Method for determining sintering process parameters of substoichiometric uranium dioxide

Abstract

The embodiment of the present application relates to the technical field of reactor fuel, and particularly relates to a method for determining sintering process parameters of substoichiometric uranium dioxide, which mainly comprises the following steps: determining average grain sizes and porosities of a plurality of different substoichiometric uranium dioxide according to the plurality of different substoichiometric uranium dioxide, and determining average grain sizes and porosities of substoichiometric uranium dioxide corresponding to optimal thermal conductivity according to the optimal thermal conductivity; and determining the sintering process parameters of the substoichiometric uranium dioxide according to the determined average grain sizes and porosities. The method accurately reflects the influence of the substoichiometric dose on the sintering process of the uranium dioxide, and can accurately determine the substoichiometric ratio corresponding to the optimal thermal conductivity and the corresponding sintering process parameters.

Description

Technical Field

[0001] The embodiments of this application relate to the technical field of reactor fuels, and more specifically to a method for determining substoichiometric uranium dioxide sintering process parameters. Background Technology

[0002] The statements herein are provided merely as background information in connection with this application and do not necessarily constitute prior art.

[0003] Uranium dioxide (UCO) is a uranium oxide widely used as ceramic fuel in various reactors due to its high melting point, excellent high-temperature stability, radiation stability, and good compatibility with cladding materials. Compared to conventional UCO, substoichiometric UCO has a lower oxygen content, enabling it to effectively reduce the core temperature of fuel pellets under high burnup conditions and improve fuel specific power in nuclear reactors. Furthermore, by adjusting the ratio of oxygen to uranium atoms in substoichiometric UCO, its melting point, thermal conductivity, and evaporation efficiency can be precisely controlled. Therefore, it is necessary to determine the impact of different substoichiometric ratios on the sintering process of UCO to optimize the performance of fuel pellets in nuclear reactors and ensure their safety and stability under high-temperature conditions. Summary of the Invention

[0004] A brief overview of this application is provided below to offer a basic understanding of certain aspects thereof. It should be understood that this overview is not an exhaustive summary of the application. It is not intended to identify key or essential parts of the application, nor is it intended to limit its scope. Its purpose is merely to present certain concepts in a simplified form as a prelude to the more detailed description that follows.

[0005] Embodiments of this application provide a method for determining the sintering process parameters of substoichiometric uranium dioxide, wherein the substoichiometric uranium dioxide is obtained by sintering a mixture comprising solid-phase uranium dioxide particles and liquid-phase uranium particles. It includes the following steps: S10: Determine the mass ratio of solid-phase uranium dioxide particles, the mass ratio of liquid-phase uranium particles, and the sizes of solid-phase uranium dioxide particles and liquid-phase uranium particles used in the sintering process; S20: Based on step S10, determine the mass ratio of solid-phase uranium dioxide particles, the mass ratio of liquid-phase uranium particles, and the sizes of solid-phase uranium dioxide particles and liquid-phase uranium particles to obtain multiple different substoichiometric ratios of uranium dioxide; S30: Based on the multiple different substoichiometric ratios of uranium dioxide from step S20, determine the average grain size and porosity of multiple different substoichiometric ratios of uranium dioxide; S40: Determine the relationship between the average grain size and porosity and the thermal conductivity of the substoichiometric ratio of uranium dioxide; S50: Based on the relationship determined in S40, determine the range of average grain size and porosity of the substoichiometric ratio of uranium dioxide corresponding to higher thermal conductivity; S60: Based on the range of average grain size and porosity determined in step S50, determine the sintering process parameters for the substoichiometric ratio of uranium dioxide.

[0006] In the embodiments of this application, by changing the mass ratio and particle size of solid-phase uranium dioxide particles to liquid-phase uranium particles, the influence of liquid-phase uranium on the preparation process of substoichiometric uranium dioxide can be introduced, overcoming the problem of neglecting the coexistence and interaction between liquid-phase uranium and solid-phase uranium dioxide in related technologies. Simultaneously, by determining the relationship between average grain size and porosity and the thermal conductivity of substoichiometric uranium dioxide, the substoichiometric ratio with high thermal conductivity, largest grain size, and lowest porosity, and its corresponding sintering process parameters, is determined. Therefore, the substoichiometric uranium dioxide prepared according to the determined sintering process parameters possesses stability and high efficiency during the operation of a nuclear reactor. Attached Figure Description

[0007] Other objects and advantages of this application will become apparent from the following description of embodiments of this application with reference to the accompanying drawings, and will help to provide a comprehensive understanding of this application.

