Method for determining the average radius of the critical nucleus of precipitates, the element concentration of the critical nucleus of precipitates and the energy barrier of the precipitates of molybdenum-rhenium alloys under irradiation conditions

Abstract

Embodiments of the present application relate to the technical field of computer material science, in particular to a method for determining the average radius of critical nucleus of precipitated phase, the element concentration of critical nucleus of precipitated phase and the energy barrier of precipitated phase of molybdenum-rhenium alloy under irradiation conditions, which comprises: determining the working condition of irradiation condition, the composition of molybdenum-rhenium alloy before irradiation, the kinetic and thermodynamic coefficients of molybdenum-rhenium alloy and the equilibrium composition concentration of precipitated phase; determining the region of critical nucleus of precipitated phase of molybdenum-rhenium alloy and the energy barrier of precipitated phase of molybdenum-rhenium alloy according to the working condition of irradiation condition, the composition of molybdenum-rhenium alloy before irradiation, the kinetic and thermodynamic coefficients of molybdenum-rhenium alloy and the equilibrium composition concentration of precipitated phase; determining the average radius of critical nucleus and the element concentration of critical nucleus according to the region of critical nucleus. The method can make up for the deficiency that the nucleation stage of precipitated phase cannot be directly observed and quantified in the prior art, and realize accurate prediction of the formation of precipitated phase of molybdenum-rhenium alloy.

Description

Technical Field

[0001] The embodiments of this application relate to the field of computer materials science and technology, specifically to a method for determining the average radius of the critical nucleus of the precipitated phase, the elemental concentration of the critical nucleus of the precipitated phase, and the energy barrier of the precipitated phase in a molybdenum-rhenium alloy under irradiation 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] After being irradiated with strong neutrons in existing reactors, the rhenium in molybdenum-rhenium alloys will precipitate, resulting in a large number of rhenium-rich, hard and brittle intermetallic compound phases inside the alloy. These nanoscale precipitates will cause severe radiation hardening and intergranular embrittlement of the molybdenum-rhenium alloy, weakening the toughness advantage brought by rhenium and significantly affecting the long-term safe service of nuclear materials made from molybdenum-rhenium alloys in reactors.

[0004] Therefore, in order to ensure that nuclear materials made from molybdenum-rhenium alloys can meet the requirements for long-term stable service under the extreme irradiation, high temperature and complex stress environment of reactors, it is necessary to accurately predict the formation of precipitates in molybdenum-rhenium alloys in order to guide the composition design of molybdenum-rhenium alloys and optimize their comprehensive performance. However, in the existing technology, there are still many defects and deficiencies in the methods for simulating and predicting the formation process of precipitates in molybdenum-rhenium alloys. 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] Embodiments of this application provide a method for determining the average radius of the critical nucleus of the precipitated phase, the elemental concentration of the critical nucleus of the precipitated phase, and the energy barrier of the precipitated phase under irradiation conditions in a molybdenum-rhenium alloy. The method includes the following steps: S10: Determining the irradiation conditions, the composition of the molybdenum-rhenium alloy before irradiation, the kinetic and thermodynamic coefficients of the molybdenum-rhenium alloy, and the equilibrium composition concentration of the precipitated phase; S20: Based on the irradiation conditions, the composition of the molybdenum-rhenium alloy before irradiation, the kinetic and thermodynamic coefficients of the molybdenum-rhenium alloy, and the equilibrium composition concentration of the precipitated phase determined in step S10, determining the region of the critical nucleus of the precipitated phase of the molybdenum-rhenium alloy and the energy barrier of the precipitated phase; S30: Based on the region of the critical nucleus of the precipitated phase of the molybdenum-rhenium alloy, determining the average radius of the critical nucleus and the elemental concentration of the critical nucleus.

