with dislocations, inducing irradiation creep and exacerbating strain accumulation. In related technologies, when simulating the structural evolution of Re-defect clusters generated by irradiation under strain conditions to determine their size distribution and number density, the constructed pure molybdenum crystal supercell typically does not consider the stress on the supercell caused by irradiation-induced defects, nor does it account for external stresses on the supercell. This leads to significant deviations between the determined size distribution and number density of the Re-defect clusters and actual values.

[0016] Based on this, embodiments of this application provide a method for determining the size distribution and number density of Re-defect clusters generated by irradiation of Mo-Re alloys under strain conditions, comprising the following steps: S10: Determine the defects in the supercell of a pure molybdenum crystal.

[0017] S20: Based on the defects of the pure molybdenum crystal supercell, determine the vacancy (V) formation energy, the interstitial atom (SIA) formation energy, and the Re atom dissolution energy, Re-V binding energy, and Re-SIA binding energy of the pure molybdenum crystal supercell.

[0018] S30: Apply strain to the supercell of a pure molybdenum crystal and determine the strain.

[0019] S40: Based on strain, determine the vacancy (V) formation energy, interstitial atom (SIA) formation energy of the pure molybdenum crystal supercell after the change, as well as the Re atom dissolution energy, Re-V binding energy, and Re-SIA binding energy after Re doping.

[0020] S50: Determine the diffusion barrier of defects based on the defects in the supercell of a pure molybdenum crystal.

[0021] S60: Apply strain to the supercell of a pure molybdenum crystal and determine the strain; based on the strain and the diffusion barrier of the defect, determine the diffusion barrier of the defect after the change.

[0022] S70: Based on the vacancy (V) formation energy and interstitial atom (SIA) formation energy of the pure molybdenum crystal supercell after the change determined in step S40, as well as the Re atom dissolution energy, Re-V binding energy, Re-SIA binding energy after Re doping, and the diffusion barrier of the defect after the change determined in step S60, determine the size distribution and number density of Re-defect clusters.

[0023] The method provided in this application for determining the size distribution and number density of Re-defects generated by irradiation of Mo-Re alloys under strain conditions involves applying strain to a pure molybdenum crystal supercell. Strain can reflect stress, and by considering the stress on the pure molybdenum crystal supercell, the method determines the vacancy (V) formation energy, interstitial atom (SIA) formation energy, Re atom dissolution energy, Re-V binding energy, and Re-SIA binding energy after Re doping. Based on this, the method incorporates the diffusion barrier of defects in the pure molybdenum crystal supercell after stress to quantify the influence of stress on the diffusion barrier. This accurately simulates the structural evolution process of Re-defect clusters generated by irradiation of Mo-Re alloys under strain conditions, making the determined size distribution and number density of Re-defect clusters more consistent with the actual situation. This improves the accuracy of predicting performance changes in Mo-Re alloys and provides accurate data support for the long-term service evaluation of Mo-Re alloy structural materials.

[0024] In some embodiments, step S10 specifically includes the following steps: S11: constructing pure molybdenum crystal supercells with different strains; S12: determining the defects of pure molybdenum crystal supercells with different strains.

[0025] In some embodiments, in step S11, the constructed pure molybdenum crystal supercell can be a 4×4×4 pure molybdenum crystal supercell containing 128 atoms or a 5×5×5 pure molybdenum crystal supercell containing 250 atoms, in order to balance computational efficiency and eliminate the interaction between defects caused by periodic boundary conditions.

[0026] Furthermore, in step S11, when constructing pure molybdenum crystal supercells with different strains, structural relaxation of the supercell is also included. Specifically, within the framework of density functional theory (DFT), the exchange-correlation functional can be set to GGA-PBE, the plane wave cutoff energy to be 400-500 eV, the k-point grid density to be 3×3×3 or higher, and the energy convergence accuracy to be 1× eV / atom is used to obtain supercells with stable eigenstate configurations, providing a standardized model basis for subsequent simulations of the evolution of Re-defect cluster structures.

[0027] In some embodiments, step S20 specifically includes the following steps: S21: Determine the vacancy (V) formation energy and interstitial atom (SIA) formation energy of the pure molybdenum crystal supercell based on the defects of the pure molybdenum crystal supercell; S22: Construct molybdenum alloy supercells with different Re doping concentrations, and determine the Re atom dissolution energy, Re-V binding energy, and Re-SIA binding energy after Re doping based on the molybdenum alloy supercells with different Re doping concentrations.