[0008] Figure 1 This is a flowchart of determining the substoichiometric uranium dioxide sintering process parameters according to one embodiment of this application.

[0009] It should be noted that the accompanying drawings are not necessarily drawn to scale, but are shown only in a schematic manner without affecting the reader's understanding. Detailed Implementation

[0010] Exemplary embodiments of this application will be described below with reference to the accompanying drawings. For clarity and brevity, not all features of actual implementations are described in the specification. However, it should be understood that many implementation-specific decisions must be made in the development of any such actual embodiment to achieve the developer's specific goals, such as complying with constraints related to the system and business, and these constraints may vary depending on the implementation. Furthermore, it should be understood that while development work can be very complex and time-consuming, such development work is merely a routine task for those skilled in the art who benefit from the content of this application.

[0011] It should also be noted that, in order to avoid obscuring this application with unnecessary details, only the equipment structure and / or processing steps closely related to the solution according to this application are shown in the accompanying drawings, while other details that are not closely related to this application are omitted.

[0012] The inventors of this application have discovered that during the sintering of substoichiometric uranium dioxide, the high-temperature atmosphere required for sintering keeps the uranium added during the sintering process in a liquid state, thus resulting in the sintering of liquid-phase uranium. However, existing uranium dioxide sintering phase-field models cannot simulate the sintering process of substoichiometric uranium dioxide by introducing liquid-phase uranium, and therefore cannot accurately reflect the sintering process of substoichiometric uranium dioxide.

[0013] Based on this, embodiments of this application provide a method for determining the sintering process parameters of substoichiometric uranium dioxide, wherein the substoichiometric uranium dioxide is obtained by sintering a mixture comprising solid-phase uranium dioxide particles and liquid-phase uranium particles. Figure 1 This is a flowchart illustrating the determination of substoichiometric uranium dioxide sintering process parameters according to one embodiment of this application. Figure 1 As shown, it includes the following steps: S10: Determine the mass ratio of solid-phase uranium dioxide particles, the mass ratio of liquid-phase uranium particles, and the sizes of solid-phase uranium dioxide particles and liquid-phase uranium particles used in the sintering process; S20: Based on step S10, determine the mass ratio of solid-phase uranium dioxide particles, the mass ratio of liquid-phase uranium particles, and the sizes of solid-phase uranium dioxide particles and liquid-phase uranium particles to obtain multiple different substoichiometric ratios of uranium dioxide; S30: Based on the multiple different substoichiometric ratios of uranium dioxide from step S20, determine the average grain size and porosity of multiple different substoichiometric ratios of uranium dioxide; S40: Determine the relationship between the average grain size and porosity and the thermal conductivity of the substoichiometric ratio of uranium dioxide; S50: Based on the relationship determined in S40, determine the range of average grain size and porosity of the substoichiometric ratio of uranium dioxide corresponding to higher thermal conductivity; S60: Based on the range of average grain size and porosity determined in step S50, determine the sintering process parameters for the substoichiometric ratio of uranium dioxide.

[0014] In the embodiments of this application, by changing the mass ratio and particle size of solid-phase uranium dioxide particles to liquid-phase uranium particles, the influence of liquid-phase uranium on the preparation process of substoichiometric uranium dioxide can be introduced, overcoming the problem of neglecting the coexistence and interaction between liquid-phase uranium and solid-phase uranium dioxide in related technologies. Simultaneously, by determining the relationship between average grain size and porosity and the thermal conductivity of substoichiometric uranium dioxide, the substoichiometric ratio with high thermal conductivity, largest grain size, and lowest porosity, and its corresponding sintering process parameters, is determined. Therefore, the substoichiometric uranium dioxide prepared according to the determined sintering process parameters possesses stability and high efficiency during the operation of a nuclear reactor.

[0015] In some embodiments, in step S20, the oxygen content in the substoichiometric uranium dioxide is determined based on the mass ratio of the liquid uranium particles, and then the corresponding substoichiometric ratio is determined based on the oxygen content. Here, the mass ratio of the liquid uranium particles refers to the ratio of the mass of the liquid uranium particles to the mass of all components.

