Analysis methods, systems, and media for the stability of vacancy-type point defects in UO2.

Abstract

The application discloses a method and system for analyzing stability of UO2 vacancy type point defects and a medium, and the method comprises the following steps: establishing a UO2 crystallographic primitive cell, testing calculation parameters of a UO2 first principle, the calculation parameters comprising a plane wave cutoff energy, a K-point grid density and a U value of a strong correlation system Hubbard model; establishing a UO2 supercell based on the UO2 crystallographic primitive cell; constructing different vacancy defect structure models containing irradiation by using the UO2 supercell; optimizing the vacancy defect structure models according to the calculation parameters, and calculating formation energy and binding energy; judging the difficulty degree of formation of different vacancy defects in UO2 after irradiation according to the formation energy and the binding energy, and analyzing the stability of the different vacancy defects. The calculation of the application does not depend on empirical parameters, has high calculation precision and strong reliability, and provides an effective calculation method for UO2 fuel irradiation damage research and theoretical support for design and modification of UO2 fuel.

Description

Technical Field

[0001] This invention relates to the field of stability analysis technology for vacancy-type point defects in UO2, specifically to analysis methods, systems, and media for the stability of vacancy-type point defects in UO2. Background Technology

[0002] UO2 oxide fuel possesses numerous superior properties, such as a high melting point (2800℃), strong fission product containment capacity, and minimal risk of zirconium-water chemical reaction with traditional zirconium alloy cladding materials, indicating excellent compatibility with fuel cladding. Furthermore, its preparation process is mature, making UO2 widely used as a commercial pressurized water reactor fuel in nuclear power plants. During service, UO2 fuel assemblies are exposed to strong particle radiation fields (neutron energies around 2 MeV) and high temperature and pressure conditions. During nuclear fission of U atoms, a large number of neutrons and fission products are generated. These energetic particles collide with atoms in the UO2 lattice, producing pKA (neutron-dependent atomic absorption spectrophotometers). When the pKA energy is sufficiently high, it slows down in UO2, generating numerous vacancies and interstitial atoms, forming ex-situ peaks and causing radiation damage to the UO2 fuel. This leads to degradation of the fuel's thermal and mechanical properties (such as reduced thermal conductivity and mechanical strength). The irradiation process of UO2 fuel occurs at the atomic level. Vacancy and interstitial atoms migrate, diffuse, and aggregate within UO2. During this evolutionary process, most of the vacancy and interstitial atoms recombine and disappear, with only a small number of defects interacting with surrounding atoms and defects to form small clusters. To improve the utilization efficiency of UO2 nuclear fuel and the economic benefits of nuclear power plants, long-life, high-burnup fuels have been proposed. However, experimental methods cannot characterize the existence form and stability of these small clusters.

[0003] In view of the above, this application is hereby submitted. Summary of the Invention

[0004] The purpose of this invention is to provide an analytical method, system, and medium for the stability of vacancy-type point defects in UO2. This invention employs a first-principles calculation method to study the stability of irradiation defects, which is not constrained by experimental conditions, is highly efficient and convenient, reduces the research cycle, and saves economic costs. It can overcome many shortcomings of experimental methods in studying microscale irradiation damage (such as difficulty in obtaining microscopic information of point defects and high experimental costs). Through this invention, a UO2 irradiation defect calculation model can be easily and quickly established to obtain the stability of different types of irradiation defects; moreover, the calculation does not rely on empirical parameters, and the calculation accuracy and reliability are high. This invention provides an effective calculation method for the study of UO2 fuel irradiation damage and provides theoretical support for the design and modification of UO2 fuel.

[0005] This invention is achieved through the following technical solution:

[0006] In a first aspect, the present invention provides a method for analyzing the stability of vacancy-type point defects in UO2, the method comprising:

[0007] A crystallographic unit cell for UO2 was established, and the first-principles calculation parameters of UO2 were tested. The calculation parameters included the plane wave cutoff energy Ecut, the K-point grid density Kmesh, and the U-value of the Hubbard model for strongly correlated systems.

[0008] Based on the UO2 crystallographic unit cell, a UO2 supercell was established; using the UO2 supercell, structural models containing different vacancy defects generated by irradiation were constructed.

[0009] Based on the calculation parameters, the vacancy defect structure model is optimized, and the formation energy and binding energy are calculated.

[0010] Based on the formation energy and binding energy, the ease of formation of different vacancy defects in UO2 after irradiation is determined, and the stability of different vacancy defects is analyzed.

[0011] The above technical solution involves establishing a UO2 crystallographic unit cell and testing the first-principles calculation parameters for UO2, including the plane wave cutoff energy Ecut, K-point grid density, and the U-value of the Hubbard model for strongly correlated systems. Then, a structural model containing different types of vacancy-type irradiated point defects and small clusters is established. The tested calculation parameters are used for structural optimization and calculation of formation and binding energies. The ease of formation of different vacancy-type irradiated defects and the stability of different defects in UO2 after irradiation are analyzed. By using the method provided by this invention, the stability of irradiated vacancy point defects and small clusters can be conveniently and quickly determined.

[0012] Furthermore, a crystallographic unit cell for UO2 was constructed, and the first-principles calculation parameters of UO2 were tested, including:

[0013] Construct a UO2 crystallographic unit cell containing 4 U atoms and 8 O atoms, with a lattice constant of...

[0014] Write a bashshell script to perform first-principles calculation parameter tests for UO2; the bashshell script is used to calculate the plane wave cutoff energy Ecut and the K-point mesh density Kmesh, and then perform the tests.