[0007] The embodiments of this application provide a method for determining the average radius of the critical nucleus, the elemental concentration of the critical nucleus, and the energy barrier of the precipitate phase in a molybdenum-rhenium alloy under irradiation conditions. This method incorporates the irradiation conditions and the kinetic and thermodynamic coefficients of the molybdenum-rhenium alloy to consider environmental factors influencing the formation of the precipitate phase and the driving forces promoting its formation. It also combines the composition of the molybdenum-rhenium alloy before irradiation with the equilibrium concentration of the precipitate phase to simulate the formation process of the precipitate phase, accurately determine the key critical stages in the nucleation process, and identify the critical nucleus. By identifying the region and its corresponding energy barrier, the nucleation process of the precipitated phase can be quantitatively characterized, effectively overcoming the shortcomings of existing technologies that cannot directly observe and quantify the nucleation stage of the precipitated phase, and enabling accurate prediction of the formation of precipitated phases in molybdenum-rhenium alloys. Furthermore, based on the region of the critical nucleus of the precipitated phase in molybdenum-rhenium alloy, the average radius and elemental concentration of the critical nucleus are determined, thus transforming the formation process of the precipitated phase into key parameters such as the average radius and elemental concentration of the critical nucleus. This provides a reliable reference for guiding the composition design of molybdenum-rhenium alloys and optimizing their overall performance. Attached Figure Description

[0008] 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.

[0009] Figure 1 This is a rhenium element concentration distribution diagram of the formation process of the molybdenum-rhenium alloy precipitate phase according to an embodiment of this application; Figure 2 This is a schematic diagram showing the changes in composition concentration and energy of an intermediate alloy state of a molybdenum-rhenium alloy according to an embodiment of this application. Figure 3 This is a rhenium concentration distribution diagram of a molybdenum-rhenium alloy at the critical point according to an embodiment of this application; Figure 4 This is a rhenium concentration distribution diagram of the final alloy state of a molybdenum-rhenium alloy according to an embodiment of this application.

[0010] 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

[0011] 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.

[0012] 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.

[0013] The formation of precipitates in molybdenum-rhenium alloys is a typical nucleation process. Nucleation usually occurs within an extremely short timescale, making it a transient and random physical event. The critical nucleus size is typically only a few nanometers, and its existence time is extremely short. Furthermore, it is accompanied by complex defect evolution behavior under irradiation. Therefore, it is extremely difficult to directly observe and quantitatively characterize this process using existing techniques. Usually, only the resulting state of the precipitates after their formation can be obtained, and the critical nucleus characteristics and corresponding energy information of the nucleation stage of the precipitates cannot be determined. This is not conducive to accurately simulating the microstructural evolution of molybdenum-rhenium alloys and makes it difficult to accurately predict the formation of precipitates in molybdenum-rhenium alloys.

[0014] Based on this, embodiments of this application provide a method for determining the average radius of the critical nucleus of the precipitated phase, the elemental concentration of the critical nucleus of the precipitated phase, and the energy barrier of the precipitated phase under irradiation conditions in a molybdenum-rhenium alloy, comprising the following steps: S10: Determine the irradiation conditions, the composition of the molybdenum-rhenium alloy before irradiation, the kinetic and thermodynamic coefficients of the molybdenum-rhenium alloy, and the equilibrium composition concentration of the precipitated phase.

[0015] S20: Based on the irradiation conditions, composition of the molybdenum-rhenium alloy before irradiation, kinetic and thermodynamic coefficients of the molybdenum-rhenium alloy, equilibrium composition concentration of the precipitated phase determined in step S10, determine the region of the critical nucleus of the precipitated phase of the molybdenum-rhenium alloy and the energy barrier of the precipitated phase of the molybdenum-rhenium alloy.

[0016] S30: Determine the average radius and elemental concentration of the critical nucleus based on the region of the critical nucleus of the precipitated phase in the molybdenum-rhenium alloy.

[0017] The embodiments of this application provide a method for determining the average radius of the critical nucleus, the elemental concentration of the critical nucleus, and the energy barrier of the precipitate phase in a molybdenum-rhenium alloy under irradiation conditions. This method incorporates the irradiation conditions and the kinetic and thermodynamic coefficients of the molybdenum-rhenium alloy to consider environmental factors influencing the formation of the precipitate phase and the driving forces promoting its formation. It also combines the composition of the molybdenum-rhenium alloy before irradiation with the equilibrium concentration of the precipitate phase to simulate the formation process of the precipitate phase, accurately determine the key critical stages in the nucleation process, and identify the critical nucleus. By identifying the region and its corresponding energy barrier, the nucleation process of the precipitated phase can be quantitatively characterized, effectively overcoming the shortcomings of existing technologies that cannot directly observe and quantify the nucleation stage of the precipitated phase, and enabling accurate prediction of the formation of precipitated phases in molybdenum-rhenium alloys. Furthermore, based on the region of the critical nucleus of the precipitated phase in molybdenum-rhenium alloy, the average radius and elemental concentration of the critical nucleus are determined, thus transforming the formation process of the precipitated phase into key parameters such as the average radius and elemental concentration of the critical nucleus. This provides a reliable reference for guiding the composition design of molybdenum-rhenium alloys and optimizing their overall performance.