[0016] In some embodiments, the relationship between the mass ratio of liquid uranium particles and the oxygen content in substoichiometric uranium dioxide conforms to the following expression:

[0017]

[0018] Where x represents x, P l This indicates the mass ratio of liquid uranium particles. and M U These are the relative molecular mass of uranium dioxide and the relative atomic mass of uranium, respectively.

[0019] In the embodiments of this application, based on the principle of mass conservation, the relationship between the mass ratio of liquid uranium particles, the relative molecular mass of uranium dioxide, the relative atomic mass of uranium, and the oxygen content in uranium dioxide with a substoichiometric ratio is determined by expression (1). Since the relative molecular mass of uranium dioxide and the relative atomic mass of uranium are both known constants, the oxygen content in uranium dioxide with a substoichiometric ratio corresponding to different liquid uranium particle mass ratios can be accurately determined through the above expression (1), thereby establishing the relationship between the mass ratio of liquid uranium particles and the substoichiometric ratio.

[0020] In some embodiments, in step S30, the average grain size and porosity of multiple different substoichiometric ratios of uranium dioxide conform to the following expression:

[0021]

[0022]

[0023] Among them, R ave P represents the average grain size of substoichiometric uranium dioxide; pore φ represents the porosity of substoichiometric uranium dioxide, n represents the number of solid-phase sintered particles, i represents the i-th grain in substoichiometric uranium dioxide, and ηi(j,k) represents the solid-phase grain order parameter of the solid-phase uranium dioxide grain; g (j, k) represents the gas phase order parameter, j and k represent the coordinates of the i-th grain, j≤Nx, k≤Ny; Nx and Ny represent the number of rows and columns of the grid after discretization of the liquid-phase uranium particles obtained by sintering; where η i (j, k) and φ g (j, k) is determined by the substoichiometric ratio of uranium dioxide.

[0024] Among them, the gas phase order parameter is used to describe the gas phase and distinguish the gas phase from other phases. When it is in the gas phase, φg = 1.0, and when it is in other phases, φg = 0. The solid phase grain order parameter is used to describe and distinguish the grain structure of the solid phase.

[0025] In the embodiments of this application, by introducing solid-phase grain order parameters and gas-phase order parameters, the influence of the gas phase and solid phase on the average grain size and porosity of substoichiometric uranium dioxide during sintering is effectively distinguished and considered. Since the solid-phase grain order parameters and gas-phase order parameters can be determined based on the substoichiometric uranium dioxide, by determining the relationship between the solid-phase grain order parameters and gas-phase order parameters and the average grain size and porosity, the relationship between the substoichiometry and the average grain size and porosity is indirectly determined. Therefore, the corresponding average grain size and porosity can be accurately determined according to different substoichiometric ratios.

[0026] In some embodiments, ηi(j, k) is determined as follows:

[0027]

[0028] Where t represents the time during the sintering process, ω grain κ represents the multiphase structure free energy density function of substoichiometric uranium dioxide. s L represents the interfacial coefficient of solid uranium dioxide. s ω represents the migration rate of solid-phase uranium dioxide during sintering. grain κ s and L s Determined by substoichiometric ratio of uranium dioxide.

[0029] In the embodiments of this application, the partial derivative of the solid-state grain order parameter with respect to sintering time is determined, thereby describing the rate of change of the solid-state grain order parameter with sintering time. Furthermore, based on the rate of change of the solid-state grain order parameter with sintering time, the cumulative change of the solid-state grain order parameter during the sintering process at any given time can be determined, and the dynamic evolution of the solid-state grain order parameter during the sintering process can be accurately reflected.

[0030] In some embodiments, ω grain Determined in the following manner:

[0031]

[0032] A s A l A g Represents the free energies of solid-phase uranium dioxide, liquid-phase uranium, and gaseous phase during sintering, respectively; γ represents the grain boundary energy of solid-phase uranium dioxide during sintering; η represents the free energy of solid-phase uranium dioxide. i η w The solid-state grain order parameter φ represents the solid-state uranium dioxide grains. g φ l This represents the gas phase sequence parameter for the gas phase and the liquid phase sequence parameter for uranium in the liquid phase.

