A method and related device for calculating the thermal neutron scattering cross section of a diffuse fuel

Abstract

The application discloses a kind of dispersion type fuel's thermal neutron scattering cross section calculation method and related device, belong to reactor material reaction cross section calculation technical field;The method first constructs the supercell of dispersion type fuel, calculates the Hellmann-Feynman force between each atom of supercell;And according to Hellmann-Feynman force, calculate phonon state density, mean square displacement matrix, dispersion relation and polarization vector;For the thermal neutron scattering law data calculation of fuel material, it can improve the accuracy of thermal neutron scattering law calculation, and then the theoretical value of thermal neutron scattering cross section is calculated;Finally, the actual experimental measurement value is compared with the aforementioned thermal neutron scattering cross section theoretical value, and the input parameters of thermal neutron scattering calculation are corrected according to the error of the two, and then the dispersion type fuel thermal neutron scattering cross section library with higher accuracy is obtained again by the corrected input parameters, and the calculation result is more accurate compared with the prior art.

Description

Technical Field

[0001] The invention belongs to the technical field of reaction cross section calculation of materials in reactors, and relates to a thermal neutron scattering cross section calculation method for dispersed fuel and a related device. Background Art

[0002] As one of the core elements in reactor design calculations, the thermal neutron scattering cross section (TCS) plays a crucial role. It directly influences the manner and efficiency of neutron interactions with nuclear fuel and other materials within the reactor, and is a key parameter for evaluating reactor performance, optimizing core structure, and ensuring safe reactor operation. Therefore, achieving accurate calculations of the TCS is crucial for improving the accuracy and reliability of reactor core neutronics calculations.

[0003] Calculation of the thermal neutron scattering law is a necessary condition for obtaining the thermal neutron scattering cross section. Currently, the three internationally released databases, ENDF / B-VIII.0, contain thermal neutron scattering law data for 34 materials, JENDL5.0 contains thermal neutron scattering law data for 37 materials, and JEFF3.3 contains thermal neutron scattering law data for 20 materials. These three databases cover thermal neutron scattering data of commonly used reactor materials such as graphite, H2O, D2O, and UO2. However, with the development of advanced reactor design, new materials such as U3Si2-Al dispersion fuel will lack available thermal scattering cross section data. The thermal scattering cross section data obtained using traditional calculation methods are not accurate enough, and it is difficult to provide a solid theoretical basis for reactor design, optimization, and operation. Summary of the Invention

[0004] The purpose of the present invention is to provide a method and related device for calculating the thermal neutron scattering cross section of a dispersed fuel, so as to solve the technical problem in the prior art that it is difficult to accurately calculate the thermal scattering cross section data.

[0005] In order to achieve the above object, the present invention adopts the following technical solutions:

[0006] In a first aspect, the present invention provides a method for calculating the thermal neutron scattering cross section of a dispersed fuel, comprising the following steps:

[0007] Constructing supercells of diffuse fuels;

[0008] Calculate the Hellmann-Feynman forces between atoms in the supercell;

[0009] Calculate the phonon state density, mean square displacement matrix, dispersion relation and polarization vector based on the Hellmann-Feynman force;

[0010] Calculate the incoherent elastic scattering law using the phonon state density; calculate the coherent elastic scattering law using the mean square displacement matrix; calculate the inelastic scattering law using the phonon state density, dispersion relation and polarization vector;

[0011] The thermal neutron scattering cross section of incoherent elastic scattering is calculated according to the incoherent elastic scattering law; the thermal neutron scattering cross section of coherent elastic scattering is calculated according to the coherent elastic scattering law; the thermal neutron scattering cross section of inelastic scattering is calculated according to the inelastic scattering law.

[0012] Furthermore, the step of constructing a supercell of a dispersion fuel specifically includes:

[0013] Use the crystal structure visualization software VESTA to construct the diffuse fuel unit cell;

[0014] Use the first-principles material simulation software package VASP to optimize the material structure of the constructed unit cell;

[0015] The lattice dynamics calculation program PHONOPY was used to expand the supercell of the optimized unit cell.

[0016] Furthermore, the step of calculating the Hellmann-Feynman force between atoms in the supercell specifically includes: using VASP software and density functional perturbation theory method to calculate the Hellmann-Feynman force between atoms in the expanded supercell.

[0017] Furthermore, the steps of calculating the incoherent elastic scattering law using the phonon state density; calculating the coherent elastic scattering law using the mean square displacement matrix; and calculating the inelastic scattering law using the phonon state density, dispersion relation, and polarization vector specifically include:

[0018] For incoherent elastic scattering, the DWF is calculated using the phonon density of states and the result is expressed as [T i ,DWF(T i )] in the form of output in the database file MF7 / MT2;

[0019] For coherent elastic scattering, the DWF is calculated using the mean square displacement matrix and the result is expressed as Output in the database file MF7 / MT2 in the form of;

[0020] For inelastic scattering, the thermal scattering law S(α, β, T) is calculated based on the phonon method using the phonon state density, dispersion relation and polarization vector, and output in the database file MF7 / MT4.

