A method of predicting precipitate size and number density of an aluminum alloy under neutron irradiation

Abstract

The application provides a method for predicting precipitate size and number density of an aluminum alloy under neutron irradiation, comprising calculating a primary knock-on atom energy spectrum, establishing a cascade database according to the primary knock-on atom energy spectrum, the cascade database comprising a plurality of matrix defect information; calculating defect energy properties, obtaining a defect equilibrium concentration according to the defect energy properties and the matrix defect information; calculating a defect diffusion coefficient of a solute atom according to the defect energy properties, and calculating an irradiation-enhanced diffusion coefficient according to the defect diffusion coefficient and the defect equilibrium concentration; calculating a solute defect generation rate, and obtaining irradiation defect information of the aluminum alloy to be predicted according to the generation rate and the irradiation-enhanced diffusion coefficient, the irradiation defect information comprising the precipitate size and the precipitate number density. The method for predicting the precipitate size and the number density of the aluminum alloy under the neutron irradiation can accurately calculate the irradiation defect information of the aluminum alloy to be predicted, so as to subsequently analyze and predict the irradiation performance and the material life.

Description

Technical Field

[0001] This application relates primarily to the field of reactor technology, and more particularly to a method for predicting the size and number density of precipitated phases in aluminum alloys under neutron irradiation. Background Technology

[0002] Nuclear energy, as a stable and clean energy source, plays a vital role in optimizing the energy structure. In nuclear energy applications, research reactors are key facilities for conducting research such as materials irradiation experiments and radioactive isotope production. Under the corresponding service environment, the core structural materials of research reactors, irradiated by high-energy particles (thermal neutrons), will develop a series of irradiation defects, leading to material hardening and embrittlement, ultimately resulting in severe degradation of the material's mechanical properties and affecting its service life. Summary of the Invention

[0003] The technical problem to be solved by this application is to provide a method for predicting the size and number density of precipitated phases in aluminum alloys under neutron irradiation, which can accurately calculate the irradiation defect information of the aluminum alloy to be predicted so as to carry out subsequent irradiation performance and material life analysis and prediction.

[0004] To address the aforementioned technical problems, this application provides a method for predicting the size and number density of precipitated phases in aluminum alloys under neutron irradiation. This method is applicable to reactor research reactors, where the reactor research reactor includes an aluminum alloy to be predicted. The aluminum alloy to be predicted includes a matrix and a solute, with the solute comprising solute atoms. The method includes the following steps: calculating the primary impact atomic energy spectrum; establishing a cascaded database based on the primary impact atomic energy spectrum, the cascaded database including multiple matrix defect information; calculating defect energy properties; obtaining the defect equilibrium concentration based on the defect energy properties and the matrix defect information; calculating the defect diffusion coefficient of the solute atoms based on the defect energy properties; calculating the irradiation-enhanced diffusion coefficient based on the defect diffusion coefficient and the defect equilibrium concentration; calculating the solute defect generation rate; and obtaining the irradiation defect information of the aluminum alloy to be predicted based on the generation rate and the irradiation-enhanced diffusion coefficient, the irradiation defect information including the precipitated phase size and the precipitated phase number density.

[0005] Optionally, the matrix includes matrix atoms, and establishing a cascade database based on the primary impact-ejection atomic energy spectrum includes: performing simulation initialization and setting a simulation box, the simulation box including the matrix atoms; extracting simulated atoms from the primary impact-ejection atomic energy spectrum, adding the simulated atoms to the simulation box to cause the simulated atoms to collide with the matrix atoms to form a collision cascade; obtaining the matrix defect information corresponding to the simulated atoms based on the collision cascade, and storing the matrix defect information in the cascade database.

[0006] Optionally, calculating the defect energy properties includes the following steps: obtaining the supercell morphology of the aluminum alloy to be predicted, adding irradiation defects to the supercell morphology to construct a crystal defect structure of the aluminum alloy to be predicted; performing relaxation calculations based on the crystal defect structure to obtain a stable configuration of the aluminum alloy to be predicted, and performing supercell energy calculations based on the stable configuration to obtain the supercell energy; and calculating the defect energy properties based on the supercell energy.

[0007] Optionally, obtaining the defect equilibrium concentration based on the defect energy properties and the matrix defect information includes: creating a cascade insertion weight file based on the primary impact atomic energy spectrum, presetting a neutron irradiation flux rate, and calculating the cascade insertion rate based on the cascade insertion weight file and the neutron irradiation flux rate; constructing a thermally activated event database based on the defect energy properties, and constructing a reaction event database based on the thermally activated event database and the spontaneous event database; dividing the reaction event database to obtain simulated reaction sub-regions, calculating the occurrence rate of each possible event in the simulated reaction sub-regions, and calculating the total occurrence rate of reaction events based on the occurrence rate of each possible event; and obtaining the defect equilibrium concentration based on the total occurrence rate of reaction events using a first defect evolution model.

[0008] Optionally, this includes calculating the occurrence rate of each of the possible events using the following formula:

[0009] in, The occurrence rate of each of the possible events; Represents the vibration rate for each of the possible events; Boltzmann's constant; The system temperature; For leapfrog energy barrier.

[0010] Optionally, the defect equilibrium concentration includes vacancy saturation concentration and / or interstitial saturation concentration.