[0015] A coordinate graph is established with the plane wave cutoff energy Ecut as the x-axis, the K-point grid density Kmesh as the y-axis, and the total system energy Etot as the z-axis.

[0016] Based on the coordinate graph, the characteristics of the graphical energy curve are analyzed. When the total energy of the system Etot no longer changes with the plane wave cutoff energy Ecut and the K-point grid density Kmesh, the plane wave cutoff energy Ecut and the K-point grid density Kmesh are the calculation parameter values ​​used by the first principle of UO2.

[0017] Furthermore, the Hubbard model U-value for strongly correlated systems includes:

[0018] The measured plane wave cutoff energy Ecut and the K-point grid density Kmesh are used to set the calculation parameters for UO2 first-principles calculations. At the same time, the spin polarization of uranium atoms needs to be considered to calculate the band structure of the UO2 crystal.

[0019] Write a bash shell script to test the U value, and obtain the calculated band gap value based on the band structure of the UO2 crystal under different U values;

[0020] The calculated bandgap width is compared with the experimentally measured bandgap width. When the calculated bandgap width equals the measured bandgap width, the U value is the correction value of GGA+U calculated by the first principles of UO2. GGA+U is the U value of the traditional GGA functional with the Hubbard parameter added.

[0021] Furthermore, the vacancy defect structure model includes:

[0022] First vacancy defect structure model: UO2 supercell computational model containing one oxygen atom vacancy;

[0023] Second vacancy defect structure model: UO2 supercell computational model containing one uranium atom vacancy, the position of the uranium atom vacancy is the nearest neighbor of the oxygen atom vacancy in the first vacancy defect structure model;

[0024] The third vacancy defect structure model: a UO2 supercell computational model containing two vacancies. A uranium atom is selected as the vacancy center, forming a double vacancy structure with the vacancy at the first nearest neighbor oxygen atom; an oxygen atom is selected as the vacancy center, forming a first structure with the vacancy at the nearest neighbor oxygen atom, a second structure with the vacancy at the second nearest neighbor oxygen atom, and a third structure with the vacancy at the third nearest neighbor oxygen atom.

[0025] The fourth vacancy defect structure model is a small cluster model containing one uranium atom vacancy and two oxygen atom vacancy. A uranium atom is selected as the vacancy center, and the two nearest oxygen atoms are selected as the vacancy. The two oxygen atoms are the first nearest neighbor atom, the second nearest neighbor atom, and the third nearest neighbor atom, respectively, forming three unequal small clusters containing one uranium atom vacancy and two oxygen atom vacancy.

[0026] Furthermore, the vacancy defect structure model is optimized based on the calculation parameters, including:

[0027] Based on the calculation parameters, the atomic positions are selected to be movable, the supercell volume is variable, or the supercell shape is variable. The conjugate gradient (CG) algorithm is used to optimize the vacancy defect structure model.

[0028] Furthermore, the formation energy and binding energy are calculated, including:

[0029] Based on the optimized vacancy defect structure model, the total energy of the UO2 supercell containing oxygen atom vacancy defects and uranium atom vacancy defects is calculated as the first total energy; and the total energy of the UO2 supercell without defect-free complete structure is calculated as the second total energy.

[0030] Based on the first total energy and the second total energy, calculate the vacancy defect formation energy of uranium atoms and the vacancy defect formation energy of oxygen atoms in UO2;

[0031] Based on the first total energy, the second total energy, and the formation energies of each vacancy defect, the binding energy of the multi-vacancy defect cluster is calculated. Furthermore, the vacancy defect formation energy E... f The expression is:

[0032] E f =E[defect]-E[perfect]+nμ x

[0033] Where, μ x The chemical potential μ of U and O atoms O and μ U Value; E[defect] represents the total energy of a UO2 supercell containing oxygen atom vacancy defects and uranium atom vacancy defects; E[perfect] represents the total energy of a UO2 supercell with a complete structure without defects;

[0034] The binding energy expression for multi-vacancy defect clusters is:

[0035] E(nV U mV O )=E(U 32-n nV U O 64-m mV O )-n×E(U 31 O 64 V U )-m×E(U 32 O 63 V O )+(m+n-1)×E(U 32 O 64 )

[0036] Among them, multi-vacancy defect clusters are composed of n U vacancies and m O vacancies; E(U 32-n nV U O 64-m mVo) is the total energy of the supercell containing n U vacancies and m O vacancies; E(U 32 O 63 Vo) is the total energy of the supercell containing one O vacancy; E(U) 31 O 64 V U E(U) represents the total energy of a supercell containing one U vacancy. 32 O 64 ) represents the total energy of the supercell without irradiation defects.

[0037] Furthermore, based on the formation energy and binding energy, the ease of formation of different vacancy defects in UO2 after irradiation is determined, and the stability of different vacancy defects is analyzed, including:

[0038] When the formation energy Ef > 0, and the larger the formation energy Ef is, the more difficult it is for vacancy defects to form; otherwise, it means that vacancy defects are easier to form.

[0039] When the binding energy E>0, it means that vacancy defects cannot bind and are unstable; when the binding energy E<0, it means that vacancy defects can bind and are stable.

[0040] Secondly, this invention provides an analysis system for the stability of vacancy-type point defects in UO2, the system comprising:

[0041] The parameter testing unit is used to establish the UO2 crystallographic unit cell and test the first-principles calculation parameters of UO2. The calculation parameters include the plane wave cutoff energy Ecut, the K-point grid density Kmesh, and the U value of the Hubbard model of strongly correlated systems.