[0028] For example, when constructing molybdenum alloy supercells with different Re doping concentrations, one can choose to construct a molybdenum alloy supercell containing 2-10 Re atoms.

[0029] In some embodiments, in step S22, the molybdenum alloy supercells with different Re doping concentrations can be 4×4×4 molybdenum alloy supercells containing 128 atoms or 5×5×5 molybdenum alloy supercells containing 250 atoms, in order to balance computational efficiency and eliminate the interaction between defects caused by periodic boundary conditions.

[0030] Furthermore, in step S22, when constructing molybdenum alloy supercells with different Re doping concentrations, structural relaxation of the supercell is also included. Specifically, within the framework of density functional theory (DFT), the exchange-correlation functional can be set to GGA-PBE, the plane wave cutoff energy to be 400-500 eV, the k-point grid density to be 3×3×3 or higher, and the energy convergence accuracy to be 1× eV / atom is used to obtain supercells with stable eigenstate configurations, providing a standardized model basis for subsequent simulations of the evolution of Re-defect cluster structures.

[0031] In some embodiments, in step S30, strain can be applied to the pure molybdenum crystal supercell by scaling its lattice constant. In this embodiment, applying strain to the pure molybdenum crystal supercell by scaling its lattice constant allows for accurate determination of the strain magnitude. This facilitates a more accurate reflection of the stress level experienced by the pure molybdenum crystal supercell, enabling a clearer understanding of the impact of the stress level on the structural evolution of Re-defect clusters and improving the accuracy of the determined size distribution and number density of the Re-defect clusters.

[0032] Specifically, in step S30, strain can be applied to the pure molybdenum crystal supercell by scaling the same lattice constant proportionally in three directions. The applied strain is a tensile or compressive strain of -5% to 5%, and hydrostatic strain can be used as an example.

[0033] In some embodiments, step S30 specifically includes the following steps: S31: Determine the lattice constant of the supercell before the change.

[0034] S32: Determine the lattice constant of the modified supercell.

[0035] S33: Determine the strain experienced by the supercell of pure molybdenum crystal based on the lattice constant of the supercell before and after the change.

[0036] Since the lattice constant of the supercell before the change is easy to determine, and the lattice constant of the supercell after the change can be determined empirically, it is beneficial to accurately obtain the lattice constants of the supercell before and after the change. Thus, by using the lattice constants before and after the change, it is relatively convenient to determine the strain on the pure molybdenum crystal supercell. This facilitates the quantification of the effects of stress on the vacancy (V) formation energy, interstitial atom (SIA) formation energy, and Re atom dissolution energy, Re-V binding energy, and Re-SIA binding energy of the pure molybdenum crystal supercell. Therefore, it is beneficial to further improve the simulation accuracy of the structural evolution process of Re-defect clusters in the alloy.

[0037] In some embodiments, in step S33, the lattice constant of the supercell before the change, the lattice constant of the supercell after the change, and the strain on the pure molybdenum crystal supercell conform to the following relationship: .

[0038] in, The lattice constant of the supercell before the change. The lattice constant of the supercell after the change. This represents the strain experienced by a pure molybdenum crystal supercell.

[0039] In this embodiment, by establishing the relationship between the lattice constant of the supercell before the change, the lattice constant of the supercell after the change, and the strain experienced by the pure molybdenum crystal supercell, the strain experienced by the pure molybdenum crystal supercell can be accurately determined based on the lattice constants of the supercell before and after the change.

[0040] In some embodiments, step S30 further includes the step of applying the same strain as that of a pure molybdenum crystal supercell to the molybdenum alloy supercells with different Re doping concentrations constructed in step S22, so as to determine the Re atom dissolution energy, Re-V binding energy, and Re-SIA binding energy after Re doping in step S40.

[0041] In some embodiments, step S40 specifically includes the following steps: S41: Based on strain, determine the total energy of a supercell containing one Re atom under strain conditions, the total energy of a supercell containing N Mo atoms under strain conditions, the total energy of a supercell containing one vacancy (V) under strain conditions, the total energy of a supercell containing one interstitial atom (SIA) under strain conditions, the total energy of a supercell containing n Re atoms and one vacancy (V) under strain conditions, the total energy of a supercell containing one interstitial atom (SIA) under strain conditions, and the total energy of a supercell containing n Re atoms and one interstitial atom (SIA) under strain conditions.

