Method for determining the degree of segregation of elements, the morphology of copper-rich phases and the evolution over time of the reactor pressure vessel steel under irradiation conditions
By calculating the concentration and free energy of Si in reactor pressure vessel steel and updating the diffusion coefficient in combination with irradiation conditions, the shortcomings of existing technologies in simulating the segregation and copper-rich phase formation process of reactor pressure vessel steel are solved, and accurate assessment of its service life and the life cycle of nuclear power plants is achieved.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- CHINA INSTITUTE OF ATOMIC ENERGY
- Filing Date
- 2026-04-24
- Publication Date
- 2026-07-21
AI Technical Summary
Existing technologies cannot accurately simulate and predict the elemental segregation and copper-rich phase formation processes of reactor pressure vessel steel under irradiation conditions, making it difficult to assess its service life and the life cycle of nuclear power plants.
By determining the concentration, chemical free energy, elastic free energy, and gradient free energy of Si in reactor pressure vessel steel, updating the diffusion coefficient in conjunction with irradiation conditions, and calculating the alloy atomic mobility tensor, the element concentration and order parameters of the copper-rich phase are accurately described, thus achieving a complete description of the segregation degree and morphology of reactor pressure vessel steel.
This improves the accuracy of predicting the segregation degree and copper-rich phase morphology of reactor pressure vessel steel under irradiation conditions, providing a reliable reference for assessing its service life and the life cycle of nuclear power plants.
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Figure CN122436083A_ABST
Abstract
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 degree of segregation, copper-rich phase morphology, and time evolution of elements in reactor pressure vessel steel under irradiation conditions. Background Technology
[0002] The statements herein are provided merely as background information in connection with this application and do not necessarily constitute prior art.
[0003] The reactor pressure vessel (RPV) is an irreplaceable core pressure-bearing component in the primary loop of a nuclear power plant. It operates for extended periods in extreme environments of strong neutron irradiation, high temperature, and high pressure. Under the influence of these extreme environments, trace elements such as Cu, Mn, Ni, and Si in the reactor pressure vessel steel undergo irradiation-induced segregation, precipitating nanoscale copper-rich phases. These nanoscale copper-rich phases lead to irradiation embrittlement and mechanical property degradation in the reactor pressure vessel steel, directly affecting the service life of the reactor pressure vessel and thus the life cycle of the nuclear power plant.
[0004] Therefore, there is an urgent need for a method that can accurately predict the elemental segregation and copper-rich phase formation process of reactor pressure vessel steel under irradiation conditions, so as to accurately assess the irradiation life of the reactor pressure vessel, predict the life cycle of the nuclear power plant, and thus provide a reference for guiding the compositional design of reactor pressure vessel steel. 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] This application provides a method for determining the degree of elemental segregation, copper-rich phase morphology, and time evolution of reactor pressure vessel steel under irradiation conditions. The reactor pressure vessel steel is composed of a pentagonal alloy of Fe, Cu, Mn, Ni, and Si. The method includes the following steps: S10: Determining the concentration of Si element in the reactor pressure vessel steel, the chemical free energy of Si element in the pentagonal alloy of Fe, Cu, Mn, Ni, and Si, as well as the elastic free energy and gradient free energy of the pentagonal alloy system; S20: Based on the chemical free energy, elastic free energy, gradient free energy, and Si element concentration determined in step S10, determining the total free energy of the matrix phase of the reactor pressure vessel steel. S30: Determine the initial diffusion coefficient of the solute element in the reactor pressure vessel steel; S40: Update the initial diffusion coefficient based on the irradiation conditions and the material properties of the reactor pressure vessel steel to obtain the updated diffusion coefficient of the element, and determine the alloy atom mobility tensor based on the updated diffusion coefficient of the element; S50: Determine the element concentration of the reactor pressure vessel steel and the order parameter of the copper-rich phase based on the total free energy of the reactor pressure vessel steel determined in step S20 and the alloy atom mobility tensor determined in step S40. The element concentration of the reactor pressure vessel steel can characterize the degree of segregation, and the order parameter of the copper-rich phase can characterize the morphology of the copper-rich phase and its evolution over time.