[0021] Furthermore, the step of calculating the thermal neutron scattering cross section of incoherent elastic scattering according to the incoherent elastic scattering law is specifically calculated by the formula:

[0022]

[0023] Where σ iel is the incoherent elastic scattering cross section; E is the incident neutron energy; σ b is the characteristic bound section; DWF is the Debye-Waller coefficient;

[0024] The step of calculating the thermal neutron scattering cross section of coherent elastic scattering according to the coherent elastic scattering law is specifically calculated as follows:

[0025]

[0026] Where σ coh is the coherent elastic scattering cross section; E i are different Bragg boundary energy points; fi is the structure factor of the unit cell;

[0027] The specific calculation formula for the step of calculating the thermal neutron scattering cross section of inelastic scattering according to the inelastic scattering law is:

[0028]

[0029] Where σ ine is the inelastic scattering cross section; E is the incident neutron energy; E′ is the outgoing neutron energy; T is the temperature; μ is the cosine of the scattering angle; k is the Boltzmann constant; α is the energy transfer; β is the energy transfer; S(α, β, T) is the thermal scattering law.

[0030] Furthermore, it also includes:

[0031] Experimental measurement of the thermal neutron scattering cross section of diffuse fuels;

[0032] The thermal neutron scattering cross section of the dispersed fuel measured experimentally is compared with the calculated thermal neutron scattering cross section of the dispersed fuel, and the input parameters of the thermal neutron scattering calculation are corrected according to the error between the two.

[0033] Then, the thermal neutron scattering cross section library of diffuse fuel is retrieved based on the thermal neutron scattering calculation program TNS using the corrected input parameters.

[0034] Furthermore, the step of experimentally measuring the thermal neutron scattering cross section of the diffuse fuel specifically includes:

[0035] The neutron transmission law of diffuse fuel products is measured using the transmission method based on an accelerator neutron source. First, a neutron source is obtained from the accelerator as the incident neutron, and the neutron count is obtained by the TOF detector in the case of an empty target. Then, the fuel sample is used as the target, and the sample is heated to a specified temperature by a heating device. The neutron count is obtained by the TOF detector, and the total cross section is calculated. The absorption cross section is then subtracted from the total cross section to obtain the thermal neutron scattering cross section. The specific calculation formula is:

[0036]

[0037] σ s =σ t -σ a

[0038] Where σ t is the total cross section, σ s is the scattering cross section, σ a is the absorption cross section, N is the number of target nuclei per unit area, N(E) I is the number of neutrons incident on the target nucleus per unit area from the neutron source, N(E) O N(E) is the number of neutrons projected after the target nucleus and neutrons react per unit area. b This is the background count under full blocking.

[0039] In a second aspect, the present invention provides a system for calculating a thermal neutron scattering cross section of a dispersed fuel, comprising:

[0040] Supercell building blocks for constructing supercells of dispersed fuels;

[0041] Hellmann-Feynman force calculation module, used to calculate the Hellmann-Feynman force between atoms in the supercell;

[0042] Input parameter calculation module, used to calculate the phonon state density, mean square displacement matrix, dispersion relation and polarization vector based on the Hellmann-Feynman force;

[0043] Thermal neutron scattering law calculation module, used to calculate incoherent elastic scattering laws using phonon state density; calculate coherent elastic scattering laws using mean square displacement matrix; calculate inelastic scattering laws using phonon state density, dispersion relation and polarization vector;

[0044] The thermal neutron scattering cross section calculation module is used to calculate the thermal neutron scattering cross section of incoherent elastic scattering according to the incoherent elastic scattering law; calculate the thermal neutron scattering cross section of coherent elastic scattering according to the coherent elastic scattering law; and calculate the thermal neutron scattering cross section of inelastic scattering according to the inelastic scattering law.

[0045] In a third aspect, the present invention provides a computer device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor implements the steps of the above method when executing the computer program.

[0046] In a fourth aspect, the present invention provides a computer-readable storage medium, wherein the computer-readable storage medium stores a computer program, and when the computer program is executed by a processor, the steps of the above method are implemented.

[0047] Compared with the prior art, the present invention has the following beneficial effects:

[0048] The present invention discloses a method and related device for calculating the thermal neutron scattering cross section of a dispersed fuel. The method comprises the following steps: firstly, constructing a supercell of the dispersed fuel, and calculating the Hellmann-Feynman force between atoms in the supercell; then, calculating the phonon state density, mean square displacement matrix, dispersion relation and polarization vector based on the Hellmann-Feynman force; providing rich input information for calculating the thermal neutron scattering law data of reactor materials, thereby improving the accuracy of the thermal neutron scattering law calculation, and further calculating the theoretical value of the thermal neutron scattering cross section; finally, comparing actual experimental measurement values ​​with the aforementioned theoretical value of the thermal neutron scattering cross section, correcting the input parameters of the thermal neutron scattering calculation based on the errors between the two, and then re-obtaining a more accurate thermal neutron scattering cross section library of the dispersed fuel based on the corrected input parameters. Compared with the prior art, the calculation results are more accurate. BRIEF DESCRIPTION OF THE DRAWINGS

[0049] In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the following briefly introduces the drawings required for use in the embodiments. It should be understood that the following drawings only illustrate certain embodiments of the present invention and therefore should not be regarded as limiting the scope. For ordinary technicians in this field, other relevant drawings can be obtained based on these drawings without paying any creative work.