[0011] Optionally, calculating the primary impact-ejected atomic energy spectrum includes the following steps: obtaining the target neutron energy spectrum and the target nuclide database; and performing a scattering matrix transformation based on the target neutron energy spectrum and the target nuclide database to obtain the primary impact-ejected atomic energy spectrum.

[0012] Optionally, the target neutron energy spectrum includes target neutron flux energy group intervals and flux values ​​of different energy groups; and / or, the target nuclide database includes one or any combination of the number, type, element number, relative atomic mass, ratio, ex-situ threshold energy, and reaction cross section of the target nuclides.

[0013] Optionally, the defect energy properties include one or any combination of defect formation energy, binding energy, and diffusion barrier.

[0014] Optionally, the defect diffusion coefficient may be calculated according to the following formula:

[0015] in, For different diffusion mechanisms, the jump coefficients are... is the lattice constant. The vibration frequency corresponding to the corresponding type of diffusion mechanism. This represents the diffusion energy barrier corresponding to the diffusion mechanism through which the defect diffuses. Boltzmann's constant, The temperature is the system temperature.

[0016] Optionally, the irradiation-enhanced diffusion coefficient may be calculated using the following formula:

[0017] in, and These are the correlation coefficients for the vacancies and interstitial diffusion mechanisms of the solute atoms, respectively. and These represent the saturation concentrations of vacancies and interstitials, respectively. and These are the diffusion coefficients of the solute atoms through vacancy and interstitial diffusion mechanisms, respectively.

[0018] Optionally, calculating the generation rate of the solute defect includes the following steps: obtaining the multi-group neutron fluence energy spectrum based on the target neutron energy spectrum; obtaining the cumulative generation amount of the solute based on the material composition of the aluminum alloy to be predicted, the reaction cross section of each nuclide, the decay constant of each nuclide, the multi-group neutron fluence energy spectrum, the neutron capture coupling differential equation set, and the decay coupling differential equation set; and obtaining the generation rate based on the cumulative generation amount.

[0019] Optionally, obtaining the irradiation defect information of the aluminum alloy to be predicted based on the generation rate and the irradiation-enhanced diffusion coefficient includes the following steps: initializing the irradiation defect evolution model through evolution simulation; calculating the diffusion flux and nucleation driving force of the solute based on the irradiation-enhanced diffusion coefficient and the generation rate, and calculating the critical nucleation radius and critical nucleation activation energy of the precipitate based on the nucleation driving force; calculating the nucleation rate based on the critical nucleation radius and the critical nucleation activation energy, and calculating the growth rate of the precipitate based on the nucleation rate; calculating the amount of precipitate generated and the size change within a simulation time based on the growth rate of the precipitate; and calculating the precipitate size and the precipitate number density based on the amount of precipitate generated and the size change.

[0020] To address the aforementioned technical problems, this application provides a system for predicting the size and number density of precipitated phases in aluminum alloys under neutron irradiation, comprising: a memory for storing instructions executable by a processor; and a processor for executing the instructions to implement the method described above.

[0021] To address the aforementioned technical problems, this application provides a computer-readable medium storing computer program code, which, when executed by a processor, implements the method described above.

[0022] Compared with existing technologies, this application establishes a cascaded database through primary impact atomic energy spectrum, which can effectively simulate the generation of irradiation defects in the aluminum alloy to be predicted by neutrons in a real nuclear reactor, and obtain information on the generation rate of matrix defects related to irradiation defects such as vacancies and interstitials. Furthermore, by calculating the energy properties of defects, the overall evolution of irradiation defects is simulated to obtain the defect equilibrium concentration, thereby calculating the irradiation-enhanced diffusion coefficient. Finally, by calculating parameters such as the generation rate of solute defects and the irradiation-enhanced diffusion coefficient, the nucleation and growth of irradiated precipitates is simulated, ultimately obtaining irradiation defect information including precipitate size and number density. This allows for accurate calculation of the irradiation defect information of the aluminum alloy to be predicted, facilitating subsequent analysis and prediction of irradiation performance and material lifetime. Attached Figure Description

[0023] The accompanying drawings are included to provide a further understanding of this application; they are incorporated into and constitute a part of this application. The drawings illustrate embodiments of this application and, together with this specification, serve to explain the principles of this application. In the drawings: Figure 1 This is a flowchart illustrating a method for predicting the size and number density of precipitated phases in aluminum alloys under neutron irradiation, according to one embodiment of this application. Figure 2 This is a schematic diagram of the primary impact atomic energy spectrum in a method for predicting the size and number density of precipitated phases in aluminum alloys under neutron irradiation, according to an embodiment of this application. Figure 3 This is a schematic diagram of the structure in which the primary ejected atoms collide with the matrix in a method for predicting the size and number density of precipitated phases in aluminum alloys under neutron irradiation, according to an embodiment of this application; Figure 4 This is a schematic diagram of the module structure of a system for predicting the size and number density of precipitated phases in aluminum alloys under neutron irradiation, according to one embodiment of this application. Detailed Implementation

[0024] To more clearly illustrate the technical solutions of the embodiments of this application, the accompanying drawings used in the description of the embodiments will be briefly introduced below. Obviously, the drawings described below are merely some examples or embodiments of this application. For those skilled in the art, these drawings can be applied to other similar scenarios without creative effort. Unless obvious from the context or otherwise specified, the same reference numerals in the drawings represent the same structures or operations.