[0018] In some embodiments, step S20 may further include the following steps: S21: Based on the composition of the molybdenum-rhenium alloy before irradiation and the equilibrium composition concentration of the precipitated phase, determine the initial alloy state of the molybdenum-rhenium alloy before the formation of precipitated phase and the final alloy state containing precipitated phase.

[0019] S22: Based on the initial alloy state and the final alloy state, determine the intermediate alloy state of the molybdenum-rhenium alloy as it changes from the initial alloy state to the final alloy state.

[0020] S23: Based on the irradiation conditions, intermediate alloy state, and the kinetic and thermodynamic coefficients of the molybdenum-rhenium alloy, determine the region of the critical core of the molybdenum-rhenium alloy at the critical point and the energy barrier of the precipitated phase of the molybdenum-rhenium alloy.

[0021] Because the composition of molybdenum-rhenium alloys changes, both the initial alloy state without precipitates and the final alloy state containing precipitates will change accordingly, and the nucleation process of the precipitates will also vary. Therefore, in this embodiment, by considering the composition of the molybdenum-rhenium alloy before irradiation and the equilibrium composition concentration of the precipitates, the initial alloy state without precipitates and the final alloy state containing precipitates are accurately determined. Based on the initial alloy state and the final alloy state containing precipitates, an intermediate alloy state is determined, so that the formation process of the precipitates can be represented by the intermediate alloy state. Compared with the current... Some technologies simplify the precipitation process into a sudden change state, which can more realistically simulate the actual formation process of molybdenum-rhenium alloy precipitates under different compositional conditions. By combining the environmental factors affecting the formation of precipitates in molybdenum-rhenium alloys and the driving forces that promote the formation of precipitates, it is possible to accurately simulate the formation process of precipitates in molybdenum-rhenium alloys, determine the critical stage of the transition from an unstable state to a stable growth state during the nucleation process of precipitates, and determine the region of the critical nucleus and its corresponding energy barrier. Thus, it is beneficial to achieve a quantitative description of the nucleation behavior of precipitates and further improve the prediction accuracy of the formation of precipitates in molybdenum-rhenium alloys.

[0022] In some embodiments, step S21 may further include the following steps: S211: Based on the composition of the molybdenum-rhenium alloy before irradiation, determine the composition of the molybdenum-rhenium alloy before the formation of precipitates, and based on the composition of the molybdenum-rhenium alloy before the formation of precipitates, determine the initial alloy state of the molybdenum-rhenium alloy before the formation of precipitates.

[0023] S212: Determine the composition of the molybdenum-rhenium alloy containing the precipitated phase based on the equilibrium composition concentration of the precipitated phase, and determine the final alloy state of the molybdenum-rhenium alloy containing the precipitated phase based on the composition of the molybdenum-rhenium alloy containing the precipitated phase.

[0024] Specifically, in step S211, the composition of the molybdenum-rhenium alloy before irradiation is equal to the composition of the molybdenum-rhenium alloy before the formation of precipitates. In step S212, the equilibrium composition concentration of the precipitates is equal to the composition of the molybdenum-rhenium alloy containing the precipitates.

[0025] In some embodiments, step S212 may further include the following steps: S2121: Determine the precipitation region, where the composition of the molybdenum-rhenium alloy in the precipitation region is the equilibrium composition concentration of the precipitated phase.

[0026] S2122: Based on the composition of the molybdenum-rhenium alloy in the precipitated region, determine the composition of the molybdenum-rhenium alloy in the non-precipitated region, so that the total content of the composition of the molybdenum-rhenium alloy in the precipitated region and the molybdenum-rhenium alloy in the non-precipitated region is consistent with the composition of the molybdenum-rhenium alloy before irradiation.

[0027] S2123: Determine the final alloy state of the molybdenum-rhenium alloy containing the precipitated phase based on the composition of the molybdenum-rhenium alloy in the precipitated region and the composition of the molybdenum-rhenium alloy in the non-precipitated region.