[0050] Figure 1 is a flow chart of the method of the present invention;

[0051] Figure 2 is a schematic diagram of the system of the present invention;

[0052] Figure 3 This is a flow chart of the theoretical calculation of the U3Si2-Al thermal neutron scattering cross section according to an embodiment of the present invention;

[0053] Figure 4 Schematic diagram of the U3Si2-Al thermal neutron scattering cross section experimental measurement in an embodiment of the present invention;

[0054] Figure 5This is a flow chart of the correction of the thermal neutron scattering cross section of U3Si2-Al according to an embodiment of the present invention;

[0055] Figure 6 Schematic diagram of U3Si2-Al cross-section measurement based on the transmission method according to an embodiment of the present invention;

[0056] Figure 7 It is a schematic diagram of the computer device structure of the present invention. DETAILED DESCRIPTION

[0057] To make the objectives, technical solutions, and advantages of the embodiments of the present invention more clear, the technical solutions of the embodiments of the present invention will be clearly and completely described below in conjunction with the accompanying drawings of the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Generally, the components of the embodiments of the present invention described and shown in the drawings herein can be arranged and designed in various different configurations.

[0058] Therefore, the following detailed description of the embodiments of the present invention provided in the accompanying drawings is not intended to limit the scope of the invention as claimed, but rather merely represents selected embodiments of the present invention. All other embodiments derived by persons of ordinary skill in the art based on the embodiments of the present invention without creative effort shall fall within the scope of protection of the present invention.

[0059] It should be noted that similar reference numerals and letters denote similar items in the following drawings, and therefore, once an item is defined in one drawing, it does not need to be further defined or explained in subsequent drawings.

[0060] In the description of the embodiments of the present invention, it should be noted that if the terms "upper," "lower," "horizontal," "inner," etc. appear, the orientation or positional relationship indicated is based on the orientation or positional relationship shown in the accompanying drawings, or the orientation or positional relationship in which the inventive product is typically placed when in use. These terms are merely for the convenience of describing the present invention and simplifying the description, and do not indicate or imply that the device or component referred to must have a specific orientation, be constructed, or operate in a specific orientation. Therefore, they should not be construed as limitations on the present invention. In addition, the terms "first," "second," etc. are used only to distinguish descriptions and should not be construed as indicating or implying relative importance.

[0061] In addition, if the term "horizontal" appears, it does not mean that the component must be absolutely horizontal, but can be slightly tilted. For example, "horizontal" only means that its direction is more horizontal than "vertical", and does not mean that the structure must be completely horizontal, but can be slightly tilted.

[0062] In the description of the embodiments of the present application, it also needs to be explained that, unless explicitly defined and limited, if the terms "arrange", "install", "connect", "connect" appear, they should be understood in a broad sense, for example, can be fixedly connected, can also be detachably connected, or integrally connected; can be mechanically connected, can also be electrically connected; can be directly connected, can also be indirectly connected through an intermediate medium, can be the communication inside two elements. For those skilled in the art, the specific meaning of the above terms in the present application can be understood according to the specific circumstances.

[0063] The present application will be further described in detail below in conjunction with the drawings:

[0064] Referring to Figure 1 , the present application discloses a method for calculating the thermal neutron scattering cross section of a dispersion type fuel, comprising the following steps:

[0065] S1, constructing a supercell of the dispersion type fuel;

[0066] Using the crystal structure visualization software VESTA to construct the dispersion type fuel cell;

[0067] Using the first principle material simulation software package VASP to optimize the material structure of the constructed cell;

[0068] Using the lattice dynamics calculation program PHONOPY to expand the supercell of the structure optimized cell.

[0069] S2, calculating the Hellmann-Feynman force between atoms in the supercell;

[0070] Using VASP software, using density functional perturbation theory method to calculate the Hellmann-Feynman force between atoms in the expanded supercell.

[0071] S3, calculating the phonon density of states, mean square displacement matrix, dispersion relation and polarization vector according to the Hellmann-Feynman force;

[0072] For incoherent elastic scattering, using the phonon density of states to calculate DWF, and outputting the results in the form of [T i , DWF(T i )] in the database file MF7 / MT2;

[0073] For coherent elastic scattering, using the mean square displacement matrix to calculate DWF, and outputting the results in the form of in the database file MF7 / MT2;

[0074] For inelastic scattering, the phonon method is used to calculate the thermal scattering law S(α, β, T) based on the phonon density of states, dispersion relation and polarization vector, and the output is in the database file MF7 / MT4.