[0042] The vacancy model building unit is used to establish a UO2 supercell based on the UO2 crystallographic unit cell; and to construct structural models containing different vacancy defects generated by irradiation using the UO2 supercell.

[0043] The optimization and calculation unit is used to optimize the vacancy defect structure model according to the calculation parameters and calculate the formation energy and binding energy.

[0044] The judgment and analysis unit is used to determine the ease of formation of different vacancy defects in UO2 after irradiation based on the formation energy and binding energy, and to analyze the stability of different vacancy defects.

[0045] Furthermore, the vacancy defect structure model includes:

[0046] First vacancy defect structure model: UO2 supercell computational model containing one oxygen atom vacancy;

[0047] Second vacancy defect structure model: UO2 supercell computational model containing one uranium atom vacancy, the position of the uranium atom vacancy is the nearest neighbor of the oxygen atom vacancy in the first vacancy defect structure model;

[0048] The third vacancy defect structure model: a UO2 supercell computational model containing two vacancies. A uranium atom is selected as the vacancy center, forming a double vacancy structure with the vacancy at the first nearest neighbor oxygen atom; an oxygen atom is selected as the vacancy center, forming a first structure with the vacancy at the nearest neighbor oxygen atom, a second structure with the vacancy at the second nearest neighbor oxygen atom, and a third structure with the vacancy at the third nearest neighbor oxygen atom.

[0049] The fourth vacancy defect structure model is a small cluster model containing one uranium atom vacancy and two oxygen atom vacancy. A uranium atom is selected as the vacancy center, and the two nearest oxygen atoms are selected as the vacancy. The two oxygen atoms are the first nearest neighbor atom, the second nearest neighbor atom, and the third nearest neighbor atom, respectively, forming three unequal small clusters containing one uranium atom vacancy and two oxygen atom vacancy.

[0050] Thirdly, the present invention also provides an electronic device, including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the computer program to implement the above-mentioned method for analyzing the stability of vacancy-type point defects in UO2.

[0051] Fourthly, the present invention provides a computer-readable storage medium storing a computer program that, when executed by a processor, implements the above-described method for analyzing the stability of vacancy-type point defects in UO2.

[0052] Compared with the prior art, the present invention has the following advantages and beneficial effects:

[0053] 1. This invention relates to a method, system, and medium for analyzing the stability of vacancy-type point defects in UO2. The invention employs first-principles calculations to study the stability of irradiated defects. It establishes a UO2 crystallographic unit cell and tests the first-principles calculation parameter settings for UO2, including the plane wave cutoff energy Ecut, K-point grid density, and the U-value of the Hubbard model for strongly correlated systems. Then, it establishes structural models containing different types of vacancy-type irradiated point defects and small clusters, and uses the tested calculation parameters for structural optimization and calculation of formation and binding energies. The ease of formation of different vacancy-type irradiated defects and the stability of different defects in UO2 after irradiation are analyzed. By using the method provided by this invention, the stability of irradiated vacancy-type point defects and small clusters can be conveniently and quickly determined.

[0054] 2. This invention provides an analytical method, system, and medium for the stability of vacancy-type point defects in UO2. This invention offers a highly efficient and convenient method for studying the stability of irradiation defects, reducing the research cycle and saving economic costs. It overcomes many shortcomings of experimental methods in studying microscale irradiation damage (such as difficulty in obtaining microscopic information about point defects and high experimental costs). This invention allows for the convenient and rapid establishment of a computational model for UO2 irradiation defects, obtaining the stability of different types of irradiation defects. Furthermore, the calculation is independent of empirical parameters, exhibiting high accuracy and reliability. This invention provides an effective computational method for studying irradiation damage in UO2 fuel and provides theoretical support for the design and modification of UO2 fuel. Attached Figure Description

[0055] The accompanying drawings, which are included to provide a further understanding of embodiments of the invention and form part of this application, do not constitute a limitation thereof. In the drawings:

[0056] Figure 1 This is a flowchart of the method for analyzing the stability of vacancy-type point defects in UO2 according to the present invention;

[0057] Figure 2 This is a schematic diagram of different types of vacancy-type irradiation defect structures in UO2 of the present invention;

[0058] Figure 3 For the purpose of this invention, the plane wave cutoff energy (a) and the K-point grid density of reciprocal space were calculated using first-principles calculations of UO2.

[0059] Figure 4 To test the corrected U values ​​of the strongly correlated Hubbard model for UO2 in this invention using first-principles calculations, (a) U = 3.0 eV, (b) U = 4.5 eV;

[0060] Figure 5 This is a schematic diagram of the U-centered atom and its first nearest neighbor O atom in this invention;

[0061] Figure 6 For the present invention, U is a central atom with different structures V O-O V O-U-O A schematic diagram of the binding energy of vacancy-type clusters;

[0062] Figure 7 This is a block diagram of the analysis system for the stability of vacancy-type point defects in UO2 according to the present invention. Detailed Implementation

[0063] To make the objectives, technical solutions, and advantages of the present invention clearer, the present invention will be further described in detail below with reference to the embodiments and accompanying drawings. The illustrative embodiments and descriptions of the present invention are only used to explain the present invention and are not intended to limit the present invention.

[0064] Currently, UO2 oxide fuel is widely used in commercial pressurized water reactors. However, irradiation damage to the fuel core leads to a decrease in its thermal and mechanical properties. Irradiation damage is caused by the generation, migration, and aggregation of irradiation defects. The stability of irradiation defects is a key influencing factor, as they can both recombine and disappear or nucleate and grow. Experimental methods for studying microscale irradiation damage have many limitations, such as expensive equipment, high experimental risks, and long experimental cycles.

