Method and system for analyzing stability of vacancy type point defect in UO2 and medium

Abstract

The invention discloses a method and a system for analyzing the stability of vacancy type point defects in UO2 and a medium, the method comprises the following steps: establishing UO2 crystallographic primitive cells, and testing calculation parameters of a first principle of UO2, the calculation parameters comprising plane wave cutoff energy, K-point grid density and a U value of a strong correlation system Hubbar model; establishing a UO2 supercell based on the UO2 crystallographic primitive cell; adopting UO2 supercells to construct a structure model containing different vacancy defects generated by irradiation; optimizing the vacancy defect structure model according to the calculation parameters, and calculating formation energy and binding energy; according to the formation energy and the binding energy, the difficulty degree of formation of different vacancy defects in the irradiated UO2 is judged, and the stability of the different vacancy defects is analyzed. The calculation does not depend on empirical parameters, the calculation precision is high, and the reliability is high; the effective calculation method is provided for UO2 fuel irradiation damage research, and theoretical support is provided for design and modification of UO2 fuel.

Description

Technical Field

[0001] The invention relates to the technical field of stability analysis of vacancy type point defects in UO2, and in particular to an analysis method, system and medium for the stability analysis of vacancy type point defects in UO2. Background Art

[0002] UO2 oxide fuel has many excellent properties, such as high melting point (2800℃), strong fission product tolerance, and is not prone to zirconium-water chemical reaction with traditional zirconium alloy cladding materials, that is, it has good compatibility with fuel cladding, and the preparation process is mature, so UO2 is widely used in nuclear power plants as commercial pressurized water reactor fuel. During the service process, UO2 fuel assemblies are in a strong particle radiation field (neutron energy is about 2MeV) and high temperature and high pressure conditions. During the nuclear fission of U atoms, a large number of neutrons and fission products are produced. These energy-carrying particles collide with atoms on the lattice of UO2 to produce PKA. When the energy of PKA is high enough, PKA slows down in UO2 to produce a large number of vacancies and interstitial atoms, forming a delocalization peak, causing irradiation damage to UO2 fuel. This leads to degradation of the thermal and mechanical properties of the fuel (such as reduced thermal conductivity and reduced mechanical strength). The irradiation process of UO2 fuel occurs at the atomic level. Vacancies and interstitial atoms migrate, diffuse, and aggregate in UO2. During the evolution of vacancies and interstitial atoms, most of the generated vacant interstitial atoms will recombine and disappear, and only a small number of defects will interact with the surrounding atoms and defects to produce small clusters. The generation of irradiation defects In order 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. The existence form and stability of small clusters cannot be characterized by experimental methods.

[0003] In view of this, this application is hereby filed. Summary of the invention

[0004] The purpose of the present invention is to provide an analysis method, system and medium for the stability of vacancy type point defects in UO2. The present invention adopts a first-principles calculation method to study the stability of irradiation defects, which is not restricted by experimental conditions, is efficient and convenient, reduces the research cycle, saves economic costs, and can make up for the many shortcomings of experimental methods in studying microscopic scale irradiation damage (such as difficulty in obtaining microscopic information of point defects and high experimental costs). Through the present invention, a UO2 irradiation defect calculation model can be conveniently and quickly established to obtain the stability of different types of irradiation defects; and the calculation does not rely on empirical parameters, with high calculation accuracy and strong reliability; the present 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] The present invention is achieved through the following technical solutions:

[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] Establish the UO2 crystallographic primitive cell and test the calculation parameters of UO2 based on the first principles, including the plane wave cutoff energy Ecut, the K-point mesh density Kmesh and the U value of the Hubbard model of the strongly correlated system;

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

[0009] According to 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 difficulty of forming different vacancy defects in UO2 after irradiation is determined, and the stability of different vacancy defects is analyzed.

[0011] The above technical scheme, the present invention establishes a UO2 crystallographic primitive cell, tests the UO2 first principle calculation parameter settings, including the plane wave cutoff energy Ecut, the K point grid density and the U value of the Hubbard model of the strongly correlated system; then establishes a structural model containing different types of vacancy-type irradiation point defects and small clusters, and uses the tested calculation parameters to perform structural optimization and calculation of formation energy and binding energy, and analyzes the difficulty of forming different vacancy-type irradiation defects in UO2 after irradiation and the stability of different defects. By using the method provided by the present invention, the stability of irradiated vacancy point defects and small clusters can be easily and quickly judged.