[0075] S4, use the phonon density of states to calculate the incoherent elastic scattering law; use the mean square displacement matrix to calculate the coherent elastic scattering law; use the phonon density of states, dispersion relation and polarization vector to calculate the inelastic scattering law;

[0076] Based on the way of storing data from the nuclear database, formulas (1), (2), (3) are the calculation formulas of the coherent elastic scattering cross section / incoherent elastic scattering cross section / inelastic scattering cross section:

[0077]

[0078] Where: σ coh is the coherent elastic scattering cross section, σ iel is the incoherent elastic scattering cross section, σ ine is the inelastic scattering cross section, E is the incident neutron energy, E' is the outgoing neutron energy, E i is the different Bragg boundary energy point, fi is the structure factor of the unit cell, DWF is the Debye-Waller coefficient, T is the temperature, μ is the scattering angle cosine, σ b is the characteristic bound cross section, k is the Boltzmann constant, α is the energy transfer, β is the energy transfer, S(α, β, T) is the thermal scattering law.

[0079] S5, calculate the thermal neutron scattering cross section of incoherent elastic scattering according to the incoherent elastic scattering law; calculate the thermal neutron scattering cross section of coherent elastic scattering according to the coherent elastic scattering law; calculate the thermal neutron scattering cross section of inelastic scattering according to the inelastic scattering law.

[0080] S6, measure the thermal neutron scattering cross section of the dispersion type fuel by experiment;

[0081] Based on the accelerator neutron source, the neutron transmission law of the dispersion type fuel sample is measured by the transmission method. First, obtain the neutron source from the accelerator as the incident neutron, and obtain the neutron count by the TOF detector in the case of empty target; then use the fuel sample as the target, heat the sample to the specified temperature by the heating device, obtain the neutron count by the TOF detector, then calculate the total cross section, and then subtract the absorption cross section from the total cross section to obtain the thermal neutron scattering cross section; the specific calculation formula is:

[0082]

[0083] σ s = σ t - σ a

[0084] In the formula, σt is the total cross section, σ s is the scattering cross section, σ a is the absorption cross section, N is the number of target nuclei per unit area, N(E) I is the number of neutrons incident on the target nucleus per unit area from the neutron source, N(E) O N(E) is the number of neutrons projected after the target nucleus and neutrons react per unit area. b This is the background count under full blocking.

[0085] S7, comparing the experimentally measured thermal neutron scattering cross section of the dispersed fuel with the calculated thermal neutron scattering cross section of the dispersed fuel, and correcting the input parameters of the thermal neutron scattering calculation according to the error between the two;

[0086] S8, then using the corrected input parameters, the diffuse fuel thermal neutron scattering cross section library is re-obtained based on the thermal neutron scattering calculation program TNS.

[0087] See also Figure 2 The embodiment of the present invention discloses a system for calculating a thermal neutron scattering cross section of a dispersed fuel, comprising:

[0088] Supercell building blocks for constructing supercells of dispersed fuels;

[0089] Hellmann-Feynman force calculation module, used to calculate the Hellmann-Feynman force between atoms in the supercell;

[0090] Input parameter calculation module, used to calculate the phonon state density, mean square displacement matrix, dispersion relation and polarization vector based on the Hellmann-Feynman force;

[0091] Thermal neutron scattering law calculation module, used to calculate incoherent elastic scattering laws using phonon state density; calculate coherent elastic scattering laws using mean square displacement matrix; calculate inelastic scattering laws using phonon state density, dispersion relation and polarization vector;

[0092] The thermal neutron scattering cross section calculation module is used to calculate the thermal neutron scattering cross section of incoherent elastic scattering according to the incoherent elastic scattering law; calculate the thermal neutron scattering cross section of coherent elastic scattering according to the coherent elastic scattering law; and calculate the thermal neutron scattering cross section of inelastic scattering according to the inelastic scattering law.

[0093] It's important to note that thermal neutron scattering data from materials is important because when neutron energies fall below a few electron volts, the neutron energy is comparable to the thermal kinetic energy of the scattering nucleus. Therefore, the target nucleus can no longer be assumed to be stationary; the scattered neutron may gain energy by scattering upwards due to the scattering nucleus's vibrations. Due to interactions between the scattering nucleus and its neighboring nuclei, its nucleus is bound and does not recoil freely when it collides with a neutron. The de Broglie wavelength of low-energy neutrons is comparable to the spacing between nuclei within the material, allowing for interference effects between neutrons scattered from different nuclei. Interference effects differentiate the scattering cross section into coherent and incoherent scattering. Chemical bonding effects distinguish between elastic and incoherent elastic scattering when considering the scattering cross section for bound nuclei. Therefore, thermal neutron scattering cross sections are calculated for all four scenarios.