[0065] Addressing the current lack of efficient and rapid methods for characterizing the morphology and stability of small defect clusters in UO2 fuel during irradiation, this invention designs a method, system, and medium for analyzing the stability of vacancy-type point defects in UO2. This invention employs first-principles calculations to study the stability of irradiated defects. It establishes a UO2 crystallographic unit cell, tests the first-principles calculation parameter settings for UO2, including the plane wave cutoff energy Ecut, K-point grid density, and the U-value of the Hubbard model for strongly correlated systems, and writes a bashshell script program to test the calculation parameters. Then, it establishes structural models containing different types of vacancy-type irradiated point defects and small clusters, and uses the tested calculation parameters to optimize the structure and calculate the formation and binding energies. The ease of formation of different vacancy-type irradiated defects and the stability of different defects in UO2 after irradiation are analyzed. By using the method provided by this invention, the stability of irradiated vacancy-type point defects and small clusters can be conveniently and quickly determined.

[0066] This invention is not constrained by experimental conditions, is highly efficient and convenient, reduces the research cycle, and saves economic costs. It can make up for many shortcomings of experimental methods in studying microscale irradiation damage (such as difficulty in obtaining microscopic information of point defects and high experimental costs). Through this invention, a UO2 irradiation defect calculation model can be easily and quickly established to obtain the stability of different types of irradiation defects. Moreover, the calculation does not rely on empirical parameters, and the calculation accuracy is high and the reliability is strong. This invention provides an effective calculation method for the study of UO2 fuel irradiation damage and provides theoretical support for the design and modification of UO2 fuel.

[0067] The specific design is as follows:

[0068] Using the crystallographic unit cell of UO2 (containing 4 U atoms and 8 O atoms), its lattice constant is... Test the calculation parameters and write a bash shell script to calculate the plane wave cutoff energy Ecut and K-point grid density Kmesh. Establish a method for analyzing and testing the cutoff energy and K-point grid density calculated by first principles: establish a coordinate graph with plane wave cutoff energy Ecut as the x-axis, K-point grid density Kmesh as the y-axis, and total system energy Etot as the z-axis. Analyze the characteristics of the energy curve based on the coordinate graph. When the total system energy Etot no longer changes with the plane wave cutoff energy Ecut and K-point grid density Kmesh, Ecut and Kmesh are the parameter values ​​used in the first principles calculation of UO2.

[0069] Corrections were made to the calculated electronic structure parameters of UO2 with strong 5f correlation effects. The Hubbard model was used for correction, adding the Hubbard parameter's U value to the traditional GGA functional (GGA+U). The plane wave cutoff energy Ecut and the K-point mesh density Kmesh were used to set the first-principles calculation parameters, while also considering the spin polarization of U atoms, to calculate the band structure of the UO2 crystal. A shell script was written to test the U value, obtaining the band gap Eg based on the UO2 crystal's band structure at different U values. By comparing the calculated Eg with the experimentally measured Eg, the U value was determined as the corrected GGA+U value for the first-principles calculation of UO2. Using the UO2 crystallographic unit cell (containing 4 U atoms and 8 O atoms) as the initial structure, the unit cell was expanded into a 2×2×2 supercell containing 96 atoms along the x, y, and z Cartesian coordinate systems, establishing vacancy defect models with different structures.

[0070] A first-principles calculation method for the formation energy of O-vacancies and U-vacancies in UO2 is established. A vacancy defect model containing irradiated vacancies is constructed to calculate the total energy E[defect] of a UO2 supercell containing O-vacancies and U-vacancies, thus establishing a binding energy characterizing the combination of m O-vacancies and n U-vacancies in UO2. First, the first-principles GGA+U method is used to optimize UO2 supercells containing different types of vacancy defects. The optimization parameters are set to allow for movable atomic positions, variable supercell volume, and variable supercell shape. Structural optimization employs the conjugate gradient (CG) algorithm, with the exchange-correlation functional chosen as the PBE functional under the generalized gradient (GGA) approximation. The convergence accuracy of the force acting on the atoms, the plane wave cutoff energy, and the K-point grid density are set. The total energy and band structure are then calculated using the GGA+U method.

[0071] A method for characterizing the stability of vacancy-type defects in UO2 based on first-principles calculations is established: the vacancy formation energy of U atoms and the vacancy formation energy of O atoms in UO2 are calculated using the following formula (1); the binding energy Eb of multi-vacancy defects is calculated using formula (2); and a method is established with different small cluster structures as the abscissa and the binding energy as the ordinate to analyze the structure of vacancy-type defects and their binding energy.

[0072] Example 1

[0073] like Figure 1 As shown, the present invention provides a method for analyzing the stability of vacancy-type point defects in UO2, the method comprising:

[0074] Step 1: Establish the UO2 crystallographic unit cell and test the first-principles calculation parameters of UO2. The calculation parameters include the plane wave cutoff energy Ecut, the K-point mesh density Kmesh, and the U-value of the Hubbard model for strongly correlated systems.

[0075] Step 1 is to establish a test method for setting the first-principles calculation parameters of UO2, and write a bashshell script program to calculate the plane wave cutoff energy Ecut and K-point mesh density Kmesh. The first-principles calculation parameter test adopts the projection-added plane wave method (PAW) in QE, and the exchange correlation functional is selected as the PBE functional under the generalized gradient approximation, i.e., GGA-PBE.