[0025] As indicated in this application and claims, unless the context clearly indicates otherwise, the words "a," "an," "an," and / or "the" are not specifically singular and may include plural forms. Generally speaking, the terms "comprising" and "including" only indicate the inclusion of explicitly identified steps and elements, which do not constitute an exclusive list, and the method or apparatus may also include other steps or elements.

[0026] Unless otherwise specifically stated, the relative arrangement, numerical expressions, and values ​​of the components and steps described in these embodiments do not limit the scope of this application. It should also be understood that, for ease of description, the dimensions of the various parts shown in the drawings are not drawn to actual scale. Techniques, methods, and devices known to those skilled in the art may not be discussed in detail, but where appropriate, such techniques, methods, and devices should be considered part of the specification. In all examples shown and discussed herein, any specific values ​​should be interpreted as merely exemplary and not as limitations. Therefore, other examples of exemplary embodiments may have different values. It should be noted that similar reference numerals and letters in the following drawings denote similar items; therefore, once an item is defined in one drawing, it need not be further discussed in subsequent drawings.

[0027] This application refers to Figure 1 A method 10 (hereinafter referred to as "Method 10") for predicting the size and number density of precipitated phases in aluminum alloys under neutron irradiation is proposed. This method is applicable to a reactor research reactor, which includes an aluminum alloy to be predicted. The aluminum alloy includes a matrix and a solute. In this embodiment, the matrix refers to pure aluminum, and the solute refers to alloying elements (e.g., magnesium) and transmutation elements (e.g., silicon). Flowcharts are used in this application to illustrate the operations performed by the system according to embodiments of this application. It should be understood that the preceding or following operations are not necessarily performed precisely in sequence. Instead, various steps can be processed in reverse order or simultaneously. Simultaneously, other operations may be added to these processes, or one or more steps may be removed from these processes. Calculation Method 10 can accurately calculate the irradiation defect information of the aluminum alloy to be predicted for subsequent irradiation performance and material lifetime analysis and prediction.

[0028] Specifically, calculation method 10 includes steps S1 to S4. Step S1 may include calculating the primary impact atomic energy spectrum and establishing a cascaded database based on the primary impact atomic energy spectrum, the cascaded database including information on multiple matrix defects; Step S2 may include calculating the defect energy properties and obtaining the defect equilibrium concentration based on the defect energy properties and matrix defect information; Step S3 may include calculating the defect diffusion coefficient based on the defect energy properties and calculating the irradiation-enhanced diffusion coefficient based on the defect diffusion coefficient and defect equilibrium concentration; Step S4 may include calculating the solute defect formation rate and obtaining the irradiation defect information of the aluminum alloy to be predicted based on the formation rate and the irradiation-enhanced diffusion coefficient, the irradiation defect information including precipitate size and precipitate number density. Steps S1 to S4 will now be described in detail.

[0029] In some embodiments, the matrix of the aluminum alloy to be predicted is pure aluminum, and the solute is other impurities such as transmutated silicon. Steps S1-S4 will be described in detail below. First, step S1 requires calculating the primary impact-ejected atom energy spectrum. The primary impact-ejected atom is the PKA atom. PKA atoms can be used to simulate the atomic morphology formed after a neutron impacts other atoms under neutron irradiation, which is the primary impact-ejected atom. To calculate the primary impact-ejected atom energy spectrum, the target neutron energy spectrum and the target nuclide database can be obtained first. Then, a scattering matrix transformation can be performed based on the target neutron energy spectrum and the target nuclide database to obtain the primary impact-ejected atom energy spectrum. Specifically, the scattering matrix transformation method can first determine the neutron irradiation environment of the reactor core to be studied, and then obtain the neutron flux rate energy spectrum data based on the existing core physics calculation report, which is the target neutron energy spectrum mentioned above. The target neutron energy spectrum includes the target neutron flux energy group range and the flux values ​​of different energy groups, which can describe the flux density of neutrons with different energies (energy range is usually from 0.001 eV to 10 MeV). Next, for aluminum alloy materials, we will compile the nuclear data of the target nuclides for aluminum alloy materials, for example, 27 Al、 24 Mg 28 Information such as the number, type, elemental sequence, relative atomic mass, proportion, extinction threshold energy, and reaction cross section of target nuclides like Si is collected. A target nuclide database is then established based on this information. The obtained target neutron energy spectrum and the target nuclide database are used as input to the scattering matrix. For example, SPECTRA-PKA can be used for calculation, outputting the neutron transport equation and the PKA energy spectrum (primary impact-ejected atom energy spectrum). (Refer to...) Figure 2 The diagram shows the energy distribution of PKA produced by different nuclides (Al, Mg, Si, etc.).