[0094] For new types of dispersed fuels, this embodiment uses a thermal neutron scattering cross-section calculation method based on dynamic structure factors and phonon density of states correction. First, the unit cell is constructed using the open source crystal structure visualization software VESTA. Then, the first-principles materials simulation software package VASP and the lattice dynamics calculation program PHONOPY are used to perform structural optimization, supercell establishment, Hellmann-Feynman force calculations, dynamic matrix calculations, and Burleigh zone sampling to prepare the input parameters required for the thermal neutron scattering law calculation.

[0095] The second step is to calculate the thermal neutron scattering law. First, the phonon density of states, dispersion relation, polarization vector, and mean square displacement matrix are used as inputs to the thermal neutron scattering calculation program TNS for core materials. The program uses these input parameters to calculate the thermal neutron scattering law required for each scattering cross section. The incoherent elastic scattering law is calculated using the phonon density of states parameters. The coherent scattering law is obtained using the mean square displacement matrix through the anisotropic displacement parameter method. This method modifies the cubic approximation. In other words, the traditional method assumes that nuclear displacements are isotropic and independent of lattice position and nucleus type. Using the mean square displacement matrix as a parameter fully accounts for the actual nuclear displacements, resulting in higher accuracy. The inelastic scattering law is calculated using the phonon density of states, dispersion relation, and polarization vector. Traditional methods use an incoherent approximation to simplify the calculation of the inelastic scattering cross section, ignoring the coherent term due to the small contribution of the coherent term in inelastic scattering. This approach, however, abandons the incoherent approximation and reconsiders the contribution of the coherent term, improving the accuracy of the inelastic scattering calculation. The above thermal scattering law data are stored in the nuclear database file MF7.

[0096] The third step is to calculate the thermal neutron scattering cross section: In fact, in order to facilitate the storage and calculation of the thermal neutron scattering cross section, the database does not directly store the final thermal scattering law data S (α, β, T), but stores it according to the actual scattering type. For incoherent elastic scattering, the Debye-Waller (DWF) coefficient calculated based on the phonon state density is stored, specifically in the form of tab1 table [T i , DWF(T i )] is output in the database file MF7 / MT2; for coherent elastic scattering, specifically in the form of tabl table The output is in the database file MF7 / MT2. The DWF is calculated using the mean square displacement matrix as a parameter. For inelastic scattering, the thermal scattering law S(α, β, T) calculated directly based on the phonon method using the phonon state density, dispersion relation and polarization vector is stored and output in the database file MF7 / MT4.

[0097] Based on the way the nuclear database stores data, formulas (1), (2), and (3) are the calculation formulas for the coherent elastic scattering cross section / incoherent elastic scattering cross section / inelastic scattering cross section:

[0098]

[0099] Where: coh is the coherent elastic scattering cross section, σ iel is the incoherent elastic scattering cross section, σ ine is the inelastic scattering cross section, E is the incident neutron energy, E′ is the outgoing neutron energy, and E i are different Bragg boundary energy points, fi is the structure factor of the unit cell, DWF is the Debye-Waller coefficient, T is the temperature, μ is the cosine of the scattering angle, σ b is the characteristic binding cross section, k is the Boltzmann constant, α is the energy transfer, β is the energy transfer, and S(α,β,T) is the thermal scattering law.

[0100] After completing the theoretical calculation, it is necessary to measure the thermal neutron scattering cross section of the diffuse fuel. The neutron transmittance of the fuel sample is measured using the transmission method based on the accelerator neutron source. The transmission method refers to a method of calculating the total cross section size by measuring the change in the number of neutron counts measured by the detector when there is a fuel sample and when there is no fuel sample under the same experimental conditions. The principle is shown in formulas (4) and (5): First, the number of neutrons measured by the detector under the two conditions of empty target and fuel sample target is subtracted from the background count when the target is blocked to obtain the actual number of useful neutrons. Then, the total cross section is calculated, and the total thermal neutron scattering cross section of the fuel sample is subtracted from the absorption cross section.

[0101]

[0102] σ s =σ t -σ a (5)

[0103] Where: t is the total cross section, σ s is the scattering cross section, σ a is the absorption cross section, N is the number of target nuclei per unit area, N(E) I is the number of neutrons incident on the target nucleus per unit area from the neutron source, N(E) O N(E) is the number of neutrons projected after the target nucleus and neutrons react per unit area. b This is the background count under full blocking.

[0104] Schematic diagram of transmission method measurement Figure 6 As shown, the items required for the experiment include a neutron source generated by an accelerator, fuel samples, TOF detectors, monitoring detectors, etc.

[0105] After obtaining the measured experimental data, the final step is to correct the thermal neutron scattering cross section: first, the experimentally measured thermal neutron scattering data is compared with the theoretically calculated data, and the theoretically calculated parameters such as the phonon density of states of the diffuse fuel are corrected to obtain a phonon density of states and dynamic structure factor that are more consistent with the measured values. Secondly, using the corrected phonon density of states and dynamic structure factor as input, a more accurate thermal neutron scattering cross section library for the diffuse fuel is re-derived based on a nuclear data processing program. This verified, multi-temperature thermal neutron scattering cross section library for the diffuse fuel will provide a cross section library foundation for analyzing the thermal neutron scattering effects of reactors with heterogeneous fuels.