[0042] S42: Determine the vacancy (V) formation energy of the supercell containing one vacancy (V) under strain conditions and the total energy of the supercell containing N Mo atoms under strain conditions.

[0043] S43: Determine the formation energy of the interstitial atom (SIA) in the supercell of the pure molybdenum crystal after the change, based on the total energy of the supercell containing one interstitial atom (SIA) under strain conditions and the total energy of the supercell containing N Mo atoms under strain conditions.

[0044] S44: Determine the dissolution energy of Re atoms after Re doping based on the total energy of a supercell containing one Re atom under strain conditions and the total energy of a supercell containing N Mo atoms under strain conditions.

[0045] S45: Determine the Re-V binding energy after Re doping based on the total energy of a supercell containing one vacancy (V) under strain conditions, the total energy of a supercell containing one Re atom under strain conditions, the total energy of a supercell containing n Re atoms and one vacancy (V) under strain conditions, and the total energy of a supercell containing N Mo atoms under strain conditions.

[0046] S46: The Re-SIA binding energy after Re doping is calculated based on the total energy of a supercell containing one interstitial atom (SIA) under strain conditions, the total energy of a supercell containing one Re atom under strain conditions, the total energy of a supercell containing n Re atoms and one interstitial atom (SIA) under strain conditions, and the total energy of a supercell containing N Mo atoms under strain conditions.

[0047] In this embodiment, based on the strain experienced by the supercell, the total energy of a supercell containing one Re atom, a supercell containing N Mo atoms, a supercell containing one vacancy (V), a supercell containing one interstitial atom (SIA), a supercell containing n Re atoms and one vacancy (V), a supercell containing one interstitial atom (SIA), and a supercell containing n Re atoms and one interstitial atom (SIA) are determined under the strain condition. This is to quantify the influence of stress level on the supercell, thereby accurately determining the vacancy (V) formation energy, the interstitial atom (SIA) formation energy, the Re atom dissolution energy, the Re-V binding energy, and the Re-SIA binding energy of the pure molybdenum crystal supercell after the change.

[0048] In some embodiments, in step S42, the total energy of a supercell containing one vacancy (V) under strain conditions, the total energy of a supercell containing N Mo atoms under strain conditions, and the vacancy (V) formation energy of the modified pure molybdenum crystal supercell conform to the following relationship: .

[0049] in, The vacancy (V) formation energy of the supercell of the transformed pure molybdenum crystal. Let V be the total energy of a supercell containing one vacancy (V) under strain conditions. Let be the total energy of a supercell containing N Mo atoms under strain conditions, where N is the number of Mo atoms in the supercell.

[0050] In this embodiment, the relationship between the total energy of a supercell containing one vacancy (V) under strain conditions, the total energy of a supercell containing N Mo atoms, and the vacancy (V) formation energy of the supercell of the pure molybdenum crystal after the change is established, so as to further accurately determine the vacancy (V) formation energy of the supercell of the pure molybdenum crystal after strain.

[0051] In some embodiments, in step S43, the total energy of a supercell containing one interstitial atom (SIA) under strain conditions, the total energy of a supercell containing N Mo atoms under strain conditions, and the interstitial atom (SIA) formation energy of the modified pure molybdenum crystal supercell conform to the following relationship: .

[0052] in, The interstitial atom (SIA) formation energy of the supercell of the transformed pure molybdenum crystal. Let be the total energy of a supercell containing one interstitial atom (SIA) under strain conditions. Let be the total energy of a supercell containing N Mo atoms under strain conditions, where N is the number of Mo atoms in the supercell.

[0053] In this embodiment, the relationship between the total energy of a supercell containing one interstitial atom (SIA) under strain conditions, the total energy of a supercell containing N Mo atoms, and the interstitial atom (SIA) formation energy of the supercell of a pure molybdenum crystal after the change is established, so as to further accurately determine the interstitial atom (SIA) formation energy of the supercell of a pure molybdenum crystal after strain.

[0054] In some embodiments, in step S44, the total energy of a supercell containing one Re atom under strain conditions, the total energy of a supercell containing N Mo atoms under strain conditions, and the dissolution energy of Re atoms after Re doping conform to the following relationship: .

[0055] in, This represents the dissolution energy of Re atoms after Re doping. This represents the total energy of a supercell containing one Re atom under strain conditions. This represents the total energy of a supercell containing N Mo atoms under strain conditions. ν is the energy of a Re atom in the ground state, and N is the number of Mo atoms in the supercell.