[0033] The multiphase structure free energy density function of uranium dioxide with substoichiometric ratio determined in the embodiments of this application involves the free energy of solid-phase uranium dioxide, liquid-phase uranium, gas phase, and grain boundary energy of solid-phase uranium dioxide. It takes into account the interaction of the three phases of solid-phase uranium dioxide, liquid-phase uranium, and gas phase, and solves the problem that liquid-phase uranium and solid-phase uranium dioxide cannot coexist in related technologies. At the same time, the multiphase structure free energy density function can effectively distinguish the free energy of liquid-phase uranium and solid-phase uranium dioxide, and thus can comprehensively and accurately reflect the distribution of uranium and oxygen elements in the three-phase sintering system of solid-phase uranium dioxide, liquid-phase uranium, and gas phase.

[0034] In some embodiments, κ s Determined in the following manner:

[0035]

[0036] Where, σ s Represents the surface energy and l of solid uranium dioxide s This indicates the width of the interface of solid-phase uranium dioxide.

[0037] In the embodiments of this application, the surface energy and interface width of solid-phase uranium dioxide determined by the substoichiometry are introduced. At the same time, the relationship between the surface energy, interface width, and interface coefficient of solid-phase uranium dioxide is determined, thereby indirectly determining the relationship between different substoichiometry and the interface coefficient of solid-phase uranium dioxide. Thus, the interface coefficient of solid-phase uranium dioxide can be accurately determined according to different substoichiometry.

[0038] In some embodiments, the surface energy σ of solid-phase uranium dioxide corresponding to different substoichiometric ratios can be obtained by performing low-scale simulation calculations on multiple uranium dioxides with different substoichiometric ratios. s The interfacial width L between solid uranium dioxide and solid phase s .

[0039] In some embodiments, the surface energy σ of solid uranium dioxide s The surface energy σ of solid-phase uranium dioxide with different substoichiometric ratios is determined by low-scale simulation calculations on multiple uranium dioxides with different substoichiometric ratios. s .

[0040] In some embodiments, the surface energy σ of solid uranium dioxide s The value is 0.6 J·m -2 The interfacial width L of solid-phase uranium dioxide s The value is 6nm.

[0041] In some embodiments, A s A l A g The following method is used to determine:

[0042]

[0043] n = s, l, g, σ n Represents the surface energy of solid-phase uranium dioxide, liquid-phase uranium, or gaseous uranium and l n This indicates the width of the interface between the solid phase uranium dioxide, the liquid phase uranium, or the gaseous phase.

[0044] In the embodiments of this application, by determining the general relationship between surface energy, interface width and free energy, it is possible to accurately determine the corresponding free energy of each phase based on its surface energy and interface width.

[0045] In some embodiments, the surface energies of solid uranium dioxide, liquid uranium, and gaseous uranium are each taken as 0.6 J·m. -2 0.3 J·m -2 0.002 J·m -2The interface widths of the solid phase uranium dioxide, liquid phase uranium, and gas phase are all the same and are 6 nm.

[0046] In some embodiments, φ g (j, k) is determined as follows:

[0047]

[0048] Where, ω s ω represents the giant potential density of solid-phase uranium dioxide, the value of which can be experimentally determined at the sintering temperature; t represents the time during the sintering process; ω represents the time during the sintering process. grain κ represents the multiphase structure free energy density function of substoichiometric uranium dioxide. g L represents the interfacial coefficient of the gas phase. g The value of h(x) represents the migration rate of the gas phase during sintering, and h(x) is an interpolation function of the independent variable x, where h(x) = x. 3 (6x 2 -15x+10), h′(x) represents the first derivative of the interpolation function h(x) with respect to x, where x=φ g .

[0049] In the embodiments of this application, the partial derivative of the gas phase sequence parameter with respect to sintering time is determined, thereby describing the rate of change of the gas phase sequence parameter with sintering time. Furthermore, based on the rate of change of the gas phase sequence parameter with sintering time, the cumulative change of the gas phase sequence parameter at any time during the sintering process can be determined, and the dynamic evolution of the gas phase sequence parameter during the sintering process can be accurately reflected.

[0050] In some embodiments, φ is determined as follows:

[0051]

[0052] In this example, represents the giant potential density of liquid uranium, the value of which can be found in a thermodynamic database at the sintering temperature; t represents the time during the sintering process; and ω... grain κ represents the multiphase structure free energy density function of substoichiometric uranium dioxide. l L represents the interfacial coefficient of liquid uranium. l h(x) represents the mobility of liquid uranium during sintering, and is an interpolation function of the independent variable x, where h(x) = x 3 (6x 2 -15x+10), h′(x) represents the first derivative of the interpolation function h(x) with respect to x, where x=φ l -φ g .