[0106] Example:

[0107] This paper uses the novel U3Si2-Al dispersion fuel as an example to disclose a method for calculating and verifying the thermal neutron scattering cross section of the U3Si2-Al dispersion fuel. Currently, no major databases in the world contain thermal neutron scattering data for the U3Si2-Al dispersion fuel, and traditional calculation methods employ approximate processing, resulting in inaccurate results. To accurately calculate thermal neutron scattering data, first-principles lattice dynamics simulation calculation methods have rapidly developed. These methods can provide rich input information for calculating thermal neutron scattering law data for reactor materials, enabling more accurate calculation of thermal neutron scattering data for materials. However, these methods are purely theoretical calculations, with significant errors in some areas. Therefore, they must be combined with experiments to obtain the most accurate thermal neutron scattering cross section. Therefore, the present invention calculates the theoretical thermal neutron scattering cross section of a novel dispersed material, U3Si2-Al, from first principles. Then, using an accelerator neutron source, the actual thermal neutron scattering cross section of a U3Si2-Al fuel sample is measured using the transmission method. The experimental data are compared with the theoretically calculated data, and parameters such as the theoretically calculated phonon state density are modified to obtain a phonon state density and dynamic structure factor that are more consistent with the measured values. Finally, these parameters are used as input to re-derive a more accurate thermal neutron scattering cross section library for the U3Si2-Al dispersed fuel using the nuclear data processing program TNS. The specific implementation steps are as follows:

[0108] Step 1: First, use the crystal structure visualization software VESTA to construct the U3Si2-Al unit cell.

[0109] Step 2: Then use the first-principles material simulation software package VASP to optimize the material structure of the constructed unit cell to obtain the lattice constant of the unit cell when it is most stable.

[0110] Step 3: Use the lattice dynamics calculation program PHONOPY to expand the supercell of the optimized high-precision unit cell.

[0111] Step 4: Using VASP again, density functional perturbation theory is used to calculate the Hellmann-Feynman forces between atoms in the expanded supercell. The pseudopotential file is the most important input file, used to simulate the molecular mechanics position. The exchange-correlation potential is solved using the generalized gradient approximation or local density approximation theory in the pseudopotential library. Accurately solving the exchange-correlation term is crucial for improving the accuracy of the KS equation. The projected cone-added wave (PAW) method is used to describe electron-ion interactions. The k-point mesh size in the Burleyoun zone is set, and the Monkhost-Pack scheme is used to sample the generated k-point mesh. Finally, the Hellmann-Feynman force is calculated.

[0112] Step 5: Based on the Hellmann-Feynman force obtained above, use the PHONOPY program to calculate the dynamic matrix, and then calculate the phonon state density, mean square displacement matrix, dispersion relation and polarization vector.

[0113] Step 6: According to the calculation method of thermal scattering law in TNS, for incoherent elastic scattering, use the phonon state density to calculate DWF and express the result as [T i ,DWF(T i )] in the form of database file MF7 / MT2; for coherent elastic scattering, the mean square displacement matrix is ​​used to calculate DWF, and the result is output as For inelastic scattering, the thermal scattering law S(α, β, T) is calculated based on the phonon method using the phonon state density, dispersion relation and polarization vector and output in the database file MF7 / MT4.

[0114] Step 7: Based on the database, the heat scattering cross section is calculated using the heat scattering law data of formulas (1), (2), and (3). The theoretical calculation flow chart is as follows: Figure 3 shown.

[0115]

[0116] Step 8: Measure the thermal neutron scattering cross section of the U3Si2-Al fuel sample through experiments. The neutron transmittance of the U3Si2-Al fuel sample is measured by the transmission method based on the accelerator neutron source. First, a neutron source is obtained from the accelerator as the incident neutron, and the neutron count is obtained through the TOF detector in the case of an empty target; then the U3Si2-Al fuel sample is used as the target target, and the sample is heated to a specified temperature by a heating device, and the neutron count is obtained through the TOF detector. The total cross section is then calculated using formulas (4) and (5), and the thermal neutron scattering cross section is obtained by subtracting the absorption cross section from the total cross section. The schematic diagram of the calculation method can be seen in Figure 4 .

[0117]

[0118] σ s =σ t -σ a (5)

[0119] Step 9: Compare the thermal neutron scattering data obtained from the experimental measurement with the theoretical calculation data mentioned above, and correct the theoretically calculated thermal neutron scattering data of the U3Si2-Al diffuse fuel according to the calculation error. Correct the U3Si2-Al structure, repeat the above process, correct the calculated phonon state density and other parameters, and obtain a phonon state density and corresponding dynamic structure factor that are more consistent with the measured values. Then, using the corrected phonon state density and dynamic structure factor as input, a more accurate U3Si2-Al diffuse fuel thermal neutron scattering cross section library is obtained based on the nuclear data processing program TNS. The calculation process is as follows: Figure 5 shown.