[0007] The embodiments of this application provide a method for determining the degree of elemental segregation, copper-rich phase morphology, and time evolution of reactor pressure vessel steel under irradiation conditions. This method considers Si, which accelerates the precipitation of the copper-rich phase, and introduces the concentration of Si in the reactor pressure vessel steel and the chemical free energy of Si in the Fe, Cu, Mn, Ni, and Si pentagonal alloy. It also combines this with the elastic free energy and gradient free energy of the pentagonal alloy system driving elemental segregation within the alloy system to accurately determine the total free energy of the reactor pressure vessel steel affecting the solid-state phase transformation of the alloy. Furthermore, considering that irradiation conditions enhance the diffusion capacity of solute elements in the reactor pressure vessel steel, the diffusion coefficient of the solute elements is updated using the irradiation conditions and the material properties of the reactor pressure vessel steel. Based on the updated diffusion coefficient of the solute elements, the method accurately determines the total free energy of the reactor pressure vessel steel. Determining the alloy atom mobility tensor allows for a quantitative description of the irradiation-enhanced diffusion effect, facilitating the accurate reconstruction of solute atom migration behavior in reactor pressure vessel steel under irradiation conditions. Based on this, the elemental concentrations and order parameters of the copper-rich phase in the reactor pressure vessel steel are determined according to the determined total free energy and alloy atom mobility tensor. This provides a complete description of the transformation of the matrix phase to the copper-rich phase in reactor pressure vessel steel under irradiation conditions, making the predicted segregation degree, copper-rich phase morphology, and time evolution of the reactor pressure vessel steel more consistent with its actual service conditions in the reactor. This facilitates accurate evaluation of the comprehensive performance of the reactor pressure vessel steel, providing a reliable reference for predicting the irradiation life of the reactor pressure vessel and the life cycle of the nuclear power plant. 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 comparison diagram of the spatial distribution of Cu, Mn, Ni, Si elements and copper-rich phase in reactor pressure vessel steel with different Si element concentrations according to embodiments of this application. Figure 2 This is a comparison diagram of the spatial distribution of Cu, Mn, Ni, Si elements and copper-rich phase in reactor pressure vessel steel under different irradiation intensities according to embodiments of this application. Figure 3 This is a time evolution diagram of the maximum precipitate radius of reactor pressure vessel steel under different irradiation intensities according to embodiments of this application; Figure 4 This is a graph showing the evolution of the maximum relative concentration of Cu in reactor pressure vessel steel under different irradiation intensities over time, according to embodiments 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 inventors of this application have discovered that, in the prior art, the mainstream method currently used for simulating and predicting the evolution of the microstructure of materials is the phase-field method. However, this method has limitations such as incomplete description of the irradiation-enhanced diffusion effect, which is not conducive to accurately simulating the microstructure evolution of reactor pressure vessel steel under irradiation conditions and makes it difficult to accurately reproduce the elemental segregation and copper-rich phase formation process of reactor pressure vessel steel.
[0014] Based on this, embodiments of this application provide a method for determining the degree of elemental segregation, copper-rich phase morphology, and time evolution of reactor pressure vessel steel under irradiation conditions. The reactor pressure vessel steel is composed of a pentagonal alloy of Fe, Cu, Mn, Ni, and Si. The method includes the following steps: S10: Determine the concentration of Si in the reactor pressure vessel steel, the chemical free energy of Si in the pentagonal alloy of Fe, Cu, Mn, Ni, and Si, as well as the elastic free energy and gradient free energy of the pentagonal alloy system.
[0015] S20: Determine the total free energy of the reactor pressure vessel steel based on the chemical free energy, elastic free energy, and Si concentration determined in step S10.
[0016] S30: Determine the initial diffusion coefficient of the solute element in the reactor pressure vessel steel.
[0017] S40: Based on the irradiation conditions and the material properties of the reactor pressure vessel steel, update the initial diffusion coefficient to obtain the updated diffusion coefficient of the solute element, and determine the alloy atom mobility tensor based on the updated diffusion coefficient of the solute element.
[0018] S50: Based on the total free energy of the reactor pressure vessel steel determined in step S20 and the alloy atomic mobility tensor determined in step S40, the elemental concentration of the reactor pressure vessel steel and the order parameter of the copper-rich phase are determined. The elemental concentration of the reactor pressure vessel steel can characterize the degree of segregation, and the order parameter of the copper-rich phase can characterize the morphology of the copper-rich phase and its evolution over time.
[0019] The embodiments of this application provide a method for determining the degree of elemental segregation, copper-rich phase morphology, and time evolution of reactor pressure vessel steel under irradiation conditions. This method considers Si, which accelerates the precipitation of the copper-rich phase, and introduces the concentration of Si in the reactor pressure vessel steel and the chemical free energy of Si in the Fe, Cu, Mn, Ni, and Si pentagonal alloy. It also combines this with the elastic free energy and gradient free energy of the pentagonal alloy system driving elemental segregation within the alloy system to accurately determine the total free energy of the reactor pressure vessel steel affecting the solid-state phase transformation of the alloy. Furthermore, considering that irradiation conditions enhance the diffusion capacity of solute elements in the reactor pressure vessel steel, the diffusion coefficient of the solute elements is updated using the irradiation conditions and the material properties of the reactor pressure vessel steel. Based on the updated diffusion coefficient of the solute elements, the method accurately determines the total free energy of the reactor pressure vessel steel. Determining the alloy atom mobility tensor allows for a quantitative description of the irradiation-enhanced diffusion effect, facilitating the accurate reconstruction of solute atom migration behavior in reactor pressure vessel steel under irradiation conditions. Based on this, the elemental concentrations and order parameters of the copper-rich phase in the reactor pressure vessel steel are determined according to the determined total free energy and alloy atom mobility tensor. This provides a complete description of the transformation of the matrix phase to the copper-rich phase in reactor pressure vessel steel under irradiation conditions, making the predicted segregation degree, copper-rich phase morphology, and time evolution of the reactor pressure vessel steel more consistent with its actual service conditions in the reactor. This facilitates accurate evaluation of the comprehensive performance of the reactor pressure vessel steel, providing a reliable reference for predicting the irradiation life of the reactor pressure vessel and the life cycle of the nuclear power plant.
[0020] In some embodiments, step S10, when determining the concentration of Si in the reactor pressure vessel steel, may further include the following steps: S11: Determine the solid solubility of Si in the matrix phase of reactor pressure vessel steel, and determine the concentration of Si in a predetermined type of reactor pressure vessel steel.