[0076] Specifically, step 1 includes:

[0077] The lattice constant of UO2 was determined by calculating parameters using a UO2 crystallographic unit cell (containing 4 U atoms and 8 O atoms). Ten values ​​were selected for the plane wave cutoff energy Ecut: 280, 300, 320, ..., 460. Ten values ​​were also selected for the K-point grid density Kmesh: 3×3×3, 5×5×5, 7×7×7, ..., 21×21×21. A script automatically generated a test calculation result file containing three columns: cutoff energy, K-point grid density, and total system energy. A three-dimensional rectangular coordinate graph was established with the plane wave cutoff energy Ecut as the x-axis, the K-point grid density Kmesh as the y-axis, and the total system energy Etot as the z-axis. Based on this graph, the characteristics of the energy curve were analyzed. When the total system energy Etot no longer changes with the plane wave cutoff energy Ecut and the K-point grid density Kmesh, these values ​​represent the first-principles calculation parameters used for UO2. Figure 3 As shown, Figure 3 (a) The x-axis represents the cutoff energy, and the y-axis represents the total energy; Figure 3 (b) The horizontal axis represents the grid density at point K, and the vertical axis represents the total energy.

[0078] Correction parameters for calculating the electronic structure of UO2 with 5f strong correlation effects were established. In this invention, the Hubbard model was used for correction, adding the U value of the Hubbard parameters to the traditional GGA functional, i.e., GGA+U. The measured plane wave cutoff energy Ecut and K-point grid density Kmesh were used to set the first-principles calculation parameters for UO2, while also considering the spin polarization of uranium atoms to calculate the band structure of the UO2 crystal. A bash shell script was written to test the U value, taking U values ​​of 2eV, 2.5eV, ..., 6eV respectively. At different U values, the band gap width was calculated based on the band structure of the UO2 crystal. The calculated band gap width was compared with the experimentally measured band gap width. When the calculated band gap width equals the measured band gap width, the U value is the correction value of GGA+U calculated in the first-principles calculation of UO2. Figure 4 As shown, Figure 4 (a) The x-axis represents the k-path along the high symmetry direction of the first Brillouin zone in the reciprocal space, and the y-axis represents the energy corresponding to different k points without U-value correction. Figure 4 (b) The x-axis represents the k-path along the high symmetry direction of the first Brillouin zone in the reciprocal space, and the y-axis represents the energy corresponding to different k points when the U-value correction is added; GGA+U is the U-value of the traditional GGA functional with the Hubbard parameter added.

[0079] Step 2: Based on the UO2 crystallographic unit cell, establish the UO2 supercell; using the UO2 supercell, construct structural models containing different vacancy defects generated by irradiation;

[0080] Step 2 involves establishing the UO2 supercell by using the UO2 crystallographic unit cell (containing 4 U atoms and 8 O atoms) as the initial structure and expanding it into a 2×2×2 supercell containing 96 atoms along the x, y, and z Cartesian coordinate systems. This supercell is then used to construct structural models of different vacancy defects, such as... Figure 2 As shown.

[0081] Specifically, the vacancy defect structure model includes:

[0082] (1) First vacancy defect structure model: Establish a UO2 supercell computational model containing one oxygen atom vacancy, and establish an O atom vacancy in a supercell containing 96 atoms;

[0083] (2) Second vacancy defect structure model: Establish a UO2 supercell computational model containing one uranium atom vacancy. In a supercell containing 96 atoms, establish a U atom vacancy. The position of the U atom vacancy is the nearest neighbor of the O atom vacancy in the first vacancy defect structure model.

[0084] (3) Third vacancy defect structure model: A UO2 supercell computational model containing two vacancies is established. A U29 atom is selected as the vacancy center, and V forms with the vacancy at the first nearest neighbor O atom. O15-U1 (The remaining 5 O atoms are equivalent) a double-vacancy structure; the O28 atom is selected as the vacancy center, forming a V-shaped structure with the vacancy at the nearest neighboring O57 (O15, O21) atom. O28-O57 The structure forms a V atom with the vacancy at the second nearest neighbor O atom. O28-O56 The structure forms a V atom with the vacancy at the third nearest neighbor O atom. O28-O35 Structure, such as Figure 5 As shown;

[0085] (4) Fourth Vacancy Defect Structure Model: A small cluster model containing three vacancies (one uranium atom vacancy and two oxygen atom vacancy) is established. Under irradiation damage, a neutral three-vacancy irradiation defect structure with a U:O ratio of 1:2 is generated in UO2. Therefore, the three-vacancy small cluster contains one U vacancy and two O atom vacancies. Centered on one U atom vacancy, with the two nearest neighboring O atoms as vacancies, the two O atoms are the first nearest neighbor atom, the second nearest neighbor atom, and the third nearest neighbor atom, respectively forming V. O28-U29-O57 V O28-U29-O56 V O28-U29-O35 There are three types of inequivalent small clusters containing one U vacancy and two O vacancy sites, such as Figure 6 As shown, Figure 6 The x-axis represents small clusters of two O vacancies at different distances and one U vacancy at different distances, and the y-axis represents the binding energy.

[0086] Step 3: Optimize the vacancy defect structure model based on the calculation parameters, and calculate the formation energy and binding energy;

[0087] In step 3, the vacancy defect structure model is optimized based on the calculation parameters, including:

[0088] Based on the calculation parameters, the atomic positions are selected to be movable, the supercell volume is variable, or the supercell shape is variable. The conjugate gradient (CG) algorithm is used to optimize the vacancy defect structure model.

[0089] In step 3, a calculation method based on first-principles calculations is established to determine the formation of O and U vacancies in UO2, including the calculation of formation energy and binding energy.