[0028] In this embodiment, by determining the precipitation region and determining the composition of the molybdenum-rhenium alloy in the precipitation region as the equilibrium concentration of the precipitated phase, and then determining the composition of the molybdenum-rhenium alloy in the non-precipitated region, the total content of the molybdenum-rhenium alloy composition in the precipitated region and the non-precipitated region is consistent with the composition of the molybdenum-rhenium alloy before irradiation. This facilitates obtaining accurate composition of the molybdenum-rhenium alloy in the precipitation region and the non-precipitated region, thereby improving the accuracy of the final alloy state of the molybdenum-rhenium alloy containing the precipitated phase determined accordingly.

[0029] In some embodiments, in step S2123, the final alloy state of the molybdenum-rhenium alloy containing the precipitated phase is the molybdenum-rhenium element concentration ratio in the molybdenum-rhenium alloy containing the precipitated phase.

[0030] Specifically, such as Figure 1 As shown, Figure 1 The diagram illustrates the rhenium concentration distribution during the formation process of the molybdenum-rhenium alloy precipitate phase according to an embodiment of this application. The left diagram shows the rhenium concentration distribution of the molybdenum-rhenium alloy before the formation of the precipitate phase, the right diagram shows the rhenium concentration distribution of the molybdenum-rhenium alloy after the formation of the precipitate phase, and the middle diagram shows the rhenium concentration distribution during the formation process of the molybdenum-rhenium alloy precipitate phase. In the diagram, 100 represents the precipitation region, and the remaining regions represent the non-precipitated regions.

[0031] In some embodiments, step S22 may further include the following steps: S221: The initial alloy state is used as the first endpoint to represent the precipitation process, and the final alloy state is used as the second endpoint to represent the precipitation process.

[0032] S222: Perform linear interpolation on the first endpoint and the second endpoint to determine multiple intermediate points representing the precipitation process, and make the concentration of the molybdenum-rhenium alloy represented by the multiple intermediate points increase smoothly from small to large, and make the concentration of the molybdenum-rhenium alloy represented by each intermediate point consistent with the total concentration of the component before irradiation.

[0033] S223: Determine the intermediate alloy states of molybdenum-rhenium alloy from the initial alloy state to the final alloy state based on multiple intermediate points.

[0034] In this embodiment, the precipitation process of molybdenum-rhenium alloy is represented as a series of continuous intermediate alloy states through the above steps. This allows the process of the precipitated phase gradually developing from local segregation to a stable precipitated phase to unfold in a smooth transition, and also makes the change in the composition concentration of molybdenum-rhenium alloy present a smooth transition. Compared with the prior art, which simplifies the precipitation process to an abrupt state, this can effectively avoid non-physical errors and more realistically simulate the actual formation process of the precipitated phase gradually developing from local segregation to a stable precipitated phase under irradiation conditions. This improves the accuracy of the determined intermediate alloy states, thereby helping to further improve the prediction accuracy of the formation of precipitated phases in molybdenum-rhenium alloy.

[0035] Specifically, such as Figure 2 As shown, Figure 2 This diagram illustrates the compositional concentration changes and energy changes of an intermediate alloying state of a molybdenum-rhenium alloy according to an embodiment of this application. In this diagram, 10 represents the initial alloying state, i.e., the first endpoint of the precipitation process, and 20 represents the final alloying state, i.e., the second endpoint of the precipitation process. Figure 2 It can be seen that the concentration of the molybdenum-rhenium alloy represented by the multiple intermediate points between the first and second endpoints increases smoothly from small to large.

[0036] In some embodiments, step S23 may further include the following steps: S231: Determine the energy at each point in the intermediate alloy state based on the irradiation conditions, the intermediate alloy state, and the kinetic and thermodynamic coefficients of the molybdenum-rhenium alloy.

[0037] S232: Based on the energy at each point, determine the region of the critical core of the molybdenum-rhenium alloy at the critical point and the energy barrier of the precipitated phase of the molybdenum-rhenium alloy.

[0038] This embodiment considers the environmental factors affecting the formation of precipitates in molybdenum-rhenium alloys and the driving forces promoting precipitate formation. It systematically analyzes the intermediate alloy states representing the precipitate formation process of molybdenum-rhenium alloys, accurately determining the energy at each point in the intermediate alloy state. This allows for a complete representation of the energy change process as the precipitate evolves from local segregation to a stable growth stage. Based on this, the critical stage of the transition from an unstable to a stable growth state is accurately identified according to the energy at each point. Compared to existing technologies that empirically set the critical nucleus size or assume nucleation conditions for the precipitate, this effectively avoids the influence of artificial thresholds on the determination of the critical stage. It ensures that the determination of the critical nucleus region and energy barrier is consistent with the actual evolution path of the precipitation process, thus facilitating accurate simulation of the precipitate formation process in molybdenum-rhenium alloys and enhancing the prediction accuracy of precipitate formation.