[0012] Furthermore, a UO2 crystallographic primitive cell was established to test the first-principles calculation parameters of UO2, including:

[0013] The UO2 crystallographic unit cell is established. The UO2 crystallographic unit cell contains 4 U atoms and 8 O atoms. Its lattice constant

[0014] Write a bash shell script program to test the calculation parameters of UO2 first principle; the bash shell script program is used to calculate the plane wave cutoff energy Ecut and K point mesh density Kmesh, and perform tests;

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

[0016] Based on the coordinate diagram, the characteristics of the energy curve of the graph are analyzed. When the total energy Etot of the system no longer changes with the change of the plane wave cutoff energy Ecut and the K-point mesh density Kmesh, the plane wave cutoff energy Ecut and the K-point mesh density Kmesh at this time are the calculation parameter values ​​adopted by the UO2 first principles.

[0017] Furthermore, the U value of the Hubbard model of the strongly correlated system includes:

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

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

[0020] The calculated value of the bandgap width is compared with the experimentally measured value of the bandgap width. When the calculated value of the bandgap width is equal to the tested value of the bandgap width, the U value at this time is the corrected value of GGA+U calculated by the first principles of UO2; GGA+U is the U value obtained by adding the Hubbard parameter to the traditional GGA functional.

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

[0022] The first vacancy defect structure model: a UO2 supercell computational model containing an oxygen atom vacancy;

[0023] Second vacancy defect structure model: a UO2 supercell calculation model containing a uranium atom vacancy, where 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 calculation model containing two vacancies, where a uranium atom is selected as the vacancy center to form a double vacancy structure with the vacancy at the first nearest oxygen atom; an oxygen atom is selected as the vacancy center to form the first structure with the vacancy at the nearest oxygen atom, the second structure with the vacancy at the second nearest oxygen atom, and the third structure with the vacancy at the third nearest oxygen atom;

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

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

[0027] According to the calculation parameters, the atomic position is movable, the supercell volume is variable or the supercell shape is variable, and 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 defects and complete structure is calculated as the second total energy;

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

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

[0032] E f =E[defect]-E[perfect]+nμ x

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

[0034] The binding energy expression of small clusters of multi-vacancy defects 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, the multi-vacancy defect cluster is composed of n U vacancies and m O vacancies; E(U 32-n nV U O 64-m mVo) is the total energy of a supercell containing n U vacancies and m O vacancies; E(U 32 O 63 Vo) is the total energy of the supercell containing an O vacancy; E(U 31 O 64 V U ) is the total energy of the supercell containing a U vacancy; E(U 32 O 64 ) is the total energy of the supercell without irradiation defects.

[0037] Furthermore, the formation energy and binding energy are used to determine the difficulty of forming different vacancy defects in UO2 after irradiation, and the stability of different vacancy defects is analyzed, including:

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

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

[0040] In a second aspect, the present invention further provides an analysis system for the stability of vacancy point defects in UO2, the system comprising:

[0041] Parameter testing unit, used to establish the UO2 crystallographic primitive cell and test the calculation parameters of UO2 first principles, including the plane wave cutoff energy Ecut, K-point mesh density Kmesh and the U value of the Hubbard model of the strongly correlated system;

[0042] Vacancy model building unit, used to build UO2 supercell based on UO2 crystallographic primitive cell; using UO2 supercell, construct different vacancy defect structure models generated by irradiation;

[0043] An optimization and calculation unit, used to optimize the vacancy defect structure model according to calculation parameters, and calculate the formation energy and binding energy;

[0044] The judgment and analysis unit is used to judge the difficulty of forming 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] The first vacancy defect structure model: a UO2 supercell computational model containing an oxygen atom vacancy;

[0047] Second vacancy defect structure model: a UO2 supercell calculation model containing a uranium atom vacancy, where 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 calculation model containing two vacancies, where a uranium atom is selected as the vacancy center to form a double vacancy structure with the vacancy at the first nearest oxygen atom; an oxygen atom is selected as the vacancy center to form the first structure with the vacancy at the nearest oxygen atom, the second structure with the vacancy at the second nearest oxygen atom, and the third structure with the vacancy at the third nearest oxygen atom;

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

[0050] In a third aspect, the present invention provides an electronic device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor implements the above-mentioned method for analyzing the stability of vacancy-type point defects in UO2 when executing the computer program.

[0051] In a fourth aspect, the present invention further provides a computer-readable storage medium, which stores a computer program, and when the computer program is executed by a processor, the above-mentioned method for analyzing the stability of vacancy type point defects in UO2 is implemented.