[0090] Based on the optimized vacancy defect structure model, the total energy E[defect] of the UO2 supercell containing oxygen atom vacancy defects and uranium atom vacancy defects is calculated as the first total energy; and the total energy E[perfect] of the UO2 supercell without defects is calculated as the second total energy.

[0091] Based on the first total energy and the second total energy, calculate the vacancy defect formation energy E of uranium atoms and oxygen atoms in UO2. f ;Vacation defect formation energy E f The expression is:

[0092] E f = E[defect] - E[perfect] + nμ x (1)

[0093] Where, μ x The chemical potential μ of U and O atoms O and μ U Value; E[defect] represents the total energy of a UO2 supercell containing oxygen atom vacancy defects and uranium atom vacancy defects; E[perfect] represents the total energy of a UO2 supercell with a complete structure without defects;

[0094] A formula is established to calculate the binding energy E (bonding energy) when vacancies at different positions in UO2 combine to form small clusters. It is assumed that each small cluster is composed of n U vacancies and m O vacancies. Based on the first total energy, the second total energy, and the formation energy of each defect, the binding energy of multi-vacancy defect small clusters is calculated. The expression for the binding energy of multi-vacancy defect small clusters is:

[0095] E(nV U mV O )=E(U 32-n nV U O 64-m mV O )-n×E(U 31 O 64 V U )-m×

[0096] E(U 32 O 63 V O )+(m+n-1)×E(U 32 O 64 (2)

[0097] Among them, multi-vacancy defect clusters are composed of n U vacancies and m O vacancies; E(U 32-n nV U O 64-m mVo) is the total energy of the supercell containing n U vacancies and m O vacancies; E(U 32 O 63 Vo) is the total energy of the supercell containing one O vacancy; E(U) 31 O 64 V U E(U) represents the total energy of a supercell containing one U vacancy.32 O 64 ) represents the total energy of the supercell without irradiation defects.

[0098] Optimization of UO2 supercells containing irradiated vacancy defects and small clusters requires movable atomic positions, variable supercell volume, and variable supercell shape. The optimization algorithm employs the conjugate gradient (CG) algorithm, with a convergence accuracy of [value missing] for the forces acting on the atoms. The plane wave cutoff is 450 eV, the K-point grid is 9×9×9, the exchange correlation functional is the PBE functional under the generalized gradient (GGA) approximation, and the GGA+U correction method is adopted, with U value of 4.5 eV. Considering spin polarization, the total energy convergence accuracy is 1.0 × 10⁻⁶. -6 eV, during structural optimization, the total energy of the system changes with the number of optimization steps, such as Figure 3 As shown.

[0099] A method for characterizing the stability of irradiated vacancy defects and small clusters in UO2 based on first-principles calculations was established: the crystal structure of UO2 containing small clusters after irradiation was optimized using the tested parameters. The vacancy formation of U atoms in UO2 was calculated to be 5.1 eV and the vacancy formation of O atoms was calculated to be 2.2 eV using formula (1). The binding energy E of each vacancy small cluster was calculated using formula (2). An analytical graph was established with different small cluster structures as the abscissa and the binding energy as the ordinate to obtain the analysis graph of small cluster structure and its binding energy, as shown in the figure. Figure 6 As shown.

[0100] Step 4: Based on the formation energy and binding energy, determine the ease of formation of different vacancy defects in UO2 after irradiation, and analyze the stability of different vacancy defects.

[0101] Specifically, based on the formation energy and binding energy calculated in step 3 above, the following judgments are made:

[0102] When the formation energy Ef > 0, and the larger the formation energy Ef is, the more difficult it is for vacancy defects to form; otherwise, it means that vacancy defects are easier to form.

[0103] When the binding energy E>0, it means that vacancy defects cannot bind and are unstable; when the binding energy E<0, it means that vacancy defects can bind and are stable.

[0104] This invention provides a first-principles calculation method for studying the stability of irradiation defects. This method is efficient and convenient, reduces the research cycle, and saves economic costs. It can make up for many shortcomings of experimental methods in studying microscale irradiation damage (such as difficulty in obtaining microscopic information of point defects and high experimental costs). Through this invention, a UO2 irradiation defect calculation model can be easily and quickly established to obtain the stability of different types of irradiation defects, providing an effective analytical method for the study of UO2 fuel irradiation damage.

[0105] Example 2

[0106] like Figure 7 As shown, the difference between this embodiment and Embodiment 1 is that this embodiment provides an analysis system for the stability of vacancy-type point defects in UO2. This system corresponds one-to-one with the analysis method for the stability of vacancy-type point defects in UO2 in Embodiment 1. The system includes:

[0107] The parameter testing unit is used to establish the UO2 crystallographic unit cell and test the first-principles calculation parameters of UO2. The calculation parameters include the plane wave cutoff energy Ecut, the K-point grid density Kmesh, and the U value of the Hubbard model of strongly correlated systems.

[0108] The vacancy model building unit is used to establish a UO2 supercell based on the UO2 crystallographic unit cell; and to construct structural models containing different vacancy defects generated by irradiation using the UO2 supercell.

[0109] The optimization and calculation unit is used to optimize the vacancy defect structure model according to the calculation parameters and calculate the formation energy and binding energy.

[0110] The judgment and analysis unit is used to determine the ease of formation of different vacancy defects in UO2 after irradiation based on the formation energy and binding energy, and to analyze the stability of different vacancy defects.