[0053] Among them, the liquid phase sequence parameter is used to describe the liquid phase and distinguish the liquid phase from other phases. When it is in the liquid phase, φ l=1.0, φ when located in other phases l =0.

[0054] In the embodiments of this application, the partial derivative of the liquid phase sequence parameter with respect to sintering time is determined, thereby describing the rate of change of the liquid phase sequence parameter with sintering time. Furthermore, based on the rate of change of the liquid phase sequence parameter with sintering time, the cumulative change of the liquid phase sequence parameter at any time during the sintering process can be determined, and the dynamic evolution of the liquid phase sequence parameter during the sintering process can be accurately reflected.

[0055] In some embodiments, step S30 further includes the following step: determining the relationship between solid uranium dioxide, liquid uranium, and gas during the sintering process, so as to determine the kinetic relationship between solid uranium dioxide, liquid uranium, and gas through the interaction of the three phases coexisting.

[0056] In some embodiments, the relationship between solid uranium dioxide, liquid uranium, and the gas phase conforms to the following expression:

[0057]

[0058] Where t represents the time during the sintering process, φ g φ represents the gas phase sequence parameter. l η represents the liquid phase sequence parameter. i V represents the solid-state grain order parameter of solid-state uranium dioxide grains. s and V l Let represent the atomic volumes of solid-phase uranium dioxide and liquid-phase uranium, respectively; c represents the concentration field variable of uranium content; μ represents the chemical potential field variable of uranium; and D represents the diffusion coefficient tensor.

[0059] In the embodiments of this application, the partial derivative of the chemical potential field variable with respect to sintering time is determined, thereby describing the rate of change of the chemical potential field variable with sintering time. Furthermore, based on the rate of change of the chemical potential field variable with sintering time, the cumulative change of the chemical potential field variable at any time during the sintering process can be determined, and the dynamic evolution of the chemical potential field variable during the sintering process can be accurately reflected.

[0060] In some embodiments, in order to take into account the coexistence and interaction of liquid, gas and solid phases during the sintering process of substoichiometric uranium dioxide, the diffusion coefficient tensor D includes: grain boundary diffusion, surface diffusion and bulk diffusion of liquid uranium and solid uranium dioxide.

[0061] The diffusion coefficient tensor D is determined as follows:

[0062]

[0063] Among them, T s It is the surface projection tensor. I is the unit tensor, n s The surface unit normal vector; For surface diffusion of solid-phase uranium dioxide, Surface diffusion of liquid-phase uranium; D gb The grain boundary diffusion coefficient of solid-phase uranium dioxide is given. n is the grain boundary projection tensor between grain i and grain j. gb D is the surface unit normal vector of the grain boundary; b The tensor form of the volume diffusion coefficient; These are the bulk diffusion coefficients of solid-phase uranium dioxide and liquid-phase uranium, respectively.

[0064] In some embodiments, surface diffusion of solid-phase uranium dioxide The value is 8.8258 × 10 -12 m 2 ·s -1 The bulk diffusion coefficient of solid uranium dioxide The value is 7.8998 × 10 -15 m 2 ·s -1 The grain boundary diffusion coefficient D of solid-phase uranium dioxide gb Values

[0065] In some embodiments, κ g Determined in the following manner:

[0066]

[0067] Where, σ g The surface energy of gaseous uranium dioxide, l g This indicates the width of the interface of gaseous uranium dioxide.

[0068] In the embodiments of this application, the surface energy and interface width of gaseous uranium dioxide determined by the substoichiometry are introduced. At the same time, the relationship between the surface energy, interface width and interface coefficient of gaseous uranium dioxide is determined, thereby indirectly determining the relationship between different substoichiometry and the interface coefficient of gaseous uranium dioxide, so as to accurately determine the interface coefficient of gaseous uranium dioxide according to different substoichiometry.

[0069] In some embodiments, the surface energy σ of gaseous uranium dioxide g The value is 0.02 J·m -2 The interfacial width l of uranium dioxide in the gas phase g The value is 6nm.

[0070] In some embodiments, κ l Determined in the following manner:

[0071]

[0072] Where, σ l Represents the surface energy of liquid uranium and l l This indicates the width of the interface of liquid uranium.