[0056] In this embodiment, the relationship between the total energy of a supercell containing one Re atom and the total energy of a supercell containing N Mo atoms under strain conditions and the dissolution energy of Re atoms after Re doping is established. This facilitates a more accurate determination of the dissolution energy of Re atoms after Re doping, thereby making the size distribution and number density of the subsequently determined Re-defect clusters more consistent with the actual situation.

[0057] In some embodiments, in step S45, the total energy of a supercell containing one vacancy (V) under strain conditions, the total energy of a supercell containing one Re atom under strain conditions, the total energy of a supercell containing n Re atoms and one vacancy (V) under strain conditions, the total energy of a supercell containing N Mo atoms under strain conditions, and the Re-V binding energy after Re doping conform to the following relationship: .

[0058] in, This represents the Re-V binding energy after Re doping. Let V be the total energy of a supercell containing one vacancy (V) under strain conditions. This represents the total energy of a supercell containing one Re atom under strain conditions. Let be the total energy of a supercell containing n Re atoms and one vacancy (V) under strain conditions. Let n be the total energy of a supercell containing N Mo atoms under strain conditions, where n is the number of Re atoms in the supercell and N is the number of Mo atoms in the supercell.

[0059] In this embodiment, the relationship between the total energy of a supercell containing one vacancy (V) under strain conditions, the total energy of a supercell containing one Re atom, the total energy of a supercell containing n Re atoms and one vacancy (V), the total energy of a supercell containing N Mo atoms, and the Re-V binding energy after Re doping is established, so as to further accurately determine the Re-V binding energy after Re doping.

[0060] In some embodiments, in step S46, the total energy of a supercell containing one interstitial atom (SIA) under strain conditions, the total energy of a supercell containing one Re atom under strain conditions, the total energy of a supercell containing n Re atoms and one interstitial atom (SIA) under strain conditions, the total energy of a supercell containing N Mo atoms under strain conditions, and the Re-SIA binding energy after Re doping conform to the following relationship: .

[0061] in, This represents the Re-SiA binding energy after Re doping. Let be the total energy of a supercell containing one interstitial atom (SIA) under strain conditions. This represents the total energy of a supercell containing one Re atom under strain conditions. Let be the total energy of a supercell containing n Re atoms and one interstitial atom (SIA) under strain conditions. Let n be the total energy of a supercell containing N Mo atoms under strain conditions, where n is the number of Re atoms in the supercell and N is the number of Mo atoms in the supercell.

[0062] In this embodiment, the relationship between the total energy of a supercell containing one interstitial atom (SIA) under strain conditions, the total energy of a supercell containing one Re atom, the total energy of a supercell containing n Re atoms and one interstitial atom (SIA), the total energy of a supercell containing N Mo atoms, and the Re-SIA binding energy after Re doping is established, so as to further improve the accuracy of determining the Re-SIA binding energy after Re doping.

[0063] In step S50, those skilled in the art can determine the diffusion barrier of defects based on the defects in the supercell of a pure molybdenum crystal using methods disclosed in the related art.

[0064] In some embodiments, in step S60, the diffusion barrier of the defect after the change can be determined as follows: For a strained pure molybdenum crystal supercell, two Re atom migration path models for diffusion via vacancy mechanism and interstitial mechanism are constructed using the elastic band method (NEB), where the interstitial path needs to simulate its translation and rotation process. Then, by performing a transition state search on the path, the energy difference between the highest point (transition state) of the interstitial path and the starting point is determined, and the diffusion barrier of the defect after the change is obtained.

[0065] like Figure 1 As shown, Figure 1 The diagram shows the variation of the diffusion barrier of defects in a pure molybdenum crystal supercell under strain conditions, determined by the method provided in the embodiments of this application. Figure 1 Curve 10 represents the change of the diffusion energy barrier of the defect under compressive strain with strain, and curve 20 represents the change of the diffusion energy barrier of the defect under tensile strain with strain.

[0066] In some embodiments, step S60 further includes the step of applying the same strain as that of a pure molybdenum crystal supercell to the molybdenum alloy supercells with different Re doping concentrations constructed in step S22.

[0067] In some embodiments, step S70 specifically includes the following steps: S71: Determine the binding energy of the modified Re-defect clusters based on the vacancy (V) formation energy and interstitial atom (SIA) formation energy of the modified pure molybdenum crystal supercell, as well as the Re atom dissolution energy, Re-V binding energy, and Re-SIA binding energy after Re doping.