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

[0053] 1. The present invention discloses a method, system and medium for analyzing the stability of vacancy-type point defects in UO2. The present invention adopts a first-principles calculation method to study the stability of irradiated defects. The present invention establishes a UO2 crystallographic primitive cell and tests the first-principles calculation parameter settings of UO2, including the plane wave cutoff energy Ecut, the K-point grid density and the U value of the Hubbard model of the strongly correlated system; then establishes a structural model containing different types of vacancy-type irradiated point defects and small clusters, and uses the tested calculation parameters to perform structural optimization and calculation of formation energy and binding energy, and analyzes the ease of formation of different vacancy-type irradiated defects in UO2 after irradiation and the stability of different defects. By using the method provided by the present invention, the stability of irradiated vacancy-type point defects and small clusters can be judged conveniently and quickly.

[0054] 2. The present invention discloses an analysis method, system and medium for the stability of vacancy type point defects in UO2. The present invention is efficient and convenient for studying the stability of irradiation defects, reduces the research cycle, saves economic costs, and can make up for the many shortcomings of experimental methods for studying microscopic scale irradiation damage (such as difficulty in obtaining microscopic information of point defects and high experimental costs). The present invention can conveniently and quickly establish a UO2 irradiation defect calculation model to obtain the stability of different types of irradiation defects, and the calculation does not rely on empirical parameters, has high calculation accuracy and strong reliability. The present 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. BRIEF DESCRIPTION OF THE DRAWINGS

[0055] The drawings described herein are used to provide a further understanding of the embodiments of the present invention, constitute a part of this application, and do not constitute a limitation of the embodiments of the present invention. In the drawings:

[0056] Figure 1 The flowchart of the method for analyzing the stability of vacancy type point defects in UO2 of the present invention;

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

[0058] Figure 3 First-principles calculation of plane wave cutoff energy (a) and reciprocal space K-point grid density (b) for testing UO2 in the present invention;

[0059] Figure 4 The first-principles calculation of UO2 for the present invention to correct the U value of the strongly correlated Hubbard model is as follows: (a) U = 3.0 eV, (b) U = 4.5 eV;

[0060] Figure 5 This is a schematic diagram of the central atom U and its first neighboring O atom of the present invention;

[0061] Figure 6 In the present invention, U is a central atom with different structures V O-O 、V O-U-O Schematic diagram of the binding energy of vacancy clusters;

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

[0063] In order to make the objectives, technical solutions and advantages of the present invention more clearly understood, the present invention is further described in detail below in conjunction with embodiments and drawings. The exemplary embodiments of the present invention and their description are only used to explain the present invention and are not intended to limit the present invention.

[0064] At present, UO2 oxide fuel is widely used in commercial pressurized water reactors, but the radiation damage caused by the fuel in the core leads to the reduction of thermal and mechanical properties of the fuel. Radiation damage is caused by the generation, migration and aggregation of radiation defects. The stability of radiation defects is a key factor affecting radiation damage. Radiation defects can both recombine and disappear, and can also nucleate and grow. There are many shortcomings in studying microscopic radiation damage through experimental methods, such as expensive experimental equipment, high risk of experimental process and long cycle.

[0065] Based on the problem that there is no efficient and fast method for characterizing the existence form and stability analysis of small defect clusters in UO2 fuel during irradiation. The present invention designs an analysis method, system and medium for the stability of vacancy type point defects in UO2. The present invention adopts the first principle calculation method to study the stability of irradiation defects. The present invention establishes a UO2 crystallographic primitive cell, tests the first principle calculation parameter settings of UO2, including the plane wave cutoff energy Ecut, the K point grid density and the U value of the Hubbard model of the strongly correlated system, and writes a bash shell script program for calculating parameter testing; then establishes a structural model containing different types of vacancy type irradiation point defects and small clusters, and uses the tested calculation parameters to optimize the structure and calculate the formation energy and binding energy, and analyzes the difficulty of forming different vacancy type irradiation defects in UO2 after irradiation and the stability of different defects. By using the method provided by the present invention, the stability of irradiation vacancy point defects and small clusters can be judged conveniently and quickly.