[0120] In one embodiment of the present invention, see Figure 7 , provides a computer device, the computer device including a processor and a memory, the memory being used to store a computer program, the computer program including program instructions, and the processor being used to execute the program instructions stored in the computer storage medium. The processor may be a central processing unit (CPU), or may also be other general-purpose processors, digital signal processors (DSP), application-specific integrated circuits (ASIC), field-programmable gate arrays (FPGA), or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc. It is the computing core and control core of the terminal, and is suitable for implementing one or more instructions, specifically suitable for loading and executing one or more instructions in the computer storage medium to implement the corresponding method flow or corresponding function; the processor described in the embodiment of the present invention can be used for the operation of the thermal neutron scattering cross section calculation method for diffuse fuel.

[0121] The present invention also provides a storage medium, specifically a computer-readable storage medium (Memory). The computer-readable storage medium is a memory device in a computer device, used to store programs and data. It is understood that the computer-readable storage medium herein can include both built-in storage media in the computer device and, of course, extended storage media supported by the computer device. The computer-readable storage medium provides storage space, which stores the terminal's operating system. Furthermore, the storage space also stores one or more instructions suitable for being loaded and executed by a processor. These instructions can be one or more computer programs (including program code). It should be noted that the computer-readable storage medium herein can be a high-speed RAM memory or a non-volatile memory, such as at least one disk storage device. The processor can load and execute the one or more instructions stored in the computer-readable storage medium to implement the corresponding steps of the method for calculating the thermal neutron scattering cross section of a diffuse fuel in the above-mentioned embodiment.

[0122] It will be understood by those skilled in the art that embodiments of the present invention may be provided as methods, systems, or computer program products. Thus, the present invention may take the form of an entirely hardware embodiment, an entirely software embodiment, or an embodiment combining software and hardware. Furthermore, the present invention may take the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to magnetic disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0123] The present invention is described with reference to flowcharts and / or block diagrams of methods, devices (systems), and computer program products according to embodiments of the present invention. It should be understood that each process and / or block in the flowcharts and / or block diagrams, as well as combinations of processes and / or blocks in the flowcharts 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, a special-purpose computer, an embedded processor, or other programmable data processing device to produce 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 flowcharts and / or block diagrams. Figure 1 a process or multiple processes and / or boxes Figure 1 A device that provides the functions specified in a block or multiple blocks.

[0124] These computer program instructions may also be stored in a computer readable memory that can direct a computer or other programmable data processing device to work 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 1The function specified in one or more boxes.

[0125] These computer program instructions can also be loaded onto a computer or other programmable data processing device so that a series of operational steps are executed on the computer or other programmable device to produce a computer-implemented process, thereby providing the instructions executed on the computer or other programmable device 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.

[0126] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and not to limit it. Although the present invention has been described in detail with reference to the above embodiments, ordinary technicians in the field should understand that the specific implementation methods of the present invention can still be modified or replaced by equivalents. Any modification or equivalent replacement that does not depart from the spirit and scope of the present invention should be covered by the scope of protection of the claims of the present invention.

Claims

1. A method for calculating the thermal neutron scattering cross section of a diffuse fuel, characterized in that: The following steps are involved: Constructing supercells of diffuse fuels; Calculate the Hellmann-Feynman forces between atoms in the supercell; Calculate the phonon state density, mean square displacement matrix, dispersion relation and polarization vector based on the Hellmann-Feynman force; Calculate incoherent elastic scattering laws using phonon density of states; Calculate the coherent elastic scattering law using the mean square displacement matrix; Calculate inelastic scattering laws using phonon density of states, dispersion relations, and polarization vectors; Calculate the thermal neutron scattering cross section of incoherent elastic scattering according to the incoherent elastic scattering law; Calculate the thermal neutron scattering cross section of coherent elastic scattering according to the coherent elastic scattering law; Calculate the thermal neutron scattering cross section of inelastic scattering according to the inelastic scattering law; The step of calculating the thermal neutron scattering cross section of incoherent elastic scattering according to the incoherent elastic scattering law is specifically calculated as follows: Where, is the incoherent elastic scattering cross section; is the incident neutron energy; is the feature bound section; is the Debye-Waller coefficient; The step of calculating the thermal neutron scattering cross section of coherent elastic scattering according to the coherent elastic scattering law is specifically calculated as follows: Where, is the coherent elastic scattering cross section; are different Bragg boundary energy points; is the structure factor of the unit cell; The step of calculating the thermal neutron scattering cross section of inelastic scattering according to the inelastic scattering law is specifically calculated as follows: Where, is the inelastic scattering cross section; is the incident neutron energy; is the energy of the emitted neutron; is temperature; is the cosine of the scattering angle; is the Boltzmann constant; For energy transfer; For energy transfer; is the law of heat scattering.

2. The method for calculating the thermal neutron scattering cross section of a dispersion fuel according to claim 1, characterized in that: The steps of constructing a supercell of a dispersion fuel specifically include: Use the crystal structure visualization software VESTA to construct the diffuse fuel unit cell; Use the first-principles material simulation software package VASP to optimize the material structure of the constructed unit cell; The lattice dynamics calculation program PHONOPY was used to expand the supercell of the optimized unit cell.