[0039] In some embodiments, in step S231, the phase field principle diagram can be obtained by simulating the phase field using MATLAB software based on the irradiation conditions, intermediate alloy state, and the kinetic and thermodynamic coefficients of the molybdenum-rhenium alloy. This allows for a more intuitive understanding of the energy information of each point in the intermediate alloy state, which is beneficial for accurately determining the region of the critical core of the molybdenum-rhenium alloy at the critical point and the energy barrier of the precipitated phase of the molybdenum-rhenium alloy.

[0040] like Figure 2 As shown, Figure 2 The value 30 represents the critical nucleus of the molybdenum-rhenium alloy at the critical point during the precipitation process, according to... Figure 2 The energy of the molybdenum-rhenium alloy at the critical point is shown, and the region of the critical core of the molybdenum-rhenium alloy at the critical point is determined, such as... Figure 3 As shown, Figure 3 The diagram shows the rhenium concentration distribution of a molybdenum-rhenium alloy at the critical point according to an embodiment of this application, where 200 represents the region of the critical core. Figure 4 The diagram shows the rhenium concentration distribution of the final alloy state of the molybdenum-rhenium alloy according to an embodiment of this application.

[0041] In some embodiments, step S231 may further include the following steps: S2311: Based on the irradiation conditions, the kinetics and thermodynamic coefficients of the molybdenum-rhenium alloy, determine the driving force for the segregation and precipitation of rhenium during the formation of the precipitated phase in the molybdenum-rhenium alloy.

[0042] S2312: Determine the concentration at each point in the intermediate alloy state during the precipitation process based on the driving force and the intermediate alloy state.

[0043] S2313: Determine the energy at each point based on the concentration at each point.

[0044] In this embodiment, by considering the irradiation conditions and the kinetic and thermodynamic coefficients of the molybdenum-rhenium alloy, the driving force for the segregation and precipitation of rhenium in the molybdenum-rhenium alloy is accurately determined. Then, based on the determined driving force, a systematic analysis is performed on the intermediate alloy state representing the formation process of the precipitated phase in the molybdenum-rhenium alloy to accurately determine the concentration at each point in the intermediate alloy state, thereby improving the accuracy of the energy determined at each point. This allows the energy change process of the precipitated phase gradually evolving from local segregation to a stable growth stage during the formation process to be fully presented, providing an accurate data basis for determining the critical core region of the molybdenum-rhenium alloy at the critical point and the energy barrier of the precipitated phase in the molybdenum-rhenium alloy.

[0045] In some embodiments, step S2311 may further include the following steps: determining the irradiation temperature and the dose rate or vacancy generation rate of the irradiation defect generation intensity based on the irradiation conditions; determining the precipitation trend and precipitation magnitude of the intermediate alloy state based on the kinetic and thermodynamic coefficients of the molybdenum-rhenium alloy; and determining the driving force for rhenium segregation and precipitation during the formation of the molybdenum-rhenium alloy precipitate phase based on the irradiation temperature and the dose rate or vacancy generation rate of the irradiation defect generation intensity, the precipitation trend of the intermediate alloy state, and the precipitation magnitude.

[0046] In this embodiment, based on the irradiation temperature and dose rate or vacancy generation rate of irradiation defect generation intensity determined by the irradiation conditions, and the precipitation trend and magnitude of the intermediate alloy state determined by the kinetic and thermodynamic coefficients of the molybdenum-rhenium alloy, the true physical driving force promoting atomic aggregation can be accurately determined. Compared with the existing technology, which cannot determine the driving force of temperature and radiation under actual conditions, this method effectively avoids calculation errors. Based on this, according to the determined driving force, the complete process of atoms from random distribution to the formation of stable particles can be realistically reproduced, and the critical turning point when the atomic group can just exist stably and no longer disperse can be accurately locked. This makes the subsequently calculated critical nucleus size, composition, and energy barrier to be overcome for precipitation closer to the real physical situation, eliminating the uncertainty of parameters set by experience in the existing technology. Therefore, it is beneficial to improve the simulation accuracy of the formation process of the precipitated phase of molybdenum-rhenium alloy, and more accurately predict the degree of brittleness and hardening of molybdenum-rhenium alloy under actual radiation environment, providing more reliable data support for the safe use of materials.