[0073] In the embodiments of this application, the surface energy and interface width of liquid uranium determined by the substoichiometry are introduced. At the same time, the relationship between the surface energy, interface width and interface coefficient of liquid uranium are determined, thereby indirectly determining the relationship between different substoichiometry and the interface coefficient of liquid uranium, so as to accurately determine the interface coefficient of liquid uranium corresponding to different substoichiometry.

[0074] In some embodiments, the surface energy σ of liquid uranium l The value is 0.3 J·m -2 The interface width of liquid uranium l l The value is 6nm.

[0075] In some embodiments, step S30 further includes the following steps: forming a solid-phase sintered particle grain matrix, a liquid-phase uranium particle matrix, a gas phase matrix, and a chemical potential field variable matrix; determining the morphological evolution result of uranium dioxide sintered structure based on the above matrices; and determining the porosity and grain size of uranium dioxide sintered structures with different substoichiometric ratios based on the morphological evolution result of uranium dioxide sintered structure.

[0076] Based on the size of the solid uranium dioxide particles determined in step S10, the characteristic value of the normal distribution of grain radius is determined, and a solid sintered particle radius distribution vector is formed. The length of the solid sintered particle radius distribution vector is n, where n represents the number of solid sintered particles, and n is not less than 10.

[0077] A solid-state sintered particle grain matrix is ​​formed based on the solid-state sintered particle radius distribution vector. Specifically, an Nx×Ny matrix is ​​formed for each grain. The position of the grain numbered i (i≤n) is taken as η. i =1, and other positions are assigned a value of 0. The size of the solid-state sintered grain matrix is ​​Nx×Ny×n.

[0078] A matrix of liquid uranium particles is formed based on the actual area of ​​the sintered liquid uranium particles. The matrix size of the liquid uranium particles is Nx×Ny, and φ is taken within the matrix. l =1.0, and assign 0 to other positions.

[0079] For φ l =0 and η n Assigning the value φ to the position of =0 g =1, forming a gas phase matrix with size Nx×Ny.

[0080] Based on the chemical potential field variable μ with respect to φ l =1 or η n The position of =1 is assigned a value to form a chemical potential field variable matrix of size Nx×Ny.

[0081] Based on the expressions (4) reflecting the dynamic evolution of the solid phase grain order parameter during sintering, (9) reflecting the dynamic evolution of the liquid phase order parameter during sintering, and (8) reflecting the dynamic evolution of the gas phase order parameter during sintering, the solid phase sintering particle grain matrix, liquid phase uranium particle matrix, and gas phase matrix are calculated iteratively.

[0082] The chemical potential field variable matrix was iteratively calculated based on the evolution equation of μ with sintering time.

[0083] Based on the iterative calculation results of the above matrix, the evolution of the sintered microstructure of uranium dioxide was determined.

[0084] In some embodiments, the area S of the liquid uranium particles l The following method is used to determine:

[0085]

[0086] Where S is the total surface area of ​​particles excluding the gas phase.

[0087] In some embodiments, the chemical potential field variable μ is determined as follows:

[0088]

[0089] Among them, V s and V l k represents the atomic volume of the solid or liquid phase, respectively. s and k l Let represent the energy per unit volume of solid-phase uranium dioxide and liquid-phase uranium, respectively, and let c represent the concentration field variable of the solid, liquid, or gas phase. This represents the equilibrium concentration in the solid or liquid phase. Specifically, the concentration field variable in the solid phase is equal to the equilibrium concentration in the solid phase. In the liquid phase, the concentration field variable is equal to the liquid phase equilibrium concentration. In the gas phase, the concentration field variable c equals 0.

[0090] In some embodiments, the efficiency of the above matrix iterative calculation can be further improved by setting the judgment interval of the finite difference equation. Specifically, when η in the i-th grain matrix i When (r,t) is greater than the preset threshold, the value of that position point is assigned to 1, P{(i,η i ):η i(r,t)>ε}=1. By setting a judgment interval for the finite difference equation, calculations are performed only on the grid points marked as 1 in the above matrix, thereby effectively reducing the computational cost of matrix iteration calculations.