[0021] S12: Determine the concentration of Si in the reactor pressure vessel steel based on solid solubility and concentration.
[0022] In this embodiment, the concentration of Si in the reactor pressure vessel steel is determined by considering the solid solubility of Si in the matrix phase of the reactor pressure vessel steel and the concentration of Si in the predetermined type of reactor pressure vessel steel. Compared with the method in the prior art, this method can avoid deviating from the actual application scenario and ensure that the determined concentration of Si has a real physical meaning, thereby improving the accuracy of the determined concentration of Si in the reactor pressure vessel steel.
[0023] In some embodiments, step S12 may further include: determining a concentration range of Si element based on the concentration of Si element in the predetermined type of reactor pressure vessel steel; and determining the concentration of Si element in the reactor pressure vessel steel based on the concentration range of Si element and the solid solubility. In this embodiment, by referring to the concentration of Si element in the predetermined type of reactor pressure vessel steel, a concentration range of Si element is defined to ensure that the concentration of Si element in the reactor pressure vessel steel is within the specified range. This ensures that the concentration of Si element is reasonable and effective, has true physical meaning, and thus effectively improves the accuracy of the determined concentration of Si element in the reactor pressure vessel steel.
[0024] For example, in step S11, the reactor pressure vessel steel of the predetermined type can be domestically produced A508-3 reactor pressure vessel steel.
[0025] In some embodiments, step S10, when determining the chemical free energy of Si in the pentagonal alloy of Fe, Cu, Mn, Ni, and Si, and the elastic free energy of the pentagonal alloy system, may further include the following steps: S13: Determine the Gibbs free energy and gradient free energy of Si in the thermodynamic database, and determine the interaction parameters between Si and Fe, Cu, Mn, and Ni in reactor pressure vessel steel. Based on the Gibbs free energy, gradient free energy, and interaction parameters, determine the chemical free energy of Si in the pentagonal alloy of Fe, Cu, Mn, Ni, and Si.
[0026] S14: Determine the elastic free energy of the five-element alloy system based on the determined concentration of Si in the reactor pressure vessel steel.
[0027] In this embodiment, the Gibbs free energy and gradient free energy of Si element determined in the thermodynamic database, as well as the interaction parameters between Si element and Fe, Cu, Mn, and Ni in reactor pressure vessel steel, are considered to introduce the energy contribution of inter-element interaction and magnetic order transition. This fully reflects the influence of the interaction between the five elements Fe, Cu, Mn, Ni, and Si on the thermodynamic stability of the pentagonal alloy, which helps to improve the accuracy of the determined chemical free energy of Si element in the Fe, Cu, Mn, Ni, and Si pentagonal alloy.
[0028] In some embodiments, step S14 may further include the following steps: S141: Determine the CuMnNi concentration in the reactor pressure vessel steel, and based on the CuMnNi concentration, determine the elastic free energy of CuMnNi in the matrix phase and copper-rich phase of the reactor pressure vessel steel, as well as the elastic free energy of the copper-rich phase precipitation.
[0029] S142: Determine the molar volume, Young's modulus, atomic size mismatch factor, and Kronecker function of Si in the matrix and copper-rich phases of reactor pressure vessel steel, respectively.
[0030] S143: Based on the molar volume of Si, Young's modulus, atomic size mismatch factor, Kronecker function, and the concentration of Si in the reactor pressure vessel steel determined in step S142, determine the elastic free energy of Si in the pentagonal alloy of Fe, Cu, Mn, Ni, and Si.
[0031] S144: Based on the elastic free energy of Si in the pentagonal alloy of Fe, Cu, Mn, Ni and Si determined in step S143, the elastic free energy of CuMnNi in the matrix phase and copper-rich phase of reactor pressure vessel steel determined in step S141, and the elastic free energy of copper-rich phase precipitation, determine the elastic free energy of the pentagonal alloy system.
[0032] In this embodiment, by considering the molar volume, Young's modulus, atomic size mismatch factor, and Kronecker function of Si in the matrix and copper-rich phases of reactor pressure vessel steel, and combining this with the concentration of Si in the reactor pressure vessel steel, the elastic free energy of Si in the pentagonal alloy of Fe, Cu, Mn, Ni, and Si is determined. This ensures that the free energy accurately reflects the lattice distortion caused by the atomic size mismatch between Si atoms and the matrix atoms Fe, Cu, Mn, and Ni. Furthermore, by combining the elastic free energy of CuMnNi in the matrix and copper-rich phases of reactor pressure vessel steel, as well as the elastic free energy of copper-rich phase precipitation, a more accurate elastic free energy of the pentagonal alloy system can be determined. This allows for a more accurate reflection of the impact of lattice distortion caused by uneven element concentration distribution on the energy of the pentagonal alloy system. Consequently, simulations of the segregation degree, copper-rich phase morphology, and time evolution of reactor pressure vessel steel are more closely aligned with the actual service conditions of reactor pressure vessel steel in reactors.
[0033] In some embodiments, in step S144, the elastic free energy of the five-element alloy system is obtained by summing the elastic free energy of Si in the Fe, Cu, Mn, Ni, and Si pentagonal alloy, the elastic free energy of CuMnNi in the matrix phase and copper-rich phase of reactor pressure vessel steel, and the elastic free energy of copper-rich phase precipitation.