[0047] In some embodiments, step S2312 may further include the following steps: determining the atomic fraction of rhenium in the molybdenum-rhenium alloy based on the intermediate alloy state; and determining the concentration of rhenium at each point in the intermediate alloy state during the precipitation process based on the driving force and the atomic fraction of rhenium in the molybdenum-rhenium alloy.

[0048] In this embodiment, the atomic fraction of rhenium in the molybdenum-rhenium alloy is determined based on the intermediate alloy state representing the formation process of the precipitated phase in the molybdenum-rhenium alloy. Combined with the determined driving force for the segregation and precipitation of rhenium elements, it is beneficial to accurately determine the precipitation trend and precipitation amplitude of rhenium atoms. Thus, the concentration change of the precipitation process of the molybdenum-rhenium alloy can be accurately determined, and more accurate concentration data of each point in the intermediate alloy state can be obtained.

[0049] In some embodiments, step S232 may further include the following steps: S2321: Determine the region of the critical core of the molybdenum-rhenium alloy at the critical point based on the energy of each point in the intermediate alloy state.

[0050] S2322: The total energy of the region that determines the critical nucleus and the total energy of the initial alloying state of the molybdenum-rhenium alloy before the formation of precipitates.

[0051] S2323: Determine the energy barrier of the precipitated phase of the molybdenum-rhenium alloy based on the total energy of the region of the critical core and the total energy of the initial alloy state before the formation of precipitates.

[0052] Specifically, in step S2321, the point with the highest energy in each intermediate alloy state is determined to be the critical core of the molybdenum-rhenium alloy when it is critical, and the region corresponding to the critical core is the region of the critical core of the molybdenum-rhenium alloy when it is critical.

[0053] In step S2323, the difference between the total energy of the critical core region and the total energy of the initial alloy state of the molybdenum-rhenium alloy before the formation of precipitates is the energy barrier of the precipitates in the molybdenum-rhenium alloy.

[0054] 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.

[0055] 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 average radius of the critical nucleus of the precipitated phase, the elemental concentration of the critical nucleus of the precipitated phase, and the energy barrier of the precipitated phase in a molybdenum-rhenium alloy under irradiation conditions, characterized in that, It includes the following steps: S10: Determine the operating conditions of the irradiation, the composition of the molybdenum-rhenium alloy before irradiation, the kinetic and thermodynamic coefficients of the molybdenum-rhenium alloy, and the equilibrium composition concentration of the precipitated phase; S20: Based on the irradiation conditions determined in step S10, the composition of the molybdenum-rhenium alloy before irradiation, the kinetic and thermodynamic coefficients of the molybdenum-rhenium alloy, and the equilibrium composition concentration of the precipitated phase, determine the region of the critical nucleus of the precipitated phase of the molybdenum-rhenium alloy and the energy barrier of the precipitated phase of the molybdenum-rhenium alloy. S30: Determine the average radius of the critical nucleus and the elemental concentration of the critical nucleus based on the region of the critical nucleus of the precipitated phase of the molybdenum-rhenium alloy.

2. The method according to claim 1, characterized in that, Step S20 also includes the following steps: S21: Based on the composition of the molybdenum-rhenium alloy before irradiation and the equilibrium composition concentration of the precipitated phase, determine the initial alloy state of the molybdenum-rhenium alloy before the formation of precipitated phase and the final alloy state containing precipitated phase. S22: Based on the initial alloy state and the final alloy state, determine the intermediate alloy state of the molybdenum-rhenium alloy from the initial alloy state to the final alloy state; S23: Based on the irradiation conditions, the intermediate alloy state, and the kinetic and thermodynamic coefficients of the molybdenum-rhenium alloy, determine the region of the critical core of the molybdenum-rhenium alloy at the critical point and the energy barrier of the precipitated phase of the molybdenum-rhenium alloy.

3. The method according to claim 2, characterized in that, Step S21 also includes the following steps: S211: Based on the composition of the molybdenum-rhenium alloy before irradiation, determine the composition of the molybdenum-rhenium alloy before precipitation, and based on the composition of the molybdenum-rhenium alloy before precipitation, determine the initial alloy state of the molybdenum-rhenium alloy before precipitation. S212: Determine the composition of the molybdenum-rhenium alloy containing the precipitated phase based on the equilibrium composition concentration of the precipitated phase, and determine the final alloy state of the molybdenum-rhenium alloy containing the precipitated phase based on the composition of the molybdenum-rhenium alloy containing the precipitated phase.