[0068] S72: Determine the strain-dependent diffusion coefficient based on the vacancy (V) formation energy of the modified pure molybdenum crystal supercell, the Re-V binding energy after Re doping, and the diffusion barrier of the modified defect.

[0069] S73: Determine the size distribution and number density of Re-defect clusters based on the binding energy of the modified Re-defect clusters, the diffusion barrier of the modified defects, and the strain-dependent diffusion coefficient.

[0070] In this embodiment, by determining the binding energy of the modified Re-defect clusters and combining it with the diffusion energy barrier of the modified pure molybdenum crystal supercell defects determined in step S60, the temperature dependence of the diffusion coefficient is determined to obtain the strain-dependent diffusion coefficient. This quantifies the regulatory effect of strain on the diffusion behavior of defects in the pure molybdenum crystal supercell, thereby facilitating the accurate simulation of the structural evolution process of the Re-defect clusters in the alloy and improving the accuracy of the determined size distribution and number density of the Re-defect clusters.

[0071] In some embodiments, step S71 specifically includes: based on the vacancy (V) formation energy and interstitial atom (SIA) formation energy of the pure molybdenum crystal supercell after the change, as well as the Re atom dissolution energy, Re-V binding energy, and Re-SIA binding energy after Re doping, and based on the molybdenum alloy supercells with different Re doping concentrations constructed in step S22, performing structural relaxation and energy calculations to obtain the binding energy of the Re-defect clusters under the given strain condition. Further, by changing the magnitude of the strain applied to the supercell in step S60, the binding energy of the Re-defect clusters under different strains is determined in step S71.

[0072] like Figure 2 As shown, Figure 2 The diagram illustrates the relationship between the binding energy of Re-defect clusters in supercells with different Re-doping concentrations and the strain applied to the supercell, determined using the method provided in the embodiments of this application. Figure 2 In the figure, curves 1-6 represent the relationship between the binding energy of Re-defect clusters containing 2-7 Re atoms in a supercell and the strain they are subjected to.

[0073] In some embodiments, in step S72, the vacancy (V) formation energy of the modified pure molybdenum crystal supercell, the Re-V binding energy after Re doping, the diffusion barrier of the modified defect, and the strain-dependent diffusion coefficient conform to the following relationship: .

[0074] in, The diffusion coefficient is a strain-dependent factor. The vacancy (V) formation energy of the supercell of the transformed pure molybdenum crystal. This represents the Re-V binding energy after Re doping. The diffusion barrier of the defect after the change. The diffusion coefficient is the one without strain. is Boltzmann's constant, and T is temperature.

[0075] In this embodiment, the relationship between the vacancy (V) formation energy of the modified pure molybdenum crystal supercell, the Re-V binding energy after Re doping, the diffusion barrier of the modified defect, and the strain-dependent diffusion coefficient is established. This facilitates the accurate determination of the strain-dependent diffusion coefficient, thereby precisely quantifying the regulatory effect of strain on the diffusion behavior of defects in the pure molybdenum crystal supercell. This provides an accurate data basis for subsequent simulation of the structural evolution of Re-defect clusters in the alloy and for determining the size distribution and number density of Re-defect clusters.

[0076] It should be noted that in the above relation, This represents the activation energy, which is the core variable affected by the regulatory effect of strain on diffusion behavior.

[0077] In some embodiments, step S73 specifically includes the following steps: S731: Simulate the nucleation, growth and aggregation process of Re-defect clusters based on the binding energy of the changed Re-defect clusters, the diffusion barrier of the changed defects and the strain-dependent diffusion coefficient; S732: Determine the size distribution and number density of Re-defect clusters based on the simulation results.

[0078] In some embodiments, in step S731, the binding energy of the modified Re-defect cluster, the diffusion barrier of the modified defect, and the strain-dependent diffusion coefficient can be input into the cluster dynamics simulation model, and different boundary conditions such as strain intensity, Re atom concentration, and defect injection rate can be set to simulate the entire process of nucleation, growth, and aggregation of Re-defect clusters.