[0030] After obtaining the PKA energy spectrum, a cascaded database can be established based on the PKA energy spectrum. Specific steps include simulation initialization and setting up the simulation box. Simulation initialization includes defining a variable `i` as a simulation count counter, initializing this variable to 0 at the start of the simulation (i.e., initializing the simulation count to 0). Then, the face-centered cubic crystal structure of pure aluminum can be used as the simulation box. For example, the lattice constant can be set to 4.0495 Å, creating a cubic box with a side length 100 times the lattice constant as the simulation box. The boundary conditions can be set to periodic boundary conditions. In this embodiment, refer to... Figure 3 As shown, to simulate real physical processes, the simulation box can be divided into an internal free region S11 and an external hot bath region S22. The internal free region S11 is a cubic box with a side length of 94 times the lattice constant, which can be used to observe cascade collisions and defect evolution. The external hot bath region S22 is a boundary region with a boundary thickness of 3 times the lattice constant, which can be used to simulate heat dissipation processes. For example, the energy of the created simulation box can be minimized using the conjugate gradient method to eliminate the stress introduced by the initial construction. Subsequently, the simulation system is brought to thermal equilibrium at the target simulation temperature (e.g., Tm = 323.15 K, i.e., 50°C), atomic thermal vibration velocities are assigned using the Maxwell-Boltzmann distribution method, and the system is run in an isothermal-isobaric (NPT) ensemble for 20 ps to bring the system to a stable thermodynamic state, thus completing the initialization of the simulation box.

[0031] Furthermore, simulated atoms are extracted from the PKA energy spectrum. These simulated atoms have specific energies; for example, in this embodiment, simulated atoms at representative energy points of 0.5 keV, 1 keV, 3 keV, 5 keV, 10 keV, 20 keV, and 50 keV are extracted for PKA cascade simulation. These simulated atoms are the PKA atoms. A PKA atom with a specific energy and random direction of motion is added to the simulation box one at a time. Multiple simulations are then performed on this PKA atom to complete one independent simulation round; for example, 20 simulations are performed on the 0.5 keV PKA atom. Subsequently, corresponding simulations are performed on PKA atoms of different energies (for example, 20 simulations are performed on each energy PKA atom). After selecting PKA atoms, the representative energy mentioned above is used as the kinetic energy of the PKA atom. The velocity corresponding to the PKA energy is calculated using the kinetic energy-velocity conversion formula and then assigned to the PKA atom. After gaining kinetic energy, the PKA atom can collide with pure aluminum atoms within the simulation chamber. The direction of PKA motion is randomly generated. For example, the initial position and direction of the PKA atom in each round of simulation can be randomized to ensure statistical accuracy. In a single simulation, during the collision process, PKA atoms will collide with pure aluminum atoms, producing secondary, tertiary, and even more secondary displaced atoms, thus forming... Figure 3The elliptical dashed line shows the collision cascade 13. During the simulation, all pure aluminum atoms in the simulation box can be traversed. The interaction forces between atoms are calculated based on the interaction potential between pure aluminum atoms and PKA atoms. The acceleration, velocity, and position of each atom are calculated, and this process is repeated to advance the simulation time. The above process is the process of neutrons colliding with pure aluminum atoms under simulated neutron irradiation conditions.

[0032] In some embodiments, when PKA atoms undergo collision cascading, a microcanonical (NVE) ensemble can be used to run for approximately 5 ps to maintain total energy conservation and simulate energy transfer during the collision process. Simultaneously, temperature control can be applied to the atoms in the external hot bath region S22 to simulate energy dissipation to the external environment and prevent excessive overall system temperature rise. The simulation phase can employ a short time step and high-frequency data output to capture rapid dynamic processes such as high-energy collisions and initial defect cluster formation within picoseconds, thus completing the cascade collision simulation process. During the cascade collision simulation, collisions between atoms generate vacancies and gaps, which are point defects produced during the collision process. Over time, these vacancies and gaps accumulate and form irradiation defect voids and dislocation loops. In some embodiments, after the simulation ends, the entire system enters a relaxation phase, continuing the simulation under the NVE ensemble for approximately 100 ps. This allows point defects (vacancies, gaps) to migrate and recombine, causing the defect cluster structure to relax, reaching a metastable state, and forming a stable collision cascade. Furthermore, the collision cascades obtained in the above steps can be analyzed using the Wigner-Seitz cell method to accurately identify and statistically analyze the type, quantity, spatial coordinates, and size distribution of all vacancies, interstitial atoms, and their clusters, forming corresponding matrix defect information. The matrix defect information corresponding to simulated atoms of different energies is summarized and normalized, then stored in the cascade database. After each simulation, it can be determined whether the required number of simulations (i) has been reached. If the required number of simulations has been reached, a new round of simulation can be performed using PKA atoms of different energies. If the required number of simulations has not been reached, simulations continue using PKA atoms of the same energy until the required number of simulations is reached.