4. The method according to claim 3, characterized in that, Step S212 also includes the following steps: S2121: Determine the precipitation region, wherein the composition of the molybdenum-rhenium alloy in the precipitation region is the equilibrium composition concentration of the precipitated phase; S2122: Based on the composition of the molybdenum-rhenium alloy in the precipitated region, determine the composition of the molybdenum-rhenium alloy in the non-precipitated region, such that the total content of the composition of the molybdenum-rhenium alloy in the precipitated region and the composition of the molybdenum-rhenium alloy in the non-precipitated region is consistent with the composition of the molybdenum-rhenium alloy before irradiation. S2123: Determine the final alloy state of the molybdenum-rhenium alloy containing the precipitated phase based on the composition of the molybdenum-rhenium alloy in the precipitated region and the composition of the molybdenum-rhenium alloy in the non-precipitated region.

5. The method according to claim 2, characterized in that, Step S22 also includes the following steps: S221: The initial alloy state is used as the first endpoint to represent the precipitation process, and the final alloy state is used as the second endpoint to represent the precipitation process; S222: Perform linear interpolation on the first endpoint and the second endpoint to determine multiple intermediate points representing the precipitation process, and make the concentration of the molybdenum-rhenium alloy represented by the multiple intermediate points increase smoothly from small to large, and make the concentration of the molybdenum-rhenium alloy represented by each intermediate point consistent with the total concentration of the component before irradiation. S223: Based on the plurality of intermediate points, determine the intermediate alloy state of the molybdenum-rhenium alloy as it changes from the initial alloy state to the final alloy state.

6. The method according to claim 2, characterized in that, Step S23 also includes the following steps: S231: Determine the energy at each point in the intermediate alloy state based on the irradiation conditions, the intermediate alloy state, and the kinetic and thermodynamic coefficients of the molybdenum-rhenium alloy; S232: Based on the energy at each point, determine the region of the critical core of the molybdenum-rhenium alloy at the critical point and the energy barrier of the precipitated phase of the molybdenum-rhenium alloy.

7. The method according to claim 6, characterized in that, Step S231 also includes the following steps: S2311: Based on the irradiation conditions and the kinetic and thermodynamic coefficients of the molybdenum-rhenium alloy, determine the driving force for the segregation and precipitation of rhenium during the formation of the precipitated phase in the molybdenum-rhenium alloy. S2312: Determine the concentration at each point in the intermediate alloy state during the precipitation process based on the driving force and the intermediate alloy state; S2313: Determine the energy of each point based on the concentration at each point.

8. The method according to claim 7, characterized in that, Step S2311 also includes the following steps: Based on the irradiation conditions, determine the irradiation temperature and the dose rate or vacancy generation rate of the irradiation defect generation intensity. Based on the kinetic and thermodynamic coefficients of the molybdenum-rhenium alloy, the precipitation trend and precipitation magnitude of the intermediate alloy state are determined. Based on the irradiation temperature and the dose rate or vacancy generation rate of the irradiation defect generation intensity, the precipitation trend and precipitation amplitude of the intermediate alloy state, the driving force for the segregation and precipitation of rhenium element during the formation of the molybdenum-rhenium alloy precipitate phase is determined.

9. The method according to claim 7, characterized in that, Step S2312 also includes the following steps: Based on the intermediate alloy state, determine the atomic fraction of rhenium in the molybdenum-rhenium alloy; The concentration of rhenium at each point in the intermediate alloy state during the precipitation process is determined based on the driving force and the atomic fraction of rhenium in the molybdenum-rhenium alloy.

10. The method according to claim 6, characterized in that, Step S232 also includes the following steps: S2321: Determine the region of the critical core of the molybdenum-rhenium alloy at the critical point based on the energy of each point in the intermediate alloy state; S2322: Determine the total energy of the region of the critical core and the total energy of the initial alloying state of the molybdenum-rhenium alloy before the formation of precipitates; S2323: Determine the energy barrier of the precipitated phase of the molybdenum-rhenium alloy based on the total energy of the region of the critical core and the total energy of the initial alloy state of the molybdenum-rhenium alloy before the formation of precipitates.

Images