[0079] Embodiments of this application also provide a system for determining the size distribution and number density of Re-defect clusters generated by irradiation of Mo-Re alloys under strain conditions, comprising: a defect determination module and a processor. The defect determination module is configured to determine defects in a pure molybdenum crystal supercell. The processor is configured to, based on the defects in the pure molybdenum crystal supercell, determine the vacancy (V) formation energy, the interstitial atom (SIA) formation energy, and the Re atom dissolution energy, Re-V binding energy, and Re-SIA binding energy of the pure molybdenum crystal supercell; apply strain to the pure molybdenum crystal supercell and determine the strain; and, based on the strain, determine the vacancy (V) formation energy, the interstitial atom (SIA) formation energy, and the Re atom dissolution energy, Re-V binding energy, and Re-SIA binding energy of the changed pure molybdenum crystal supercell. IA binding energy; determine the diffusion barrier of defects based on the defects in the pure molybdenum crystal supercell; apply strain to the pure molybdenum crystal supercell and determine the strain; determine the diffusion barrier of the modified defects based on the strain and the diffusion barrier of the defects; determine the size distribution and number density of Re-defect clusters based on the vacancy (V) formation energy and interstitial atom (SIA) formation energy of the pure molybdenum crystal supercell after modification, as well as the Re atom dissolution energy, Re-V binding energy, Re-SIA binding energy, and the diffusion barrier of the modified defects after modification.

[0080] The system provided in this application for determining the size distribution and number density of Re-defects generated by irradiation of Mo-Re alloys under strain conditions, applies strain to a pure molybdenum crystal supercell. Strain reflects stress, and by considering the stress on the pure molybdenum crystal supercell, the system determines the vacancy (V) formation energy, interstitial atom (SIA) formation energy, Re atom dissolution energy, Re-V binding energy, and Re-SIA binding energy after Re doping. Furthermore, by incorporating the diffusion barrier of defects in the pure molybdenum crystal supercell under stress, the system quantifies the impact of stress on the diffusion barrier. This accurately simulates the structural evolution of Re-defect clusters generated by irradiation of Mo-Re alloys under strain conditions, making the determined size distribution and number density of Re-defect clusters more consistent with actual conditions. This improves the accuracy of predicting performance changes in Mo-Re alloys and provides accurate data support for the long-term service evaluation of Mo-Re alloy structural materials.

[0081] Embodiments of this application also provide a computer storage medium having a computer program stored thereon, the computer program being executed by a processor to implement the method provided in any embodiment of the first aspect of this application.

[0082] Regarding the embodiments of this application, it should also be noted that, without conflict, the embodiments of this application and the features in the embodiments can be combined with each other to obtain new embodiments.

[0083] The above are merely specific embodiments of this application, but the scope of protection of this application is not limited thereto. The scope of protection of this application shall be determined by the scope of the claims.

Claims

1. A method for determining the size distribution and number density of Re-defect clusters generated by irradiation in Mo-Re alloys under strain conditions, characterized in that, It includes the following steps: S10: Determine the defects in the supercell of a pure molybdenum crystal; S20: Based on the defects of the pure molybdenum crystal supercell, determine the vacancy (V) formation energy of the pure molybdenum crystal supercell, the interstitial atom (SIA) formation energy of the pure molybdenum crystal supercell, and the Re atom dissolution energy, Re-V binding energy, and Re-SIA binding energy after Re doping; S30: Apply strain to the pure molybdenum crystal supercell and determine the strain; S40: Based on the strain, determine the vacancy (V) formation energy, the interstitial atom (SIA) formation energy of the pure molybdenum crystal supercell after the change, and the Re atom dissolution energy, Re-V binding energy, and Re-SIA binding energy after Re doping. S50: Determine the diffusion barrier of the defects based on the defects in the pure molybdenum crystal supercell; S60: Apply strain to the pure molybdenum crystal supercell and determine the strain; determine the changed diffusion barrier of the defect based on the strain and the diffusion barrier of the defect; S70: Based on the vacancy (V) formation energy of the pure molybdenum crystal supercell after the change determined in step S40, the interstitial atom (SIA) formation energy of the pure molybdenum crystal supercell, the Re atom dissolution energy, Re-V binding energy, Re-SIA binding energy after Re doping, and the diffusion barrier of the defect after the change determined in step S60, determine the size distribution and number density of the Re-defect clusters.

2. The method according to claim 1, characterized in that, In step S30, strain is applied to the pure molybdenum crystal supercell by scaling the lattice constant of the pure molybdenum crystal supercell.

3. The method according to claim 1, characterized in that, Step S30 specifically includes the following steps: S31: Determine the lattice constant of the supercell before the change; S32: Determine the lattice constant of the modified supercell; S33: Determine the strain experienced by the pure molybdenum crystal supercell based on the lattice constant of the supercell before the change and the lattice constant of the supercell after the change.