[0034] In some embodiments, step S20 may further include the following steps: S21: Determine the matrix phase free energy and copper-rich phase free energy of the FeCuMnNi quaternary alloy in a thermodynamic database.
[0035] S22: Based on the chemical free energy of Si in the pentagonal alloy of Fe, Cu, Mn, Ni, and Si determined in step S10, determine the interaction parameters between Si and Fe, Cu, Mn, and Ni in the matrix phase and the copper-rich phase, and determine the Gibbs free energy of Si in the matrix phase and the copper-rich phase.
[0036] S23: Based on the Si concentration in the reactor pressure vessel steel determined in step S10, the matrix phase free energy and copper-rich phase free energy of the FeCuMnNi quaternary alloy determined in step S21, the interaction parameters between Si and Fe, Cu, Mn, and Ni in the matrix and copper-rich phases determined in step S22, and the Gibbs free energy of Si in the matrix and copper-rich phases, determine the chemical free energy of the matrix phase and the chemical free energy of the copper-rich phase of the reactor pressure vessel steel.
[0037] S24: Determine the total free energy of the reactor pressure vessel steel system based on the chemical free energy of the matrix phase and the copper-rich phase of the reactor pressure vessel steel determined in S23, as well as the elastic free energy and gradient free energy determined in S10.
[0038] In this embodiment, by determining the interaction parameters between Si and Fe, Cu, Mn, and Ni in the matrix and copper-rich phases, and by determining the Gibbs free energy of Si in the matrix and copper-rich phases, compared to the existing method of introducing isolated chemical free energies of Si, this approach avoids the core problems of the free energy calculation being out of sync with the actual steel grade and the resulting insufficient prediction accuracy caused by ignoring Si. It also avoids the computational stability issues easily caused by the superposition of multi-component systems, ensuring that the chemical free energies of the determined reactor pressure vessel steel in the matrix and copper-rich phases are completely matched. The actual composition and service scenarios of reactor pressure vessel steel are analyzed. Furthermore, considering the free energies of the matrix phase and copper-rich phase of the FeCuMnNi quaternary alloy determined in the thermodynamic database, and combined with the Si element concentration in the reactor pressure vessel steel determined in step S10, the quantitative contribution of Si to the thermodynamic driving force of the two phases is accurately completed. This further improves the accuracy of the determined chemical free energies of the matrix phase and copper-rich phase of the reactor pressure vessel steel, which is beneficial to ensuring the accuracy and stability of predicting the degree of segregation, the morphology of the copper-rich phase and its changes over time in the reactor pressure vessel steel under irradiation conditions.
[0039] In some embodiments, in step S21, the thermodynamic database is the CALPHAD thermodynamic database, which has well-established data recognized in the art that can accurately describe the core matrix thermodynamic behavior of reactor pressure vessel steel.
[0040] In some embodiments, in step S22, based on the CALPHAD thermodynamic database and the chemical free energy of Si in the Fe, Cu, Mn, Ni, and Si quinary alloy determined in step S10, the interaction parameters between Si and Fe, Cu, Mn, and Ni in the matrix phase and copper-rich phase, as well as the Gibbs free energy of Si in the matrix phase and copper-rich phase, can be determined. The interaction parameters include the binary and ternary subsystem interaction parameters between Si and each element in the Fe, Cu, Mn, Ni quinary system.
[0041] In some embodiments, in step S23, the concentration of Si in the reactor pressure vessel steel determined in S10, the matrix phase free energy and copper-rich phase free energy of the FeCuMnNi quaternary alloy determined in step S21, the interaction parameters between Si and Fe, Cu, Mn, and Ni in the matrix and copper-rich phases determined in step S22, the Gibbs free energy of Si in the matrix and copper-rich phases, the chemical free energy of the matrix phase of the reactor pressure vessel steel, and the chemical free energy of the copper-rich phase of the reactor pressure vessel steel conform to the following relationship: , .
[0042] in, This represents the chemical free energy of the matrix phase of the reactor pressure vessel steel. The chemical free energy of the copper-rich phase in reactor pressure vessel steel, The matrix phase free energy of the FeCuMnNi quaternary alloy is given. The free energy of the copper-rich phase in the FeCuMnNi quaternary alloy. This represents the concentration of element i in the reactor pressure vessel steel. Element i can be one of five elements: Fe, Cu, Mn, Ni, or Si. These are the interaction parameters between Si and Fe, Cu, Mn, and Ni in the matrix phase. The interaction parameters between Si and Fe, Cu, Mn, and Ni in a copper-rich phase are given. This represents the Gibbs free energy of Si in the matrix phase. is the Gibbs free energy of Si in the copper-rich phase.
[0043] In this embodiment, by establishing the relationship between the concentration of Si element in reactor pressure vessel steel, the matrix phase free energy and copper-rich phase free energy of the FeCuMnNi quaternary alloy, the interaction parameters between Si element and Fe, Cu, Mn, and Ni in the matrix and copper-rich phases, and the relationship between the Gibbs free energy of Si element in the matrix and copper-rich phases and the chemical free energy of the matrix and copper-rich phases of reactor pressure vessel steel, it is beneficial to improve the accuracy of the determined chemical free energy of the matrix and copper-rich phases of reactor pressure vessel steel. This further ensures the accuracy and stability of predicting the segregation degree, morphology of the copper-rich phase, and its changes over time in reactor pressure vessel steel under irradiation conditions.