[0033] In some embodiments, step S2 involves calculating the defect energy properties and obtaining the defect equilibrium concentration based on the defect energy properties and matrix defect information. First, calculating the defect energy properties can begin by obtaining the supercell morphology of the aluminum alloy to be predicted. Irradiation defects are then added to the supercell morphology to construct the crystal defect structure of the aluminum alloy. For example, the supercell morphology used for calculation can be constructed using the crystal visualization software VESTA, based on the face-centered cubic crystal structure of pure aluminum. After importing the crystallographic information file of pure aluminum into the software, a supercell containing 108 atoms (3×3×3 times the unit cell) is created using it as a template, with the lattice constant set to 4.05 Å. Subsequently, based on this perfect supercell morphology, various crystal defect structure models are constructed by replacing or adding atoms. Then, a projected fused wave (PAW) pseudopotential and an exchange-correlation functional in the form of the PBE based on the generalized gradient approximation (GGA) can be used to describe the interaction between ions and valence electrons in the supercell morphology. In some embodiments, the plane wave cutoff energy can be set to 400 eV, which is sufficient to ensure the convergence of the total energy. In reciprocal space, a 7×7×7 Monkhorst-Pack k-point grid centered at Gamma can be used to divide and sample the Brillouin zone. During the calculation, the convergence criterion can be that the force on all atoms is less than 0.01 eV / Å. After completing the basic calculation settings, structural relaxation calculations are performed on the constructed perfect supercell morphology and all defective supercell morphologies to obtain the stable configuration of the aluminum alloy. In some embodiments, the defect energy properties include one or any combination of the defect formation energy, binding energy, and diffusion barrier. When calculating static energies such as formation energy and binding energy, a static self-consistent calculation method can be selected to calculate the supercell energy to obtain the defect energy properties. If calculating dynamic energies such as the diffusion barrier, the transition state theory calculation can be performed using the Climbing-Micro-Motion Elastic Band (CI-NEB) method with the VTST toolkit to obtain the defect energy properties.

[0034] Furthermore, based on the defect energy properties and matrix defect information, the defect equilibrium concentration can be obtained. A cascade insertion weight file can be created using the PKA energy spectrum, and a preset neutron fluence rate can be established. The cascade insertion rate can then be calculated based on the cascade insertion weight file and the neutron fluence rate. For example, the cascade insertion rate can be calculated using the following formula:

[0035] in, Indicates neutron irradiation flux rate, This represents the off-site threshold energy in the target nuclide database. To simulate the total number of atoms in the box, The average PKA energy is given by the PKA energy spectrum. Next, the trapping radius of various defects (e.g., vacancies, interstitials) can be defined, and whether the distance between defects is less than the sum of their trapping radii is used as a prerequisite for whether a defect will react. Then, based on the diffusion barriers of the obtained defect energy properties, diffusion events in the simulation can be defined. Next, using the binding energy from the previously obtained defect energy properties plus the diffusion barriers of the dissociated defects, the dissociation barrier of the composite of pure aluminum and vacancies or interstitials can be calculated. Combined with the dissociation attempt frequency of the defect composite, dissociation events in the simulation can be defined. Furthermore, spontaneous reaction events such as agglomeration reactions when the same type of defect encounters and annihilation reactions between vacancies and interstitials are defined. Finally, the cascade database can be updated. Then, a thermally activated event database is constructed based on the defect energy properties, and a reaction event database is constructed based on the thermally activated event database and the spontaneous event database. The reaction event library is then divided to obtain simulated reaction sub-regions. For example, the lattice constant is set to 4.05 Å, the lattice type is set to FCC, and the size of the simulated reaction sub-region is set to a cube with a side length of 100 times the lattice constant. Considering grain boundary effects, the grain boundary size is set to 8100 Å. The occurrence rate of each possible event in the simulated reaction sub-region is calculated, and the total rate of reaction events is calculated based on the occurrence rate of each possible event. In this embodiment, the occurrence rate of each possible event can be understood as calculating the transition rate of each possible event, which can be calculated using the following formula:

[0036] in, Boltzmann's constant; The system temperature; The transition energy barrier is calculated from the binding energy and diffusion energy barrier in the defect energy properties. The sum of the transition rates of each event is the total rate of event occurrence. The total rate of event occurrence is then used as the input to the first defect evolution model, which can be a kinetic Monte Carlo (KMC) model. After inputting the total rate of event occurrence into the KMC model, the defect equilibrium concentration during the simulation process can be obtained, where the defect equilibrium concentration includes the vacancy saturation concentration and the interstitial saturation concentration.

[0037] Step S3 involves calculating the defect diffusion coefficient based on the defect energy properties, and then calculating the irradiation-enhanced diffusion coefficient based on the defect diffusion coefficient and the defect equilibrium concentration. For example, the defect diffusion coefficient can be calculated using the following formula:

[0038] in, This represents the jump coefficient corresponding to a certain type of diffusion mechanism. is the lattice constant. The vibration frequency corresponding to the corresponding type of diffusion mechanism. This represents the diffusion energy barrier corresponding to the diffusion mechanism through which the defect diffuses. Boltzmann's constant, Where is the system temperature. After obtaining the defect diffusion coefficient of solute atoms using the above formula, the irradiation-enhanced diffusion coefficient of solute atoms can be calculated using the following formula:

[0039] in, and The correlation coefficients for solute atom vacancies and interstitial diffusion mechanisms, respectively, can be obtained through literature data searches. and These represent the saturation concentrations of vacancies and interstitials, respectively. and These are the diffusion coefficients of solute atoms through vacancy and interstitial diffusion mechanisms, respectively.