[0091] In some embodiments, in step S40, a machine learning algorithm, such as the multilayer sensing algorithm commonly used by those skilled in the art, can be used to determine the sintered grain size and porosity range with higher equivalent thermal conductivity, and derive the corresponding thermal conductivity range, thereby determining the relationship between average grain size and porosity and thermal conductivity. Specifically, based on the average grain size and porosity determined in step S30, the corresponding equivalent thermal conductivity is determined; the mass ratio of solid uranium dioxide particles, the mass ratio of liquid uranium particles, and the sizes of solid uranium dioxide particles and liquid uranium particles determined in step S10 are used as input, and their corresponding thermal conductivity is used as output. The sintered grain size and porosity range with higher equivalent thermal conductivity is determined by a machine learning algorithm based on multilayer sensing, and the corresponding thermal conductivity range is derived, thereby determining the relationship between average grain size and porosity and thermal conductivity.

[0092] In some embodiments, in step S50, the range of average grain size and porosity corresponding to higher thermal conductivity can be determined based on the relationship between average grain size and porosity and thermal conductivity determined in step S40.

[0093] In some embodiments, step S60 further includes the following steps: S61: Determine the substoichiometry corresponding to the average grain size and porosity range determined in step S50; S62: Determine the corresponding sintering process parameters based on the substoichiometry; S63: Determine the corresponding thermal conductivity range based on the sintering process parameters determined in S62 and the relationship between the average grain size and porosity and thermal conductivity determined in S40, thereby determining the relationship between the sintering process parameters and thermal conductivity; S64: Determine the sintering process parameters with the highest equivalent thermal conductivity based on the relationship between the sintering process parameters and thermal conductivity, which are the sintering process parameters for uranium dioxide sintering with the substoichiometry.

[0094] The sintering process parameters include: the mass ratio of solid uranium dioxide particles, the mass ratio of liquid uranium particles, and the size of both solid and liquid uranium dioxide particles.

[0095] Regarding the embodiments of this application, it should also be noted that, without conflict, the embodiments of this application and the features in the embodiments can be combined with each other to obtain new embodiments.

[0096] The above description is merely a specific embodiment of this application, but the scope of protection of this application is not limited thereto. The scope of protection of this application shall be determined by the scope of the claims.

Claims

1. A method for determining substoichiometric uranium dioxide sintering process parameters, characterized in that, The substoichiometric uranium dioxide is prepared by sintering a mixture comprising solid-phase uranium dioxide particles and liquid-phase uranium particles, and includes the following steps: S10: Determine the mass ratio of the solid uranium dioxide particles, the mass ratio of the liquid uranium particles, and the size of the solid uranium dioxide particles and the liquid uranium particles used in the sintering process. S20: Determine the mass ratio of the solid uranium dioxide particles, the mass ratio of the liquid uranium particles, and the size of the solid uranium dioxide particles and the liquid uranium particles according to step S10 to obtain multiple different substoichiometric ratios of uranium dioxide. S30: Based on the multiple substoichiometric ratios of uranium dioxide from step S20, determine the average grain size and porosity of the multiple substoichiometric ratios of uranium dioxide; S40: Determine the relationship between the average grain size and porosity and the thermal conductivity of the substoichiometric uranium dioxide; S50: Based on the relationship determined in S40, determine the average grain size and porosity range of the substoichiometric uranium dioxide corresponding to the higher thermal conductivity; S60: Determine the substoichiometric uranium dioxide sintering process parameters based on the average grain size and porosity range determined in step S50.

2. The method according to claim 1, characterized in that, In step S20, the oxygen content in the substoichiometric uranium dioxide is determined based on the mass ratio of the liquid-phase uranium particles.

3. The method according to claim 2, characterized in that, in, The mass ratio of the liquid uranium particles and the oxygen content in the substoichiometric uranium dioxide conform to the following expression: Where x represents UO 2-x x, P l This indicates the mass ratio of the liquid uranium particles. and M U These are the relative molecular mass of uranium dioxide and the relative atomic mass of uranium, respectively.

4. The method according to claim 1, characterized in that, In step S30, the average grain size and porosity of multiple different substoichiometric ratios of uranium dioxide and the stoichiometric ratio of uranium dioxide conform to the following expression: Among them, R ave P represents the average grain size of the substoichiometric uranium dioxide; pore The porosity of the substoichiometric uranium dioxide is represented by η, where i represents the i-th grain in the substoichiometric uranium dioxide. i (j, k) represents the solid-state grain order parameter of solid-state uranium dioxide grains; φ g (j,k) represents the gas phase sequence parameter, j and k represent the coordinates of the i-th grain, j≤Nx, k≤Ny, Nx and Ny represent the number of rows and columns of the grid after discretization of the liquid phase uranium particles obtained by sintering; Where, η i (j, k) and φ g (j,k) is determined by the substoichiometric ratio of uranium dioxide.