[0044] Furthermore, in the above relation, This represents the interaction parameters between Si and x elements in the matrix phase, for example, This represents the interaction parameter between Si and Cu elements in the matrix phase. This represents the interaction parameters between Si and x elements in a copper-rich phase, for example, This represents the interaction parameter between Si and Cu elements in a copper-rich phase. This represents the interaction parameters between Si and the three elements x and y in the matrix phase, for example, This represents the interaction parameters between Si and Cu, Mn, and other elements in the matrix phase. This represents the interaction parameters between Si and elements x and y in a copper-rich phase, for example... This represents the interaction parameters between Si and Cu, Mn, and other elements in a copper-rich phase.
[0045] In some embodiments, step S40 may further include the following steps: S41: Determine the irradiation conditions and the material properties of the reactor pressure vessel steel, and determine the vacancy concentration of the reactor pressure vessel steel under the irradiation conditions based on the irradiation conditions and material properties.
[0046] S42: Determine the vacancy concentration of reactor pressure vessel steel under non-irradiated conditions.
[0047] S43: Determine the diffusion coefficient of the element under irradiation conditions based on the vacancy concentrations determined in step S41 and step S42.
[0048] S44: Determine the alloy atom mobility tensor based on the vacancy concentration determined in step S41, the vacancy concentration determined in step S42, and the diffusion coefficient of the elements under irradiation conditions determined in step S43.
[0049] Under thermal equilibrium, the vacancy concentration of reactor pressure vessel steel is determined solely by temperature and remains at a low level. However, neutron irradiation generates a large number of vacancy-interstitial atom pairs in the reactor pressure vessel steel, resulting in a vacancy concentration far exceeding that in thermal equilibrium. This significantly accelerates the diffusion of solute elements. Based on this, this embodiment considers irradiation conditions and combines them with the material properties of reactor pressure vessel steel to determine the vacancy concentration of reactor pressure vessel steel under irradiation conditions and the vacancy concentration of reactor pressure vessel steel under non-irradiation conditions. By combining these factors, an updated diffusion coefficient of solute elements is obtained. This facilitates a quantitative description of the actual irradiation-enhanced diffusion effect within the reactor, enabling the diffusion coefficient to accurately reflect the diffusion and segregation behavior of solute atoms in reactor pressure vessel steel during reactor operation. This improves the accuracy of the determined alloy atom mobility tensor and facilitates accurate prediction of the nucleation and evolution process of copper-rich phases.
[0050] In some embodiments, in step S44, the vacancy concentration of reactor pressure vessel steel under irradiation conditions determined in step S41, the vacancy concentration of reactor pressure vessel steel under non-irradiation conditions determined in step S42, the diffusion coefficient of elements under irradiation conditions determined in step S43, and the alloy atom mobility tensor conform to the following relationship: .
[0051] in, Let i be the alloy atom mobility tensor of element i. The concentration of element i in the reactor pressure vessel steel. Set the initial concentration for element i, which can be one of five elements: Fe, Cu, Mn, Ni, or Si. This represents the vacancy concentration in reactor pressure vessel steel under irradiation conditions. This represents the vacancy concentration in reactor pressure vessel steel under non-irradiated conditions. Let be the diffusion coefficient of the element under non-irradiated conditions. denoted as the diffusion coefficient of the element under irradiation conditions.
[0052] In this embodiment, the relationship between the vacancy concentration of reactor pressure vessel steel under irradiation conditions, the vacancy concentration of reactor pressure vessel steel under no irradiation conditions, the diffusion coefficient of elements under irradiation conditions, and the alloy atom mobility tensor is established to further improve the accuracy of the determined alloy atom mobility tensor. This is beneficial for further reconstructing the diffusion and segregation behavior of solute atoms in reactor pressure vessel steel during reactor operation, and improving the prediction accuracy of the nucleation and evolution process of copper-rich phases.
[0053] Further, in step S44, the alloy atomic mobility tensors of the five elements Fe, Cu, Mn, Ni, and Si are determined according to the relational formula. In step S50, based on the determined alloy atomic mobility tensors of the five elements Fe, Cu, Mn, Ni, and Si, and the total free energy of the reactor pressure vessel steel determined in step S20, the elemental concentrations of the reactor pressure vessel steel and the order parameter of the copper-rich phase are determined.
[0054] In some embodiments, step S41 may further include the following steps: S411: Determine the irradiation intensity, dislocation density, and dislocation well strength of the reactor pressure vessel steel; based on the irradiation intensity, dislocation density, and dislocation well strength, determine the interstitial atom absorption coefficient, vacancy mechanism diffusivity, and interstitial mechanism diffusivity of the reactor pressure vessel steel.
[0055] S412: Determine the recombination rate of vacancies and interstitial atoms based on the interstitial atom absorption coefficient, vacancy mechanism diffusion rate, and interstitial mechanism diffusion rate determined in step S411.
[0056] S413: Determine the vacancy concentration of reactor pressure vessel steel under irradiation conditions based on the dislocation density and dislocation well strength determined in step S411, and the recombination rate of vacancies and interstitial atoms determined in step S413.