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

[0067] The specific design is as follows:

[0068] Using the UO2 crystallographic unit cell (containing 4 U atoms and 8 O atoms), its lattice constant Test the calculation parameters and write a bash shell script program to calculate the plane wave cutoff energy Ecut and K-point mesh density Kmesh for testing; establish a method to analyze and test the cutoff energy size and K-point mesh density of the first-principles calculation: create a coordinate graph with plane wave truncation energy Ecut as the x-axis, K-point mesh density Kmesh as the y-axis, and system total energy Etot as the z-axis, and analyze the characteristics of the graphic energy curve based on the coordinate graph. When the system total energy Etot no longer changes with the change of plane wave truncation energy Ecut and K-point mesh density Kmesh, Ecut and Kmesh at this time are the parameter values ​​​​adopted for the UO2 first-principles calculation.

[0069] Establish the correction of the electronic structure calculation parameters of UO2 containing 5f strong correlation effect, adopt Hubbard model correction, add Hubbard parameter U value to the traditional GGA functional, that is, GGA+U. The plane wave cutoff energy Ecut and K-point mesh density Kmesh of the test are used to set the first principle calculation parameters. At the same time, the spin polarization of U atoms needs to be considered to calculate the band structure of UO2 crystal. Write a shell script to test the U value. Under different U values, the band gap width Eg is obtained according to the band structure of UO2 crystal. By comparing with the experimentally measured Eg, when the calculated Eg is equal to the experimentally measured Eg value, the U value at this time is the correction value of UO2 first principle calculation GGA+U. Take the UO2 crystallographic primitive cell (containing 4 U atoms and 8 O atoms) as the initial structure, expand the primitive cell into a 2×2×2 supercell containing 96 atoms along the three rectangular coordinate systems of x, y, and z, and build vacancy defect models with different structures.

[0070] A calculation method for the formation energy of O vacancy and U vacancy defects in UO2 based on first principles is established: the total energy E[defect] of the UO2 supercell containing O vacancies and U vacancies is calculated by using the constructed vacancy defect model containing irradiated vacancies, and the binding energy characterizing the combination of m O vacancies and n U vacancies in UO2 is established. Firstly, the first principles GGA+U method is used to optimize the UO2 supercell containing different types of vacancy defects. The parameters during optimization are selected as movable atomic positions, variable supercell volumes, and variable supercell shapes. The conjugate gradient (CG) algorithm is used for structural optimization, and the exchange-correlation functional selects the PBE functional under the generalized gradient (GGA) approximation. The convergence accuracy of the forces acting on atoms, the plane wave cutoff energy, and the K-point mesh density are set, and the total energy and band structure are 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 multiple vacancy defects is calculated using formula (2), and a method for analyzing the vacancy-type defect structure and its binding energy is established with different small cluster structures as the horizontal coordinate and the binding energy as the vertical coordinate.

[0072] Example 1

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

[0074] Step 1, establish the UO2 crystallographic primitive cell and test the calculation parameters of UO2 first principles, including the plane wave cutoff energy Ecut, K-point mesh density Kmesh and the U value of the Hubbard model of the strongly correlated system;

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

[0076] Specifically, step 1 includes:

[0077] The UO2 crystallographic unit cell (containing 4 U atoms and 8 O atoms) was used to calculate the parameters. The plane wave cutoff energy Ecut is selected as 280, 300, 320, ... 460, a total of 10 values, and the K-point mesh density Kmesh is selected as 3×3×3, 5×5×5, 7×7×7, ..., 21×21×21, a total of 10 values. The script is used to automatically generate the test calculation parameter result file, which contains 3 columns, namely the cutoff energy, K-point mesh and the total energy of the system. A three-dimensional rectangular coordinate graph is established with the plane wave cutoff energy Ecut as the x-axis, the K-point mesh density Kmesh as the y-axis, and the total energy of the system Etot as the z-axis; based on the three-dimensional rectangular coordinate graph, the characteristics of the energy curve of the graph are analyzed. When the total energy of the system Etot no longer changes with the change of the plane wave cutoff energy Ecut and the K-point mesh density Kmesh, the plane wave cutoff energy Ecut and the K-point mesh density Kmesh at this time are the calculation parameter values ​​used by the UO2 first principle, such as Figure 3 As shown, Figure 3 (a) The horizontal axis is the cutoff energy, and the vertical axis is the total energy; Figure 3 The horizontal axis of (b) is the K-point grid density, and the vertical axis is the total energy.