5. The method according to claim 4, characterized in that, η i (j, k) is determined as follows: Where t represents the time during the sintering process, ω grain κ represents the multiphase structure free energy density function of the substoichiometric uranium dioxide. s L represents the interfacial coefficient of the solid-phase uranium dioxide. s ω represents the migration rate of solid-phase uranium dioxide during sintering. grain κ s and L s It is determined by the substoichiometric ratio of uranium dioxide.

6. The method according to claim 5, characterized in that, ω grain Determined in the following manner: A s A l A g η represents the free energy of the solid-phase uranium dioxide, the liquid-phase uranium, and the gaseous phase during sintering, respectively; γ represents the grain boundary energy of the solid-phase uranium dioxide during sintering; and η represents the free energy of the gaseous phase during sintering. i η w The solid-state grain order parameter φ represents the solid-state uranium dioxide grains. g φ l This represents the gas phase sequence parameter of the gas phase and the liquid phase sequence parameter of the liquid uranium.

7. The method according to claim 5, characterized in that, κ s Determined in the following manner: Where, σ s The surface energy and l of the solid uranium dioxide are represented. s This indicates the interface width of the solid-phase uranium dioxide.

8. The method according to claim 6, characterized in that, A s A l A g The following method is used to determine: n = s, l, g, representing the solid phase, liquid phase, and gas phase respectively, σ n The surface energy of the solid-phase uranium dioxide, liquid-phase uranium, or gaseous phase is represented by l. n This indicates the interface width of the solid-phase uranium dioxide, the liquid-phase uranium, or the gaseous phase.

9. The method according to claim 4, characterized in that, φ g (j,k) is determined in the following way: Where, ω s The large potential density of the solid-phase uranium dioxide is represented, and its value at the sintering temperature can be obtained experimentally. t represents the time during the sintering process, and ω... grain κ represents the multiphase structure free energy density function of the substoichiometric uranium dioxide. g L represents the interfacial coefficient of the gas phase. g The value of h(x) represents the migration rate of the gas phase during sintering, and h(x) is an interpolation function of the independent variable x, where h(x) = x. 3 (6x 2 -15x+10), h'(x) represents the first derivative of the interpolation function h(x) with respect to x, where x = φ g .

10. The method according to claim 6, characterized in that, φ l Determined in the following manner: Where, ω l The value of the liquid-phase uranium giant potential density at the sintering temperature can be found in a thermodynamic database, where t represents the time during the sintering process, and ω represents the time during the sintering process. grain κ represents the multiphase structure free energy density function of the substoichiometric uranium dioxide. l L represents the interfacial coefficient of the liquid uranium. l h(x) represents the mobility of liquid uranium during sintering, and is an interpolation function of the independent variable x, where h(x) = x 3 (6x 2 -15x+10), h'(x) represents the first derivative of the interpolation function h(x) with respect to x, where x = φ l -φ g .

11. The method according to claim 4, characterized in that, Step S30 also includes the following step: determining the relationship between the solid uranium dioxide, the liquid uranium, and the gas phase during the sintering process.

12. The method according to claim 11, characterized in that, The relationship between the solid-phase uranium dioxide, the liquid-phase uranium, and the gaseous phase conforms to the following expression: Where t represents the time during the sintering process, φ g φ represents the gas phase sequence parameter. l η represents the liquid phase sequence parameter. i V represents the solid-state grain order parameter of solid-state uranium dioxide grains. s and V l Let represent the atomic volumes of solid-phase uranium dioxide and liquid-phase uranium, respectively; c represents the concentration field variable of uranium content; μ represents the chemical potential field variable of uranium; and D represents the diffusion coefficient tensor.

13. The method according to claim 9, characterized in that, κ g Determined in the following manner: Where, σ g The surface energy of gaseous uranium dioxide, l g This indicates the interface width of the gaseous uranium dioxide.

14. The method according to claim 10, characterized in that, κ l Determined in the following manner: Where, σ l The surface energy of the liquid uranium and l l This indicates the width of the interface of the liquid uranium.

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