[0040] In some embodiments, step S4 involves calculating the solute defect generation rate. Based on the generation rate and the irradiation-enhanced diffusion coefficient, the irradiation defect information of the aluminum alloy to be predicted is obtained. This irradiation defect information includes the precipitate size and precipitate number density. In this embodiment, the irradiation defect information can be solved by performing an evolution simulation of the aluminum alloy to be predicted. First, the multi-group neutron fluence spectrum can be obtained from the target neutron spectrum. Based on the material composition of the aluminum alloy to be predicted, the reaction cross-section of each nuclide, the decay constant of each nuclide, the multi-group neutron fluence spectrum, the neutron capture coupling differential equation set, and the decay coupling differential equation set, the cumulative amount of solute generated, i.e., the cumulative amount of precipitates generated, can be obtained. Further, the generation rate can be obtained based on the cumulative generation rate. After obtaining the generation rate, a Kampmann-Wagner numerical framework based on the open-source Kawin code, improved upon, can be input to establish a kinetic model of precipitate evolution under irradiation conditions. Specific steps may include inputting the lattice type, lattice constant, and atomic volume of the aluminum matrix, and the cumulative amount of magnesium and silicon atoms generated within the aluminum alloy (which can be obtained through the above steps), thus completing the input of the model's material property parameters. Subsequently, the Gibbs free energy, interfacial energy, and correlation coefficient of the multiphase precipitates within the aluminum alloy are input to complete the input of the model's precipitate parameters. These parameters can be obtained using existing methods, thereby initializing the evolution simulation. After the simulation begins, the diffusion flux and nucleation driving force of the solute can be calculated based on the irradiation-enhanced diffusion coefficient and generation rate obtained above. In this step, the irradiation-enhanced diffusion coefficient obtained above can be coupled into the diffusion matrix of the solute element in the matrix to calculate the diffusion flux of the solute. Then, the critical nucleation radius and critical nucleation activation energy of the precipitate can be calculated based on the nucleation driving force. The nucleation rate is calculated based on the critical nucleation radius and critical nucleation activation energy, and then the growth rate of the precipitate can be calculated using the Laplace equation and the diffusion matrix through the nucleation rate. The amount of precipitate produced and the size change within a simulation time are calculated based on the growth rate of the precipitate; the size of the precipitate and the number density of the precipitate are calculated based on the amount of precipitate produced and the size change.

[0041] This application establishes a cascaded database using primary impact atomic energy spectra, which can effectively simulate the generation of irradiation defects in the aluminum alloy to be predicted by neutrons in a real nuclear reactor, obtaining information on the generation rate of matrix defects related to irradiation defects such as vacancies and interstitials. Furthermore, by calculating the thermodynamic and kinetic properties of irradiation defects, defect interaction parameters, and other related defect property information, the overall evolution of irradiation defects is simulated to obtain the defect equilibrium concentration, thereby calculating the irradiation-enhanced diffusion coefficient. Finally, by calculating parameters such as the generation rate of solute defects, the irradiation-enhanced diffusion coefficient, and the nucleation driving force, the nucleation and growth of irradiated precipitates is simulated, ultimately obtaining irradiation defect information including precipitate size and number density. This allows for accurate calculation of the irradiation defect information of the aluminum alloy to be predicted, facilitating subsequent analysis and prediction of irradiation performance and material lifetime. One embodiment of this application also proposes a method... Figure 4 The system 40 shown predicts the size and number density of precipitated phases in aluminum alloys under neutron irradiation. According to... Figure 4 The system 40 for predicting the size and number density of precipitated phases in aluminum alloys under neutron irradiation may include an internal communication bus 41, a processor 42, a read-only memory (ROM) 43, a random access memory (RAM) 44, and a communication port 45. When applied to a personal computer, the system 40 for predicting the size and number density of precipitated phases in aluminum alloys under neutron irradiation may also include a hard disk 46.

[0042] The internal communication bus 41 enables data communication between components of the system 40 for predicting the size and number density of precipitates in aluminum alloys under neutron irradiation. The processor 42 can make judgments and issue prompts. In some embodiments, the processor 42 may consist of one or more processors. The communication port 45 enables data communication between the system 40 for predicting the size and number density of precipitates in aluminum alloys under neutron irradiation and external sources. In some embodiments, the system 40 for predicting the size and number density of precipitates in aluminum alloys under neutron irradiation can send and receive information and data from a network via the communication port 45.

[0043] The system 40 for predicting the size and number density of precipitated phases in aluminum alloys under neutron irradiation may also include different types of program storage units and data storage units, such as a hard disk 46, read-only memory (ROM) 43, and random access memory (RAM) 44, capable of storing various data files used for computer processing and / or communication, as well as possible program instructions executed by the processor 42. The processor executes these instructions to implement the main part of the method. The results of the processor processing are transmitted to the user equipment via a communication port and displayed on the user interface.

[0044] In addition, this application also proposes a computer-readable medium storing computer program code, which, when executed by a processor, implements the above-described method for predicting the size and number density of precipitated phases in aluminum alloys under neutron irradiation.

[0045] Some aspects of this application can be executed entirely by hardware, entirely by software (including firmware, resident software, microcode, etc.), or by a combination of hardware and software. The aforementioned hardware or software may be referred to as a "data block," "module," "engine," "unit," "component," or "system." The processor may be one or more application-specific integrated circuits (ASICs), digital signal processors (DSPs), digital signal processing devices (DAPDs), programmable logic devices (PLDs), field-programmable gate arrays (FPGAs), processors, controllers, microcontrollers, microprocessors, or combinations thereof. Furthermore, aspects of this application may manifest as computer products residing in one or more computer-readable media, including computer-readable program code. For example, computer-readable media may include, but are not limited to, magnetic storage devices (e.g., hard disks, floppy disks, magnetic tapes, etc.), optical discs (e.g., compressed CDs, digital multifunction DVDs, etc.), smart cards, and flash memory devices (e.g., cards, sticks, key drives, etc.).