[0111] As a further implementation, the vacancy defect structure model includes:

[0112] First vacancy defect structure model: UO2 supercell computational model containing one oxygen atom vacancy;

[0113] Second vacancy defect structure model: UO2 supercell computational model containing one uranium atom vacancy, the position of the uranium atom vacancy is the nearest neighbor of the oxygen atom vacancy in the first vacancy defect structure model;

[0114] The third vacancy defect structure model: a UO2 supercell computational model containing two vacancies. A uranium atom is selected as the vacancy center, forming a double vacancy structure with the vacancy at the first nearest neighbor oxygen atom; an oxygen atom is selected as the vacancy center, forming a first structure with the vacancy at the nearest neighbor oxygen atom, a second structure with the vacancy at the second nearest neighbor oxygen atom, and a third structure with the vacancy at the third nearest neighbor oxygen atom.

[0115] The fourth vacancy defect structure model is a small cluster model containing one uranium atom vacancy and two oxygen atom vacancy. A uranium atom is selected as the vacancy center, and the two nearest oxygen atoms are selected as the vacancy. The two oxygen atoms are the first nearest neighbor atom, the second nearest neighbor atom, and the third nearest neighbor atom, respectively, forming three unequal small clusters containing one uranium atom vacancy and two oxygen atom vacancy.

[0116] The execution process of each unit can be carried out according to the analysis method and steps of the stability of vacancy-type point defects in UO2 in Example 1, and will not be described in detail in this example.

[0117] Meanwhile, the present invention also provides an electronic device, including a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the computer program, it implements the above-mentioned method for analyzing the stability of vacancy-type point defects in UO2.

[0118] Meanwhile, the present invention also provides a computer-readable storage medium storing a computer program, which, when executed by a processor, implements the above-mentioned method for analyzing the stability of vacancy-type point defects in UO2.

[0119] Those skilled in the art will understand that embodiments of this application can be provided as methods, systems, or computer program products. Therefore, this application can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, this application can take the form of a computer program product embodied on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0120] This application is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of this application. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart... Figure 1One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0121] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0122] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0123] The specific embodiments described above further illustrate the purpose, technical solution, and beneficial effects of the present invention. It should be understood that the above description is only a specific embodiment of the present invention and is not intended to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for analyzing the stability of vacancy-type point defects in UO2, characterized in that, The method includes: A crystallographic unit cell for UO2 was established, and the first-principles calculation parameters of UO2 were tested. The calculation parameters include plane wave cutoff energy, K-point grid density, and the U-value of the Hubbard model for strongly correlated systems. Based on the UO2 crystallographic unit cell, a UO2 supercell is established; using the UO2 supercell, structural models containing different vacancy defects generated by irradiation are constructed. Based on the calculation parameters, the vacancy defect structure model is optimized, and the formation energy and binding energy are calculated. Based on the formation energy and binding energy, the ease of formation of different vacancy defects in UO2 after irradiation is determined, and the stability of different vacancy defects is analyzed. The vacancy defect structure model includes a fourth vacancy defect structure model: a small cluster model containing one uranium atom vacancy and two oxygen atom vacancy. A uranium atom is selected as the vacancy center, and the two nearest oxygen atoms are selected as the vacancy. The two oxygen atoms are the first nearest neighbor atom, the second nearest neighbor atom, and the third nearest neighbor atom, respectively, forming three unequal small clusters containing one uranium atom vacancy and two oxygen atom vacancy. Calculate the formation energy and binding energy, including: Based on the optimized vacancy defect structure model, the total energy of the UO2 supercell containing oxygen atom vacancy defects and uranium atom vacancy defects is calculated as the first total energy; and the total energy of the UO2 supercell without defect-free complete structure is calculated as the second total energy. Based on the first total energy and the second total energy, calculate the vacancy defect formation energy of uranium atoms and the vacancy defect formation energy of oxygen atoms in UO2; The binding energy of multi-vacancy defect clusters is calculated based on the first total energy, the second total energy, and the formation energy of each vacancy defect.

2. The method for analyzing the stability of vacancy-type point defects in UO2 according to claim 1, characterized in that, Establish the crystallographic unit cell of UO2 and test the first-principles calculation parameters of UO2, including: Establish a UO2 crystallographic unit cell containing 4 U atoms and 8 O atoms, with a lattice constant of [missing value]. ; Write a bashshell script to perform first-principles calculation parameter tests for UO2; the bashshell script is used to calculate the plane wave cutoff energy Ecut and the K-point mesh density Kmesh, and perform the tests. A coordinate graph is established with the plane wave cutoff energy Ecut as the x-axis, the K-point grid density Kmesh as the y-axis, and the total system energy Etot as the z-axis. Based on the coordinate diagram, the characteristics of the graphical energy curve are analyzed. When the total energy of the system Etot no longer changes with the plane wave cutoff energy Ecut and the K-point grid density Kmesh, the plane wave cutoff energy Ecut and the K-point grid density Kmesh are the calculation parameter values ​​used by the first principles of UO2.

3. The method for analyzing the stability of vacancy-type point defects in UO2 according to claim 2, characterized in that, The Hubbard model U-value of the strongly correlated system includes: The measured plane wave cutoff energy Ecut and the K-point grid density Kmesh are used to set the first-principles calculation parameters for UO2. The band structure of the UO2 crystal is calculated while considering the spin polarization of uranium atoms. Write a bash shell script to test the U value, and obtain the calculated band gap value based on the band structure of the UO2 crystal when the U value is different. The calculated bandgap width is compared with the experimentally measured bandgap width. When the calculated bandgap width equals the measured bandgap width, the U value is the correction value of GGA+U calculated by UO2 in the first principles. GGA+U is the U value of adding Hubbard parameters to the traditional GGA functional.