3. The method for calculating the thermal neutron scattering cross section of a dispersion fuel according to claim 1, characterized in that: The step of calculating the Hellmann-Feynman force between atoms in the supercell specifically includes: using VASP software and a density functional perturbation theory method to calculate the Hellmann-Feynman force between atoms in the expanded supercell.

4. The method for calculating the thermal neutron scattering cross section of a dispersion fuel according to claim 1, wherein: The incoherent elastic scattering law is calculated using the phonon state density; Calculate the coherent elastic scattering law using the mean square displacement matrix; The steps for calculating the inelastic scattering law using the phonon density of states, dispersion relations, and polarization vectors include: For incoherent elastic scattering, the DWF is calculated using the phonon density of states and the result is expressed as [ , ] in the form of output in the database file MF7 / MT2; For coherent elastic scattering, the DWF is calculated using the mean square displacement matrix and the result is expressed as [ , ] in the form of output in the database file MF7 / MT2; For inelastic scattering, the thermal scattering law is calculated based on the phonon method using the phonon density of states, dispersion relations, and polarization vectors. , which is output in the database file MF7 / MT4.

5. The method for calculating the thermal neutron scattering cross section of a dispersion fuel according to claim 1, characterized in that: Also includes: Experimental measurement of the thermal neutron scattering cross section of diffuse fuels; The thermal neutron scattering cross section of the dispersed fuel measured experimentally is compared with the calculated thermal neutron scattering cross section of the dispersed fuel, and the input parameters of the thermal neutron scattering calculation are corrected according to the error between the two. Then, the thermal neutron scattering cross section library of diffuse fuel is retrieved based on the thermal neutron scattering calculation program TNS using the corrected input parameters.

6. The method for calculating the thermal neutron scattering cross section of a dispersion fuel according to claim 5, characterized in that: The step of experimentally measuring the thermal neutron scattering cross section of the dispersed fuel specifically includes: The neutron transmission law of diffuse fuel products is measured using the transmission method based on an accelerator neutron source. First, a neutron source is obtained from the accelerator as the incident neutron, and the neutron count is obtained by the TOF detector in the case of an empty target. Then, the fuel sample is used as the target, and the sample is heated to a specified temperature by a heating device. The neutron count is obtained by the TOF detector, and the total cross section is calculated. The absorption cross section is then subtracted from the total cross section to obtain the thermal neutron scattering cross section. The specific calculation formula is: Where, is the total cross section, is the scattering cross section, is the absorption cross section, is the number of target nuclei per unit area, is the number of neutrons incident on the target nucleus per unit area by the neutron source, is the number of neutrons projected after the target nucleus and neutrons react per unit area, This is the background count under full blocking.

7. A thermal neutron scattering cross section calculation system for diffuse fuel, characterized in that: include: Supercell building blocks for constructing supercells of dispersed fuels; Hellmann-Feynman force calculation module, used to calculate the Hellmann-Feynman force between atoms in the supercell; Input parameter calculation module, used to calculate the phonon state density, mean square displacement matrix, dispersion relation and polarization vector based on the Hellmann-Feynman force; Thermal neutron scattering law calculation module, used to calculate incoherent elastic scattering laws using phonon state density; Calculate the coherent elastic scattering law using the mean square displacement matrix; Calculate inelastic scattering laws using phonon density of states, dispersion relations, and polarization vectors; Thermal neutron scattering cross section calculation module, used to calculate the thermal neutron scattering cross section of incoherent elastic scattering according to the incoherent elastic scattering law; Calculate the thermal neutron scattering cross section of coherent elastic scattering according to the coherent elastic scattering law; Calculate the thermal neutron scattering cross section of inelastic scattering according to the inelastic scattering law; The step of calculating the thermal neutron scattering cross section of incoherent elastic scattering according to the incoherent elastic scattering law is specifically calculated as follows: Where, is the incoherent elastic scattering cross section; is the incident neutron energy; is the feature bound section; is the Debye-Waller coefficient; The step of calculating the thermal neutron scattering cross section of coherent elastic scattering according to the coherent elastic scattering law is specifically calculated as follows: Where, is the coherent elastic scattering cross section; are different Bragg boundary energy points; is the structure factor of the unit cell; The step of calculating the thermal neutron scattering cross section of inelastic scattering according to the inelastic scattering law is specifically calculated as follows: Where, is the inelastic scattering cross section; is the incident neutron energy; is the energy of the emitted neutron; is temperature; is the cosine of the scattering angle; is the Boltzmann constant; For energy transfer; For energy transfer; is the law of heat scattering.

8. A computer 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 steps of the method according to any one of claims 1 to 6 are implemented.

9. A computer-readable storage medium storing a computer program, characterized in that: When the computer program is executed by a processor, the steps of the method according to any one of claims 1 to 6 are implemented.

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