[0046] A computer-readable medium may contain a propagated data signal containing computer program code, for example, on baseband or as part of a carrier wave. This propagated signal may take various forms, including electromagnetic, optical, and so on, or suitable combinations thereof. A computer-readable medium can be any computer-readable medium other than a computer-readable storage medium, which can be connected to an instruction execution system, apparatus, or device to enable communication, propagation, or transmission of a program for use. The program code located on the computer-readable medium can be propagated through any suitable medium, including radio, cable, fiber optic cable, radio frequency signals, or similar media, or any combination of the above media.

[0047] The basic concepts have been described above. Obviously, for those skilled in the art, the above disclosure is merely illustrative and does not constitute a limitation of this application. Although not explicitly stated herein, those skilled in the art may make various modifications, improvements, and corrections to this application. Such modifications, improvements, and corrections are suggested in this application, and therefore remain within the spirit and scope of the exemplary embodiments of this application.

[0048] Furthermore, this application uses specific terms to describe embodiments of the application. For example, "an embodiment," "one embodiment," and / or "some embodiments" refer to a particular feature, structure, or characteristic related to at least one embodiment of the application. Therefore, it should be emphasized and noted that "an embodiment," "one embodiment," or "an alternative embodiment" mentioned twice or more in different locations in this specification do not necessarily refer to the same embodiment. In addition, certain features, structures, or characteristics in one or more embodiments of the application can be appropriately combined.

[0049] Similarly, it should be noted that, in order to simplify the description of the present application and thus aid in the understanding of one or more embodiments, the foregoing description of the embodiments of the present application sometimes combines multiple features into a single embodiment, drawing, or description thereof. However, this disclosure method does not imply that the subject matter of the present application requires more features than those mentioned in the claims. In fact, the embodiments contain fewer features than all the features of the single embodiments disclosed above.

[0050] In some embodiments, numbers describing the quantity of components and attributes are used. It should be understood that such numbers used in the description of embodiments are modified in some examples with the terms "approximately," "approximately," or "generally." Unless otherwise stated, "approximately," "approximately," or "generally" indicates that the numbers are allowed to vary by ±20%. Accordingly, in some embodiments, the numerical parameters used in the specification and claims are approximate values, which may be changed depending on the characteristics required by individual embodiments. In some embodiments, numerical parameters should take into account specified significant digits and employ a general method of digit reservation. Although the numerical ranges and parameters used to confirm their breadth of scope in some embodiments of this application are approximate values, in specific embodiments, such values ​​are set as precisely as feasible.

[0051] Although this application has been described with reference to specific embodiments, those skilled in the art should recognize that the above embodiments are only used to illustrate this application, and various equivalent changes or substitutions can be made without departing from the spirit of this application. Therefore, any changes or modifications to the above embodiments within the essential spirit of this application will fall within the scope of the claims of this application.

Claims

1. A method for predicting the size and number density of precipitated phases in aluminum alloys under neutron irradiation, applicable to a reactor research reactor, wherein the reactor research reactor comprises an aluminum alloy to be predicted, the aluminum alloy to be predicted comprises a matrix and a solute, the solute comprising solute atoms, characterized in that, Includes the following steps: Calculate the primary impact atomic energy spectrum, and establish a cascade database based on the primary impact atomic energy spectrum. The cascade database includes information on multiple matrix defects. Calculate the defect energy properties, and obtain the defect equilibrium concentration based on the defect energy properties and the matrix defect information; The defect diffusion coefficient of the solute atom is calculated based on the defect energy properties, and the irradiation-enhanced diffusion coefficient is calculated based on the defect diffusion coefficient and the defect equilibrium concentration. The solute defect formation rate is calculated, and the irradiation defect information of the aluminum alloy to be predicted is obtained based on the formation rate and the irradiation-enhanced diffusion coefficient. The irradiation defect information includes the precipitate size and the precipitate number density.

2. The method for predicting the size and number density of precipitated phases in aluminum alloys under neutron irradiation as described in claim 1, characterized in that, The matrix includes matrix atoms, and the cascade database is established based on the primary impact atomic energy spectrum, including: Perform simulation initialization and set up the simulation box, which includes the matrix atoms; Simulated atoms are extracted from the primary impact atomic energy spectrum and added to the simulation box to cause the simulated atoms to collide with the matrix atoms to form a collision cascade. The matrix defect information corresponding to the simulated atom is obtained according to the collision cascade, and the matrix defect information is stored in the cascade database.

3. The method for predicting the size and number density of precipitated phases in aluminum alloys under neutron irradiation as described in claim 1, characterized in that, The calculation of the defect energy properties includes the following steps: The supercell morphology of the aluminum alloy to be predicted is obtained, and irradiation defects are added to the supercell morphology to construct the crystal defect structure of the aluminum alloy to be predicted. Relaxation calculations are performed based on the crystal defect structure to obtain the stable configuration of the aluminum alloy to be predicted, and supercell energy calculations are performed based on the stable configuration to obtain the supercell energy. The defect energy properties are calculated based on the supercell energy.