[0078] Establish the correction parameters for the calculation of the electronic structure of UO2 containing the strong correlation effect of 5f. In the present invention, the Hubbard model is used for correction, and the U value of the Hubbard parameter is added to the traditional GGA functional, that is, GGA+U. Use the tested plane wave cutoff energy Ecut and the K-point mesh density Kmesh to set the calculation parameters of the UO2 first principles. At the same time, it is necessary to consider the spin polarization of uranium atoms and calculate the band structure of the UO2 crystal; write a bash shell script to test the U value, take 2eV, 2.5eV, ..., 6eV at the U value, and obtain the calculated value of the bandgap width according to the band structure of the UO2 crystal at different U values; compare the calculated value of the bandgap width with the experimentally measured test value of the bandgap width. When the calculated value of the bandgap width is equal to the test value of the bandgap width, the U value at this time is the correction value of the UO2 first principle calculation GGA+U, such as Figure 4 As shown, Figure 4 The horizontal axis of (a) is the k path along the high symmetry direction of the first Brillouin zone in the reciprocal space, and the vertical axis is the energy corresponding to different k points when no U value correction is added; Figure 4 The horizontal axis of (b) is the k-path along the high symmetry direction of the first Brillouin zone in the reciprocal space, and the vertical axis is 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 plus the Hubbard parameter.

[0079] Step 2, based on the UO2 crystallographic primitive cell, a UO2 supercell is established; using the UO2 supercell, a structural model containing different vacancy defects generated by irradiation is constructed;

[0080] In step 2, the UO2 supercell is established by taking the UO2 crystallographic primitive cell (containing 4 U atoms and 8 O atoms) as the initial structure and expanding the primitive cell into a 2×2×2 supercell containing 96 atoms along the three rectangular coordinate systems of x, y, and z. This supercell is used to construct different vacancy defect structure models, such as Figure 2 shown.

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

[0082] (1) The first vacancy defect structure model: a UO2 supercell computational model containing one oxygen atom vacancy is established, and an O atom vacancy is established in a supercell containing 96 atoms;

[0083] (2) Second vacancy defect structure model: A UO2 supercell computational model containing a uranium atom vacancy is established. A U atom vacancy is established in the supercell containing 96 atoms. 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) The third vacancy defect structure model: A UO2 supercell calculation model with two vacancies is established. A U29 atom is selected as the vacancy center, and a V is formed with the vacancy at the first neighboring O atom. O15-U1 (The remaining 5 O atoms are equivalent) double vacancy structure; select O28 atom as the vacancy center and form V with the vacancy at the nearest neighbor O57 (O15, O21) atom O28-O57 structure, forming a V with the vacancy at the second nearest O atom O28-O56 structure, forming a V with the vacancy at the third nearest O atom O28-O35 Structure, such as Figure 5 As shown;

[0085] (4) The fourth vacancy defect structure model: A small cluster model containing three vacancies (one uranium atom vacancy and two oxygen atom vacancies) is established, and a neutral three-vacancy irradiation defect structure with a U:O ratio of 1:2 is generated in UO2 under irradiation damage. Therefore, the three-vacancy small cluster contains one U vacancy and two O atom vacancies. With one U atom vacancy as the center and two neighboring O atoms as vacancies, the two O atoms are the first neighbor atoms, the second neighbor atoms, and the third neighbor atoms, respectively, forming V O28-U29-O57 、V O28-U29-O56 、V O28-U29-O35 There are three inequivalent small clusters containing one U vacancy and two O vacancies, such as Figure 6 As shown, Figure 6 The horizontal axis is two O vacancies at different distances, two O vacancies at different distances and one U vacancy cluster, and the vertical axis is the binding energy.

[0086] Step 3, optimizing the vacancy defect structure model according to the calculation parameters, and calculating the formation energy and binding energy;

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

[0088] According to the calculation parameters, the atomic position is movable, the supercell volume is variable or the supercell shape is variable, and 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 is established to calculate the formation of O vacancy and U vacancy defects in UO2, and the formation energy and binding energy are calculated, including:

[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 and complete structure 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 the uranium atom and the oxygen atom in UO2. f ; Vacancy defect formation energy E f The expression is:

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

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

[0094] A calculation formula for the binding energy E (bonding energy) when vacancies at different positions in UO2 combine to form small clusters is established. It is assumed that the small cluster is composed of n U vacancies and m O vacancies. The binding energy of the small cluster with multiple vacancy defects is calculated based on the first total energy, the second total energy and the formation energy of each vacancy defect. The binding energy expression of the small cluster with multiple vacancy defects 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, the multi-vacancy defect cluster is composed of n U vacancies and m O vacancies; E(U 32-n nV U O 64-m mVo) is the total energy of a supercell containing n U vacancies and m O vacancies; E(U 32 O 63 Vo) is the total energy of the supercell containing an O vacancy; E(U 31 O 64 V U ) is the total energy of the supercell containing a U vacancy; E(U32 O 64 ) is the total energy of the supercell without irradiation defects.