4. The method according to claim 3, characterized in that, In step S33, the lattice constant of the supercell before the change, the lattice constant of the supercell after the change, and the strain experienced by the pure molybdenum crystal supercell conform to the following relationship: ， in, The lattice constant of the supercell before the change is given. The lattice constant of the modified supercell is given. The strain experienced by the supercell of the pure molybdenum crystal is denoted as .

5. The method according to claim 1, characterized in that, Step S40 specifically includes the following steps: S41: Based on the strain, determine the total energy of a supercell containing one Re atom under strain conditions, the total energy of a supercell containing N Mo atoms under strain conditions, the total energy of a supercell containing one vacancy (V) under strain conditions, the total energy of a supercell containing one interstitial atom (SIA) under strain conditions, the total energy of a supercell containing n Re atoms and one vacancy (V) under strain conditions, the total energy of a supercell containing one interstitial atom (SIA) under strain conditions, and the total energy of a supercell containing n Re atoms and one interstitial atom (SIA) under strain conditions. S42: Determine the vacancy (V) formation energy of the supercell containing one vacancy (V) under the strain condition and the total energy of the supercell containing N Mo atoms under the strain condition. S43: Determine the interstitial atom (SIA) formation energy of the supercell containing one interstitial atom (SIA) under the strain conditions and the total energy of the supercell containing N Mo atoms under the strain conditions. S44: Determine the Re atom dissolution energy after Re doping based on the total energy of the supercell containing one Re atom under the strain conditions and the total energy of the supercell containing N Mo atoms under the strain conditions; S45: Determine the Re-V binding energy after Re doping based on the total energy of the supercell containing one vacancy (V) under the strain conditions, the total energy of the supercell containing one Re atom under the strain conditions, the total energy of the supercell containing n Re atoms and one vacancy (V) under the strain conditions, and the total energy of the supercell containing N Mo atoms under the strain conditions. S46: Determine the Re-SIA binding energy after Re doping based on the total energy of the supercell containing one interstitial atom (SIA) under the strain conditions, the total energy of the supercell containing one Re atom under the strain conditions, the total energy of the supercell containing n Re atoms and one interstitial atom (SIA) under the strain conditions, and the total energy of the supercell containing N Mo atoms under the strain conditions.

6. The method according to claim 5, characterized in that, In step S42, the total energy of the supercell containing one vacancy (V) under the strain condition, the total energy of the supercell containing N Mo atoms under the strain condition, and the vacancy (V) formation energy of the changed pure molybdenum crystal supercell conform to the following relationship: ， in, The vacancy (V) formation energy of the supercell of the pure molybdenum crystal after the aforementioned change. Let V be the total energy of the supercell containing one vacancy (V) under the strain condition. Let N be the total energy of a supercell containing N Mo atoms under the strain condition, where N is the number of Mo atoms in the supercell.

7. The method according to claim 5, characterized in that, In step S43, the total energy of the supercell containing one interstitial atom (SIA) under the strain condition, the total energy of the supercell containing N Mo atoms under the strain condition, and the interstitial atom (SIA) formation energy of the modified pure molybdenum crystal supercell conform to the following relationship: ， in, The interstitial atom (SIA) formation energy of the supercell of the pure molybdenum crystal after the aforementioned transformation. Let be the total energy of the supercell containing one interstitial atom (SIA) under the strain condition. Let N be the total energy of a supercell containing N Mo atoms under the strain condition, where N is the number of Mo atoms in the supercell.

8. The method according to claim 5, characterized in that, In step S44, the total energy of the supercell containing one Re atom under the strain condition, the total energy of the supercell containing N Mo atoms under the strain condition, and the dissolution energy of the Re atom after Re doping conform to the following relationship: ， in, The dissolution energy of the Re atoms after Re doping is given. The total energy of a supercell containing one Re atom under the strain condition is given. The total energy of the supercell containing N Mo atoms under the strain condition is given. is the energy of a Re atom in the ground state, and N is the number of Mo atoms in the supercell.