[0057] In this embodiment, by considering the irradiation intensity, the dislocation density, and the dislocation well strength of the reactor pressure vessel steel, the interstitial atom absorption coefficient, vacancy mechanism diffusivity, and interstitial mechanism diffusivity of the reactor pressure vessel steel are determined. Based on this, the precise recombination rate of vacancies and interstitial atoms is determined. On this basis, the vacancy concentration of the reactor pressure vessel steel under irradiation conditions is determined to fully consider the influence of irradiation conditions on the irradiation vacancy concentration, so that the determined vacancy concentration can reflect its dynamic adjustment with irradiation conditions. Thus, a more accurate vacancy concentration of the reactor pressure vessel steel that can be adjusted with temperature and irradiation intensity is determined, which is beneficial for determining a more accurate diffusion coefficient of the updated solute elements.
[0058] It should be noted that in step S41, the irradiation conditions include the irradiation intensity received by the reactor pressure vessel steel, and the material properties of the reactor pressure vessel steel include the dislocation density and the dislocation well strength.
[0059] In some embodiments, step S42 may further include the following steps: S421: Determine the formation energy of vacancies, Boltzmann constant, and irradiation temperature in the Fe matrix phase.
[0060] S422: Determine the vacancy concentration of reactor pressure vessel steel under non-irradiation conditions based on the vacancy formation energy, Boltzmann constant, and irradiation temperature in the matrix phase Fe determined in step S421.
[0061] In this embodiment, the vacancy concentration of reactor pressure vessel steel under non-irradiation conditions is determined by considering the formation energy of vacancies in the Fe matrix phase, the Boltzmann constant, and the irradiation temperature. This fully accounts for the influence of irradiation temperature on the equilibrium vacancy concentration, allowing the determined vacancy concentration to reflect its dynamic adjustment with irradiation temperature. Consequently, a more accurate vacancy concentration of reactor pressure vessel steel under non-irradiation conditions is determined, which is beneficial for determining a more accurate diffusion coefficient of the updated solute element.
[0062] In some embodiments, in step S50, the total free energy of the reactor pressure vessel steel determined in step S20, the alloy atom mobility tensor determined in step S40, the elemental concentration of the reactor pressure vessel steel, and the order parameter of the copper-rich phase conform to the following relationship: .
[0063] in, Let t represent the concentration of element i in a predetermined space r within the reactor pressure vessel steel at time t, where t is the time. Let i be the alloy atom mobility tensor of element i. This represents the concentration of element i in the reactor pressure vessel steel. Element i consists of five elements: Fe, Cu, Mn, Ni, and Si. The total free energy of the reactor pressure vessel steel. For phase length coefficient, For the order parameter of the copper-rich phase, This represents the value of the copper-rich phase at time t in a predetermined space r within the reactor pressure vessel steel.
[0064] In this embodiment, the relationship between the total free energy of reactor pressure vessel steel, the alloy atomic mobility tensor, the elemental concentration of reactor pressure vessel steel, and the order parameter of the copper-rich phase is established to further improve the accuracy of the determined elemental concentration of reactor pressure vessel steel and the order parameter of the copper-rich phase. This is beneficial to further improve the predicted segregation degree of reactor pressure vessel steel, the morphology of the copper-rich phase, and the degree to which the evolution over time reflects the actual service conditions of the reactor pressure vessel in the reactor.
[0065] It should be noted that in the above formula, the predetermined space r represents any space in the reactor pressure vessel steel. This represents the concentration of element i at time t in this space.
[0066] Using reactor pressure vessel steels with different Cu, Mn, and Si contents as the prediction targets, the method provided in the embodiments of this application is used to determine the degree of elemental segregation, copper-rich phase morphology, and evolution over time in the reactor pressure vessel steel, so as to verify the applicability of this application to reactor pressure vessel steels with different alloy composition systems.
[0067] Please see Figure 1 , Figure 1 This diagram illustrates a comparison of the spatial distribution of Cu, Mn, Ni, Si, and copper-rich phases in reactor pressure vessel steels with different Si concentrations according to embodiments of this application. Figure 1 In the image, from top to bottom, the spatial distribution of Cu, Mn, Ni, and Si elements and the copper-rich phase at different Si concentrations for Fe15Cu1Mn1Ni1Si, Fe15Cu1Mn5Ni1Si, and Fe15Cu1Mn1Ni5Si at 823 K, under no-irradiation conditions, and in a simulation with a step size of 4000. Figure 1It can be seen that Ni, Mn, and Si all accumulate on the precipitation surface of the copper-rich phase. Increasing the content of Mn and Si elements in reactor pressure vessel steel will increase the element segregation area and the precipitation volume.
[0068] Furthermore, using Fe15Cu1Mn1Ni1Si as the prediction object, the method provided in the embodiments of this application is adopted to determine the degree of elemental segregation, copper-rich phase morphology, and time evolution of reactor pressure vessel steel under different irradiation intensities.
[0069] Please see Figure 2-4 , Figure 2 The diagram shows a comparison of the spatial distribution of Cu, Mn, Ni, Si elements and copper-rich phases in reactor pressure vessel steel under different irradiation intensities, according to embodiments of this application. Figure 3 The diagram illustrates the evolution of the maximum precipitate radius over time for reactor pressure vessel steel under different irradiation intensities, according to embodiments of this application. Figure 4 The graph shows the evolution of the maximum relative concentration of Cu in reactor pressure vessel steel under different irradiation intensities over time, according to an embodiment of this application.