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

[0099] A method for characterizing the stability of vacancy defects and small clusters in UO2 after irradiation based on first-principles calculations was established: the tested parameters were used to optimize the crystal structure of UO2 containing small clusters after irradiation, and the tested parameters were used to optimize the crystal structure of UO2 containing small clusters after irradiation. Formula (1) was used to calculate that the vacancy formation of U atoms in UO2 was 5.1 eV, and the vacancy formation of O atoms was 2.2 eV; Formula (2) was used to calculate the binding energy E of each vacancy small cluster, and a graph with different small cluster structures as the horizontal coordinate and binding energy as the vertical coordinate was established to obtain an analysis diagram of the small cluster structure and its binding energy, as shown in Figure 2. Figure 6 shown.

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

[0101] Specifically, according to the formation energy and binding energy calculated in step 3 above, the judgment is as follows:

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

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

[0104] The present invention is based on the first principles calculation method to study the stability of irradiation defects, which is efficient and convenient, reduces the research cycle, saves economic costs, and can make up for the many shortcomings of experimental methods in studying microscopic scale irradiation damage (such as the difficulty in obtaining microscopic information of point defects and high experimental costs). Through the present invention, a UO2 irradiation defect calculation model can be conveniently and quickly established to obtain the stability of different types of irradiation defects, providing an effective analysis 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, and the system corresponds to the analysis method for the stability of vacancy type point defects in UO2 in embodiment 1 in a one-to-one manner; the system includes:

[0107] Parameter testing unit, used to establish the UO2 crystallographic primitive cell and test the calculation parameters of UO2 first principles, including the plane wave cutoff energy Ecut, K-point mesh density Kmesh and the U value of the Hubbard model of the strongly correlated system;

[0108] Vacancy model building unit, used to build UO2 supercell based on UO2 crystallographic primitive cell; using UO2 supercell, construct different vacancy defect structure models generated by irradiation;

[0109] An optimization and calculation unit, used to optimize the vacancy defect structure model according to calculation parameters, and calculate the formation energy and binding energy;

[0110] The judgment and analysis unit is used to judge the difficulty of forming 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] The first vacancy defect structure model: a UO2 supercell computational model containing an oxygen atom vacancy;

[0113] Second vacancy defect structure model: a UO2 supercell calculation model containing a uranium atom vacancy, where 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 calculation model containing two vacancies, where a uranium atom is selected as the vacancy center to form a double vacancy structure with the vacancy at the first nearest oxygen atom; an oxygen atom is selected as the vacancy center to form the first structure with the vacancy at the nearest oxygen atom, the second structure with the vacancy at the second nearest oxygen atom, and the third structure with the vacancy at the third nearest oxygen atom;

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

[0116] Among them, the execution process of each unit can be performed according to the process steps of the analysis method for the stability of vacancy type point defects in UO2 in Example 1, and will not be repeated one by one in this embodiment.

[0117] At the same time, 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, the above-mentioned method for analyzing the stability of vacancy type point defects in UO2 is implemented.

[0118] At the same time, the present invention also provides a computer-readable storage medium, which stores a computer program. When the computer program is executed by a processor, the above-mentioned method for analyzing the stability of vacancy type point defects in UO2 is implemented.

[0119] Those skilled in the art will appreciate that the embodiments of the present application may be provided as methods, systems, or computer program products. Therefore, the present application may adopt the form of a complete hardware embodiment, a complete software embodiment, or an embodiment in combination with software and hardware. Moreover, the present application may adopt the form of a computer program product implemented in one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) that include computer-usable program code.

[0120] The present application is described with reference to the flowcharts and / or block diagrams of the methods, devices (systems), and computer program products according to the embodiments of the present application. It should be understood that each process and / or box in the flowchart and / or block diagram, as well as the combination of the processes and / or boxes in the flowchart and / or block diagram, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing device to generate a machine, so that the instructions executed by the processor of the computer or other programmable data processing device generate instructions for implementing the processes in the flowchart and / or block diagram. Figure 1A process or multiple processes and / or boxes Figure 1 A device that provides the functions specified in a block or multiple blocks.

[0121] These computer program instructions may also be stored in a computer-readable memory capable of directing a computer or other programmable data processing device to operate in a specific manner, so that the instructions stored in the computer-readable memory produce an article of manufacture comprising an instruction device, which implements the process Figure 1 A process or multiple processes and / or boxes Figure 1 A function specified in one or more boxes.