4. The method for predicting the size and number density of precipitated phases in aluminum alloys under neutron irradiation as described in claim 1, characterized in that, The defect equilibrium concentration is obtained based on the defect energy properties and the matrix defect information, including: A cascade insertion weight file is created based on the primary impact atomic energy spectrum, a neutron irradiation fluence rate is preset, and the cascade insertion rate is calculated based on the cascade insertion weight file and the neutron irradiation fluence rate. A thermal activation event database is constructed based on the defect energy properties, and a reaction event database is constructed based on the thermal activation event database and the spontaneous event database. The reaction event library is divided into simulated reaction sub-regions, and the occurrence rate of each possible event in the simulated reaction sub-regions is calculated. The total occurrence rate of reaction events is calculated based on the occurrence rate of each possible event. The first defect evolution model obtains the defect equilibrium concentration based on the total rate of occurrence of the reaction events.

5. The method for predicting the size and number density of precipitated phases in aluminum alloys under neutron irradiation as described in claim 4, characterized in that, This includes calculating the occurrence rate of each of the possible events using the following formula: in, The occurrence rate of each of the possible events; Represents the vibration rate for each of the possible events; Boltzmann's constant; The system temperature; For leapfrog energy barrier.

6. The method for predicting the size and number density of precipitated phases in aluminum alloys under neutron irradiation as described in claim 4, characterized in that, The defect equilibrium concentration includes vacancy saturation concentration and / or interstitial saturation concentration.

7. The method for predicting the size and number density of precipitated phases in aluminum alloys under neutron irradiation as described in claim 1, characterized in that, Calculating the primary impact atomic energy spectrum includes the following steps: Obtain the target neutron energy spectrum and target nuclide database; The primary impact atomic energy spectrum is obtained by performing a scattering matrix transformation based on the target neutron energy spectrum and the target nuclide database.

8. The method for predicting the size and number density of precipitated phases in aluminum alloys under neutron irradiation as described in claim 7, characterized in that, The target neutron energy spectrum includes target neutron flux energy group intervals and flux values ​​for different energy groups; and / or, The target nuclide database includes one or any combination of the following: the number, type, element number, relative atomic mass, ratio, exposition threshold energy, and reaction cross section of the target nuclide.

9. The method for predicting the size and number density of precipitated phases in aluminum alloys under neutron irradiation as described in claim 1, characterized in that, The defect energy properties include one or any combination of defect formation energy, binding energy, and diffusion barrier.

10. The method for predicting the size and number density of precipitated phases in aluminum alloys under neutron irradiation as described in claim 1, characterized in that, This includes calculating the defect diffusion coefficient according to the following formula: in, For different diffusion mechanisms, the jump coefficients are... is the lattice constant. The vibration frequency corresponding to the corresponding type of diffusion mechanism. This represents the diffusion energy barrier corresponding to the diffusion mechanism through which the defect diffuses. Boltzmann's constant, The temperature is the system temperature.

11. The method for predicting the size and number density of precipitated phases in aluminum alloys under neutron irradiation as described in claim 1, characterized in that, The irradiation-enhanced diffusion coefficient is calculated using the following formula: in, and These are the correlation coefficients for the vacancies and interstitial diffusion mechanisms of the solute atoms, respectively. and These represent the saturation concentrations of vacancies and interstitials, respectively. and These are the diffusion coefficients of the solute atoms through vacancy and interstitial diffusion mechanisms, respectively.

12. The method for predicting the size and number density of precipitated phases in aluminum alloys under neutron irradiation as described in claim 7, characterized in that, Calculating the formation rate of the solute defects includes the following steps: Obtain the multi-group neutron flux spectrum based on the target neutron energy spectrum; The cumulative amount of solute generated is obtained based on the material composition of the aluminum alloy to be predicted, the reaction cross section of each nuclide, the decay constant of each nuclide, the multi-group neutron fluence energy spectrum, the neutron capture coupling differential equation set, and the decay coupling differential equation set. The generation rate is obtained based on the cumulative generation amount.

13. The method for predicting the size and number density of precipitated phases in aluminum alloys under neutron irradiation as described in claim 1, characterized in that, Obtaining the irradiation defect information of the aluminum alloy to be predicted based on the generation rate and the irradiation-enhanced diffusion coefficient includes the following steps: The evolution simulation of the irradiation defect evolution model is initialized. The diffusion flux and nucleation driving force of the solute are calculated based on the irradiation-enhanced diffusion coefficient and the generation rate, and the critical nucleation radius and critical nucleation activation energy of the precipitated phase are calculated based on the nucleation driving force. The nucleation rate is calculated based on the critical nucleation radius and the critical nucleation activation energy, and the growth rate of the precipitated phase is calculated based on the nucleation rate. The amount of precipitation and the size change of the precipitate within a simulated time period are calculated based on the growth rate of the precipitate. The precipitate size and the precipitate number density are calculated based on the amount of production and the amount of size change.

14. A system for predicting the size and number density of precipitated phases in aluminum alloys under neutron irradiation, comprising: Memory is used to store instructions that can be executed by the processor; and a processor for executing the instructions to implement the method as claimed in any one of claims 1-13.

15. A computer-readable medium storing computer program code that, when executed by a processor, implements the method as claimed in any one of claims 1-13.

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