[0070] exist Figure 2 In the middle, from top to bottom, they represent Fe15Cu1Mn1Ni1Si in 2× dpa / s, 1× dpa / s, 5× Spatial distribution of Cu, Mn, Ni, Si elements and copper-rich phase under irradiation intensity of dpa / s, in Figure 3 and Figure 4 In the figure, each curve represents Fe15Cu1Mn1Ni1Si at 0 dPa / s and 2× dpa / s, 1× dpa / s, 5× The evolution of the maximum precipitated phase radius and the maximum relative concentration of Cu over time at an irradiation intensity of dpa / s.
[0071] according to Figure 2-4 It can be seen that, compared with the case without irradiation, the relative concentration of Cu approaches 1 faster under irradiation conditions. Irradiation significantly accelerates the formation of the copper-rich phase of Fe15Cu1Mn1Ni1Si, and the greater the irradiation intensity, the faster the Cu precipitation rate.
[0072] 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.
[0073] 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 degree of elemental segregation, copper-rich phase morphology, and time evolution of reactor pressure vessel steel under irradiation conditions, wherein the reactor pressure vessel steel is composed of a pentagonal alloy of Fe, Cu, Mn, Ni, and Si, characterized in that, It includes the following steps: S10: Determine the concentration of Si in the reactor pressure vessel steel, the chemical free energy of Si in the five-element alloy of Fe, Cu, Mn, Ni, and Si, the elastic free energy of the five-element alloy system, and the gradient free energy. S20: Determine the total free energy of the reactor pressure vessel steel based on the chemical free energy, elastic free energy, gradient free energy, and Si element concentration determined in step S10. S30: Determine the initial diffusion coefficient of the solute element in the reactor pressure vessel steel; S40: Based on the irradiation conditions and the material properties of the reactor pressure vessel steel, update the initial diffusion coefficient, determine the updated diffusion coefficient of the solute element, and determine the alloy atom mobility tensor based on the updated diffusion coefficient of the solute element. S50: Based on the total free energy of the reactor pressure vessel steel determined in step S20 and the atomic mobility tensor of the alloy determined in step S40, the elemental concentration of the reactor pressure vessel steel and the order parameter of the copper-rich phase are determined. The elemental concentration of the reactor pressure vessel steel can characterize the degree of segregation, and the order parameter of the copper-rich phase can characterize the morphology of the copper-rich phase and its evolution over time.
2. The method according to claim 1, characterized in that, Step S40 also includes the following steps: S41: Determine the irradiation conditions and the material properties of the reactor pressure vessel steel, and determine the vacancy concentration of the reactor pressure vessel steel under the irradiation conditions based on the irradiation conditions and the material properties; S42: Determine the vacancy concentration of the reactor pressure vessel steel under irradiation-free conditions; S43: Determine the diffusion coefficient of the element under irradiation conditions based on the vacancy concentrations determined in step S41 and step S42. S44: Determine the alloy atom mobility tensor based on the vacancy concentration determined in step S41, the vacancy concentration determined in step S42, and the diffusion coefficient of the elements under irradiation conditions determined in step S43.
3. The method according to claim 2, characterized in that, In step S44, the vacancy concentration of the reactor pressure vessel steel under irradiation conditions determined in step S41, the vacancy concentration of the reactor pressure vessel steel under non-irradiation conditions determined in step S42, the diffusion coefficient of the element under irradiation conditions determined in step S43, and the atom mobility tensor of the alloy conform to the following relationship: ， in, Let i be the alloy atom mobility tensor of element i. The concentration of element i in the reactor pressure vessel steel. Set the initial concentration for element i, which can be one of five elements: Fe, Cu, Mn, Ni, or Si. The vacancy concentration of the reactor pressure vessel steel under the irradiation conditions. The vacancy concentration of the reactor pressure vessel steel under the aforementioned radiation-free conditions. Let be the diffusion coefficient of the element under non-irradiated conditions. is the diffusion coefficient of the element under the irradiation conditions.
4. The method according to claim 1, characterized in that, In step S50, the total free energy of the reactor pressure vessel steel determined in step S20, the atom mobility tensor of the alloy determined in step S40, the elemental concentration of the reactor pressure vessel steel, and the order parameter of the copper-rich phase conform to the following relationship: ， in, Let t represent the concentration of element i in a predetermined space r within the reactor pressure vessel steel at time t, where t is the time. Let i be the alloy atom mobility tensor of element i. The concentration of element i in the steel of the reactor pressure vessel is given by the element i, which is one of five elements: Fe, Cu, Mn, Ni, and Si. The total free energy of the reactor pressure vessel steel is given. For phase length coefficient, For the order parameter of the copper-rich phase, This represents the value of the copper-rich phase at time t in a predetermined space r within the reactor pressure vessel steel.
5. The method according to claim 1, characterized in that, Step S10 also includes the following steps: S11: Determine the solid solubility of Si in the matrix phase of the reactor pressure vessel steel, and determine the concentration of Si in the reactor pressure vessel steel of a predetermined type. S12: Determine the concentration of Si element in the reactor pressure vessel steel based on the solid solubility and the concentration.
6. The method according to claim 1, characterized in that, Step S10 also includes the following steps: S13: Determine the Gibbs free energy and gradient free energy of Si element in the thermodynamic database, and determine the interaction parameters between Si element and Fe, Cu, Mn, and Ni in reactor pressure vessel steel. Based on the Gibbs free energy, the gradient free energy, and the interaction parameters, determine the chemical free energy of Si element in the pentagonal alloy of Fe, Cu, Mn, Ni, and Si. S14: Determine the elastic free energy of the five-element alloy system based on the determined concentration of Si in the reactor pressure vessel steel.