[0122] These computer program instructions can also be loaded onto a computer or other programmable data processing device so that a series of operating steps are executed on the computer or other programmable device to produce a computer-implemented process, thereby providing instructions for implementing the process. Figure 1 A process or multiple processes and / or boxes Figure 1 A step that specifies a function in one or more boxes.

[0123] The specific implementation methods described above further illustrate the objectives, technical solutions and beneficial effects of the present invention in detail. It should be understood that the above description is only a specific implementation method 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 in the scope of protection of the present invention.

Claims

1. The analysis method of the stability of vacancy point defects in UO2 is characterized by: The method includes: Establish a UO2 crystallographic primitive cell and test the calculation parameters of UO2 first principles, including plane wave cutoff energy, K-point grid density and U value of Hubbard model of strongly correlated system; Based on the UO2 crystallographic primitive cell, a UO2 supercell is established; using the UO2 supercell, a structural model containing different vacancy defects generated by irradiation is constructed; According to the calculation parameters, the vacancy defect structure model is optimized, and the formation energy and the binding energy are calculated; According to the formation energy and binding energy, the difficulty of forming different vacancy defects in UO2 after irradiation is determined, and the stability of different vacancy defects is analyzed.

2. The method for analyzing the stability of vacancy point defects in UO2 according to claim 1, characterized in that: Establish UO2 crystallographic primitive cell and test the calculation parameters of UO2 first principles, including: A UO2 crystallographic unit cell is established, wherein the UO2 crystallographic unit cell contains 4 U atoms and 8 O atoms, and its lattice constant is Write a bash shell script program to perform a UO2 first principle calculation parameter test; the bash shell script program is a script program used to calculate the plane wave cutoff energy Ecut and the K point mesh density Kmesh, and perform the test; A coordinate diagram is established with the plane wave cutoff energy Ecut as the x-axis, the K-point mesh density Kmesh as the y-axis, and the total energy of the system Etot as the z-axis; Based on the coordinate diagram, the characteristics of the graphic energy curve are analyzed. When the total energy Etot of the system no longer changes with the change of the plane wave cutoff energy Ecut and the K-point mesh density Kmesh, the plane wave cutoff energy Ecut and the K-point mesh density Kmesh at this time are the calculation parameter values ​​adopted by the UO2 first principles.

3. The method for analyzing the stability of vacancy point defects in UO2 according to claim 2, characterized in that: The U value of the Hubbard model of the strongly correlated system includes: The tested plane wave cutoff energy Ecut and K-point mesh density Kmesh are used to set the calculation parameters of UO2 first principles, and the spin polarization of uranium atoms is considered to calculate the band structure of UO2 crystal. Write a bash shell script for testing the U value, and obtain the calculated value of the bandgap width according to the energy band structure of the UO2 crystal at different U values; The calculated value of the bandgap width is compared with the experimentally measured value of the bandgap width. When the calculated value of the bandgap width is equal to the tested value of the bandgap width, the U value at this time is the corrected value of GGA+U calculated by the first principles of UO2; the GGA+U is the U value of the traditional GGA functional plus the Hubbard parameter.

4. The method for analyzing the stability of vacancy point defects in UO2 according to claim 1, characterized in that: The vacancy defect structure model includes: The first vacancy defect structure model: a UO2 supercell computational model containing an oxygen atom vacancy; Second vacancy defect structure model: a UO2 supercell calculation model containing a 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 calculation model containing two vacancies, where a uranium atom is selected as the vacancy center to form a double vacancy structure with the vacancy at the first nearest oxygen atom; an oxygen atom is selected as the vacancy center to form the first structure with the vacancy at the nearest oxygen atom, the second structure with the vacancy at the second nearest oxygen atom, and the third structure with the vacancy at the third nearest oxygen atom; The fourth vacancy defect structure model: a small cluster model containing one uranium atom vacancy and two oxygen atom vacancies. A uranium atom is selected as the vacancy center, and the two neighboring oxygen atoms are taken as vacancies. The two oxygen atoms are the first neighbor atom, the second neighbor atom, and the third neighbor atom, respectively, forming three inequivalent small clusters containing one uranium atom vacancy and two oxygen atom vacancies.

5. The method for analyzing the stability of vacancy point defects in UO2 according to claim 1, characterized in that: Optimizing the vacancy defect structure model according to the calculation parameters includes: According to the calculation parameters, the atomic position is movable, the supercell volume is variable or the supercell shape is variable, and the vacancy defect structure model is optimized by using a conjugate gradient algorithm.