9. The method according to claim 5, characterized in that, In step S45, the total energy of the supercell containing one vacancy (V) under the strain condition, the total energy of the supercell containing one Re atom under the strain condition, the total energy of the supercell containing n Re atoms and one vacancy (V) under the strain condition, the total energy of the supercell containing N Mo atoms under the strain condition, and the Re-V binding energy after Re doping conform to the following relationship: ， in, The Re-V binding energy after Re doping is given. Let V be the total energy of the supercell containing one vacancy (V) under the strain condition. The total energy of a supercell containing one Re atom under the strain condition is given. Let be the total energy of the supercell containing n Re atoms and one vacancy (V) under the strain condition. Let n be the total energy of a supercell containing N Mo atoms under the strain condition, where n is the number of Re atoms in the supercell and N is the number of Mo atoms in the supercell.

10. The method according to claim 5, characterized in that, In step S46, the total energy of the supercell containing one interstitial atom (SIA) under the strain condition, the total energy of the supercell containing one Re atom under the strain condition, the total energy of the supercell containing n Re atoms and one interstitial atom (SIA) under the strain condition, the total energy of the supercell containing N Mo atoms under the strain condition, and the Re-SIA binding energy after Re doping conform to the following relationship: ， in, The Re-SiA binding energy after Re doping is given. Let be the total energy of the supercell containing one interstitial atom (SIA) under the strain condition. The total energy of a supercell containing one Re atom under the strain condition is given. Let be the total energy of the supercell containing n Re atoms and one interstitial atom (SIA) under the strain condition. Let n be the total energy of a supercell containing N Mo atoms under the strain condition, where n is the number of Re atoms in the supercell and N is the number of Mo atoms in the supercell.

11. The method according to claim 1, characterized in that, Step S70 specifically includes the following steps: S71: Determine the binding energy of the modified Re-defect clusters based on the vacancy (V) formation energy of the modified pure molybdenum crystal supercell, the interstitial atom (SIA) formation energy of the modified pure molybdenum crystal supercell, and the Re atom dissolution energy, Re-V binding energy, and Re-SIA binding energy after Re doping. S72: Determine the strain-dependent diffusion coefficient based on the vacancy (V) formation energy of the modified pure molybdenum crystal supercell, the Re-V binding energy after Re doping, and the diffusion barrier of the modified defect. S73: Determine the size distribution and number density of the Re-defect clusters based on the binding energy of the modified Re-defect clusters, the diffusion barrier of the modified defects, and the strain-dependent diffusion coefficient.

12. The method according to claim 11, characterized in that, In step S72, the vacancy (V) formation energy of the modified pure molybdenum crystal supercell, the Re-V binding energy after Re doping, the diffusion barrier of the modified defect, and the strain-dependent diffusion coefficient conform to the following relationship: ， in, The strain-dependent diffusion coefficient is... The vacancy (V) formation energy of the supercell of the pure molybdenum crystal after the aforementioned change. The Re-V binding energy after Re doping is given. The diffusion barrier of the defect after the change. The diffusion coefficient is the one without strain. is Boltzmann's constant, and T is temperature.

13. A system for determining the size distribution and number density of Re-defect clusters generated by irradiation in Mo-Re alloys under strain conditions, characterized in that, It includes: A defect determination module, configured to determine defects in a pure molybdenum crystal supercell; The processor is configured to determine, based on the defects of the pure molybdenum crystal supercell, the vacancy (V) formation energy of the pure molybdenum crystal supercell, the interstitial atom (SIA) formation energy of the pure molybdenum crystal supercell, and the Re atom dissolution energy, Re-V binding energy, and Re-SIA binding energy of the Re-doped Re atom. Strain is applied to the pure molybdenum crystal supercell, and the strain is determined; Based on the strain, the vacancy (V) formation energy, the interstitial atom (SIA) formation energy of the pure molybdenum crystal supercell after the change, and the Re atom dissolution energy, Re-V binding energy, and Re-SIA binding energy after Re doping are determined. Based on the defects in the pure molybdenum crystal supercell, determine the diffusion barrier of the defects; Strain is applied to the pure molybdenum crystal supercell, and the strain is determined; based on the strain and the diffusion barrier of the defect, the diffusion barrier of the defect after the change is determined; The size distribution and number density of Re-defect clusters are determined based on the vacancy (V) formation energy of the modified pure molybdenum crystal supercell, the interstitial atom (SIA) formation energy of the pure molybdenum crystal supercell, the Re atom dissolution energy, Re-V binding energy, Re-SIA binding energy, and the diffusion barrier of the modified defects.

14. A computer storage medium, characterized in that, It stores a computer program thereon, which is executed by a processor to implement the method as described in any one of claims 1-12.

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