7. The method according to claim 6, characterized in that, Step S14 also includes the following steps: S141: Determine the CuMnNi concentration in the reactor pressure vessel steel, and based on the CuMnNi concentration, determine the elastic free energy of CuMnNi in the matrix phase and copper-rich phase of the reactor pressure vessel steel, as well as the elastic free energy of the copper-rich phase precipitation. S142: Determine the molar volume, Young's modulus, atomic size mismatch factor, and Kronecker function of Si in the matrix phase and copper-rich phase of the reactor pressure vessel steel, respectively. S143: Based on the molar volume of Si, Young's modulus, atomic size mismatch factor, Kronecker function, and concentration of Si in the reactor pressure vessel steel determined in step S142, determine the elastic free energy of Si in the pentagonal alloy of Fe, Cu, Mn, Ni, and Si. S144: Based on the elastic free energy of Si in the pentagonal alloy of Fe, Cu, Mn, Ni, and Si determined in step S143, the elastic free energy of CuMnNi in the matrix phase and copper-rich phase of the reactor pressure vessel steel determined in step S141, and the elastic free energy of copper-rich phase precipitation, determine the elastic free energy of the pentagonal alloy system.
8. The method according to claim 1, characterized in that, Step S20 also includes the following steps: S21: Determine the matrix phase free energy and copper-rich phase free energy of the FeCuMnNi quaternary alloy in a thermodynamic database; S22: Based on the chemical free energy of Si in the pentagonal alloy of Fe, Cu, Mn, Ni and Si determined in step S10, determine the interaction parameters between Si and Fe, Cu, Mn and Ni in the matrix phase and copper-rich phase, and determine the Gibbs free energy of Si in the matrix phase and copper-rich phase. S23: Based on the concentration of Si in the reactor pressure vessel steel determined in step S10, the matrix phase free energy and copper-rich phase free energy of the FeCuMnNi quaternary alloy determined in step S21, the interaction parameters between Si and Fe, Cu, Mn, and Ni in the matrix phase and copper-rich phase determined in step S22, and the Gibbs free energy of Si in the matrix phase and copper-rich phase, determine the chemical free energy of the matrix phase and the chemical free energy of the copper-rich phase of the reactor pressure vessel steel. S24: Determine the total free energy of the reactor pressure vessel steel system based on the chemical free energy of the matrix phase and the copper-rich phase of the reactor pressure vessel steel determined in S23, and the elastic free energy and gradient free energy determined in S10.
9. The method according to claim 8, characterized in that, In step S23, the concentration of Si in the reactor pressure vessel steel determined in S10, the matrix phase free energy and copper-rich phase free energy of the FeCuMnNi quaternary alloy determined in step S21, the interaction parameters between Si and Fe, Cu, Mn, and Ni in the matrix and copper-rich phases determined in step S22, the Gibbs free energy of Si in the matrix and copper-rich phases, the chemical free energy of the matrix phase of the reactor pressure vessel steel, and the chemical free energy of the copper-rich phase of the reactor pressure vessel steel conform to the following relationship: ， ， in, The chemical free energy of the matrix phase of the reactor pressure vessel steel is given. The chemical free energy of the copper-rich phase of the reactor pressure vessel steel is given. The matrix phase free energy of the FeCuMnNi quaternary alloy is given. The free energy of the copper-rich phase in the FeCuMnNi quaternary alloy is given. The concentration of element i in the steel of the reactor pressure vessel is given by the given element i, which is one of five elements: Fe, Cu, Mn, Ni, and Si. These are the interaction parameters between Si and Fe, Cu, Mn, and Ni in the matrix phase. The interaction parameters between Si and Fe, Cu, Mn, and Ni in a copper-rich phase are given. This represents the Gibbs free energy of Si in the matrix phase. is the Gibbs free energy of Si in the copper-rich phase.
10. The method according to claim 2, characterized in that, Step S41 also includes the following steps: S411: Determine the irradiation intensity of the reactor pressure vessel steel, the dislocation density of the reactor pressure vessel steel, and the potential well strength of the dislocations. Based on the irradiation intensity, the dislocation density of the reactor pressure vessel steel, and the potential well strength of the dislocations, the interstitial atom absorption coefficient, vacancy mechanism diffusivity, and interstitial mechanism diffusivity of the reactor pressure vessel steel are determined. S412: Determine the recombination rate of vacancies and interstitial atoms based on the interstitial atom absorption coefficient, vacancy mechanism diffusion rate and interstitial mechanism diffusion rate determined in step S411. S413: Determine the vacancy concentration of the reactor pressure vessel steel under irradiation conditions based on the dislocation density and dislocation well strength determined in step S411, and the recombination rate of the vacancies and interstitial atoms determined in step S413.
11. The method according to claim 2, characterized in that, Step S42 also includes the following steps: S421: Determine the formation energy of vacancies, Boltzmann constant, and irradiation temperature in the Fe matrix phase; S422: Determine the vacancy concentration of the reactor pressure vessel steel under non-irradiation conditions based on the vacancy formation energy, Boltzmann constant, and irradiation temperature in the matrix phase Fe determined in step S421.