6. The method for analyzing the stability of vacancy point defects in UO2 according to claim 1, characterized in that: Calculate formation and binding energies, 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 defects and complete structure is calculated as the second total energy; Calculating the vacancy defect formation energy of uranium atoms and the vacancy defect formation energy of oxygen atoms in UO2 according to the first total energy and the second total energy; The binding energy of the multi-vacancy defect cluster is calculated based on the first total energy, the second total energy and the formation energy of each vacancy defect.

7. The method for analyzing the stability of vacancy point defects in UO2 according to claim 6, characterized in that: The vacancy defect formation energy E f The expression is: It is f =E[defective]-E[perfect]+nμ x Among them, μ x represents the chemical potential μ of U and O atoms O and μ U value; E[defect] represents the total energy of the UO2 supercell containing oxygen atom vacancy defects and uranium atom vacancy defects; E[perfect] represents the total energy of the UO2 supercell with a complete structure without defects; The binding energy expression of the multi-vacancy defect cluster is: E(nV U mV O )=E(U 32-n nV U About 64-m mV O )-n×E(U 31 About 64 In U )-m×E(U 32 About 63 In O )+(m+n-1)×E(U 32 About 64 ) Among them, the multi-vacancy defect cluster is composed of n U vacancies and m O vacancies; E(U 32-n nV U O 64-m mVo) is the total energy of a supercell containing n U vacancies and m O vacancies; E(U 32 O 63 Vo) is the total energy of the supercell containing an O vacancy; E(U 31 O 64 V U ) is the total energy of the supercell containing a U vacancy; E(U 32 O 64 ) is the total energy of the supercell without irradiation defects.

8. The method for analyzing the stability of vacancy point defects in UO2 according to claim 1, characterized in that: According to the formation energy and binding energy, the difficulty of forming different vacancy defects in UO2 after irradiation is judged, and the stability of different vacancy defects is analyzed, including: When the formation energy Ef>0, and the larger the formation energy Ef, the more difficult it is for the vacancy defect to form; otherwise, the easier it is for the vacancy defect to form; When the binding energy E>0, it means that the vacancy defect cannot be combined and the vacancy defect is unstable; when the binding energy E<0, it means that the vacancy defect can be combined and the vacancy defect is stable.

9. An analysis system for the stability of vacancy point defects in UO2, characterized in that the system comprises: Parameter testing unit, used to establish UO2 crystallographic primitive cell and test the calculation parameters of UO2 first principle, including plane wave cutoff energy, K point grid density and U value of Hubbard model of strong correlation system; A vacancy model building unit is used to build a UO2 supercell based on the UO2 crystallographic primitive cell; and to use the UO2 supercell to build a structural model containing different vacancy defects generated by irradiation; An optimization and calculation unit, used to optimize the vacancy defect structure model according to the calculation parameters, and calculate the formation energy and the binding energy; The judging and analyzing unit is used to judge the difficulty of forming different vacancy defects in UO2 after irradiation according to the formation energy and binding energy, and analyze the stability of different vacancy defects.

10. The analysis system for the stability of vacancy point defects in UO2 according to claim 9, characterized in that: The vacancy defect structure model includes: The first vacancy defect structure model: a UO2 supercell computational model containing an oxygen atom vacancy; Second vacancy defect structure model: a UO2 supercell calculation model containing a 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 calculation model containing two vacancies, where a uranium atom is selected as the vacancy center to form a double vacancy structure with the vacancy at the first nearest oxygen atom; an oxygen atom is selected as the vacancy center to form the first structure with the vacancy at the nearest oxygen atom, the second structure with the vacancy at the second nearest oxygen atom, and the third structure with the vacancy at the third nearest oxygen atom; The fourth vacancy defect structure model: a small cluster model containing one uranium atom vacancy and two oxygen atom vacancies. A uranium atom is selected as the vacancy center, and the two neighboring oxygen atoms are taken as vacancies. The two oxygen atoms are the first neighbor atom, the second neighbor atom, and the third neighbor atom, respectively, forming three inequivalent small clusters containing one uranium atom vacancy and two oxygen atom vacancies.

11. An electronic device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein: When the processor executes the computer program, the method for analyzing the stability of vacancy type point defects in UO2 as described in any one of claims 1 to 8 is implemented.

12. A computer-readable storage medium storing a computer program, characterized in that: When the computer program is executed by a processor, the method for analyzing the stability of vacancy type point defects in UO2 as described in any one of claims 1 to 8 is implemented.

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