4. The method for analyzing the stability of vacancy-type point defects in UO2 according to claim 1, characterized in that, The vacancy defect structure model also includes: First vacancy defect structure model: UO2 supercell computational model containing one oxygen atom vacancy; Second vacancy defect structure model: UO2 supercell computational model containing one uranium atom vacancy, wherein the position of the uranium atom vacancy is the nearest neighbor of the oxygen atom vacancy in the first vacancy defect structure model; The third vacancy defect structure model: a UO2 supercell computational model containing two vacancies. A uranium atom is selected as the vacancy center, forming a double vacancy structure with the vacancy at the first nearest neighbor oxygen atom; an oxygen atom is selected as the vacancy center, forming a first structure with the vacancy at the nearest neighbor oxygen atom, a second structure with the vacancy at the second nearest neighbor oxygen atom, and a third structure with the vacancy at the third nearest neighbor oxygen atom.

5. The method for analyzing the stability of vacancy-type point defects in UO2 according to claim 1, characterized in that, The vacancy defect structure model is optimized based on the calculated parameters, including: Based on the calculation parameters, the atomic positions are selected to be movable, the supercell volume is variable, or the supercell shape is variable. The conjugate gradient algorithm is used to optimize the vacancy defect structure model.

6. The method for analyzing the stability of vacancy-type point defects in UO2 according to claim 5, characterized in that, The vacancy defect formation energy The expression is: ； in, Represents the chemical potential of U and O atoms and value; This represents the total energy of the UO2 supercell containing oxygen atom vacancy defects and uranium atom vacancy defects; This represents the total energy of the UO2 supercell, which has a complete structure without defects. The binding energy expression for the multi-vacancy defect cluster is: ； Among them, multi-vacancy defect clusters are composed of n U vacancy sites and m O vacancy sites; Let be the total energy of the supercell containing n U vacancies and m O vacancies; The total energy of a supercell containing one O vacancy; The total energy of a supercell containing one U vacancy; This represents the total energy of a supercell without irradiation defects.

7. The method for analyzing the stability of vacancy-type point defects in UO2 according to claim 1, characterized in that, Based on the formation energy and binding energy, the ease of formation of different vacancy defects in UO2 after irradiation is determined, and the stability of different vacancy defects is analyzed, including: When the forming energy If the value is greater than 0 and the formation energy Ef is larger, it indicates that vacancy defects are more difficult to form; otherwise, it indicates that vacancy defects are more easy to form. When the binding energy E>0, it means that the vacancy defect cannot bind and the vacancy defect is unstable; when the binding energy E<0, it means that the vacancy defect can bind and the vacancy defect is stable.

8. A system for analyzing the stability of vacancy-type point defects in UO2, characterized in that, The system includes: The parameter testing unit is used to establish the UO2 crystallographic unit cell and test the first-principles calculation parameters of UO2. The calculation parameters include the plane wave cutoff energy, K-point grid density, and the U-value of the Hubbard model for strongly correlated systems. A vacancy model construction unit is used to establish a UO2 supercell based on the UO2 crystallographic unit cell; and to construct structural models containing different vacancy defects generated by irradiation using the UO2 supercell. An optimization and calculation unit is used to optimize the vacancy defect structure model according to the calculation parameters, and to calculate the formation energy and binding energy. The judgment and analysis unit is used to judge the ease of formation of different vacancy defects in UO2 after irradiation based on the formation energy and binding energy, and to analyze the stability of different vacancy defects. The vacancy defect structure model includes a fourth vacancy defect structure model: a small cluster model containing one uranium atom vacancy and two oxygen atom vacancy. A uranium atom is selected as the vacancy center, and the two nearest oxygen atoms are selected as the vacancy. The two oxygen atoms are the first nearest neighbor atom, the second nearest neighbor atom, and the third nearest neighbor atom, respectively, forming three unequal small clusters containing one uranium atom vacancy and two oxygen atom vacancy. Calculate the formation energy and binding energy, including: Based on the optimized vacancy defect structure model, the total energy of the UO2 supercell containing oxygen atom vacancy defects and uranium atom vacancy defects is calculated as the first total energy; and the total energy of the UO2 supercell without defect-free complete structure is calculated as the second total energy. Based on the first total energy and the second total energy, calculate the vacancy defect formation energy of uranium atoms and the vacancy defect formation energy of oxygen atoms in UO2; The binding energy of multi-vacancy defect clusters is calculated based on the first total energy, the second total energy, and the formation energy of each vacancy defect.

9. The analysis system for the stability of vacancy-type point defects in UO2 according to claim 8, characterized in that, The vacancy defect structure model also includes: First vacancy defect structure model: UO2 supercell computational model containing one oxygen atom vacancy; Second vacancy defect structure model: UO2 supercell computational model containing one uranium atom vacancy, wherein the position of the uranium atom vacancy is the nearest neighbor of the oxygen atom vacancy in the first vacancy defect structure model; The third vacancy defect structure model: a UO2 supercell computational model containing two vacancies. A uranium atom is selected as the vacancy center, forming a double vacancy structure with the vacancy at the first nearest neighbor oxygen atom; an oxygen atom is selected as the vacancy center, forming a first structure with the vacancy at the nearest neighbor oxygen atom, a second structure with the vacancy at the second nearest neighbor oxygen atom, and a third structure with the vacancy at the third nearest neighbor oxygen atom.

10. An electronic device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, When the processor executes the computer program, it implements the method for analyzing the stability of vacancy-type point defects in UO2 as described in any one of claims 1 to 7.

11. A computer-readable storage medium storing a computer program, characterized in that, When the computer program is executed by the processor, it implements the method for analyzing the stability of vacancy-type point defects in UO2 as described in any one of claims 1 to 7.

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