Method for determining metal fuel multi-phase structure irradiation microstructure evolution and performance change

Abstract

The invention discloses a method for determining metal fuel multi-phase structure irradiation microstructure evolution and performance change. Related physical property parameters are calculated through molecular dynamics and a first principle, and a diffusion coefficient is corrected by utilizing an irradiation acceleration theory to obtain a diffusion coefficient under a metal fuel irradiation condition; the method comprises the following steps: constructing a metal fuel polycrystalline multiphase organization structure evolution phase field model, defining phase field variables required in the model, and determining an evolution equation of the phase field variables; calculating to obtain a phase-field variable initial value, then solving the phase-field variable evolution equation, and obtaining a phase-field variable numerical solution; the phase field variable numerical solution is subjected to visualization processing, and a metal fuel polycrystalline multiphase structure distribution diagram is obtained; calculating the size and distribution of an irradiation structure in the metal fuel to obtain an evolution rule of the irradiation structure along with fuel consumption; and calculating the thermal conductivity, swelling and stress in the metal fuel by using the size and distribution of the irradiation structure in the metal fuel, and obtaining the change rule of the performance of the metal fuel along with fuel consumption.

Description

Technical Field

[0001] The invention relates to the technical field of metal fuels, and in particular to a method for determining the irradiation microstructural evolution and performance change of multiphase tissues of metal fuels. Background Art

[0002] In the field of metal fuel, irradiation microstructure evolution and changes in fuel performance after irradiation are important topics. Among them, fission gas release and fuel swelling are the primary technical challenges faced by metal fuel because they directly lead to cladding pressure and core-cladding contact (Fuel Cladding Mechanical Interaction, FCMI) and cause cladding damage. Due to the importance of fission gas release and fuel swelling in metal fuel performance, researchers have conducted a lot of research on them. There are many related reports in the literature, and people's understanding of them has continued to deepen and mature. However, existing studies have focused more on the mechanism of fission gas bubble growth and aggregation, but have ignored the correlation between other characteristics of metal fuel and fission gas behavior, such as the disconnection between the evolution of metal fuel phase distribution and the evolution of fission bubbles. The study of the irradiation microstructure evolution of complex multiphase metal fuels that couples the evolution of metal fuel phases and fission bubbles is to more deeply and comprehensively crack the evolution of irradiation microstructures of metal fuels and their correlation, and to provide a theoretical basis and technical support for improving the fuel consumption and safety of metal fuel operation. The coupled model of metal fuel phase distribution and fission bubble evolution is consistent with the actual physical process. The influence of metal fuel phase evolution on bubble evolution is real-time, achieving a strong interaction between the two, making the evolution of bubbles in metal fuel more accurate and reasonable. In addition, the evolution of metal fuel microstructure will affect the distribution of fuel thermal conductivity, thereby affecting the heat transfer performance of the fuel. Bubble evolution will cause swelling of the fuel, thereby affecting the mechanical properties of the fuel. Therefore, in-depth research on the evolution of irradiated microstructure of multiphase metal fuel and its influence on thermal conductivity and mechanical properties will help to better understand the behavior of metal fuel under irradiation conditions and provide more accurate reference and guidance for the design and development of fast reactor fuel. Summary of the invention

[0003] The purpose of the present invention is to provide a method for determining the irradiation microstructural evolution and performance changes of the multiphase organization of metal fuel, to determine the organization evolution of the metal fuel during irradiation and its influence on the fuel performance, and to determine the morphology and size distribution of each phase under different fuel consumption and its influence on thermal conductivity and mechanical properties. This method can realize the coupling effect of the metal fuel phase distribution and bubble evolution, and provide a prediction method for the irradiation organization evolution of the metal fuel and its influence on thermal conductivity and mechanical properties.

[0004] In order to achieve the above object, the present invention adopts the following technical solution:

[0005] The method for determining the irradiation microstructural evolution and property change of metal fuel multiphase structure comprises the following steps:

[0006] Step S1: using the first principles and molecular dynamics methods to calculate the physical properties of polycrystalline multiphase metal fuel under unirradiated conditions, including vacancy formation energy, migration energy and diffusion coefficient, gas atom formation energy, migration energy and diffusion coefficient, metal fuel component atomic diffusion coefficient and mutual diffusion coefficient, metal fuel grain boundary energy and interface energy, metal fuel grain boundary mobility and phase boundary mobility; using the radiation accelerated diffusion theory to correct the diffusion coefficient, and obtain the metal fuel related diffusion coefficient under irradiated conditions, including the vacancy diffusion coefficient, gas atomic diffusion coefficient and metal fuel component atomic diffusion coefficient;

[0007] Step S2: Establish a phase field model for the evolution of polycrystalline multiphase microstructure of metal fuel under irradiation conditions. First, define the phase field variables required in the phase field model, including the vacancy concentration c v , gas atomic concentration c g , the atomic concentration of metal fuel components c s , bubble order parameter η, grain order parameter φ with different orientations i , i=1,2,…p, p is the total number of grain orientations; then determine the above phase field variable evolution equations, where the vacancy concentration, gas atom concentration and metal fuel component atomic concentration evolution equations are Cahn-Hilliard equations, and the bubble order parameter and different orientation grain order parameter evolution equations are Allen-Cahn equations; construct a free energy expression of the phase field model of the polycrystalline multiphase microstructure evolution of metal fuel under irradiation conditions, the free energy expression is a function of all phase field variables, and the free energy expression is also related to temperature and external macroscopic stress;

[0008] Step S3: obtaining the initial values ​​of the phase field variables in the phase field model of the polycrystalline multiphase microstructure evolution of the metal fuel under irradiation conditions in step S2, wherein the initial value of the vacancy concentration is its thermodynamic equilibrium concentration, the initial value of the gas atom concentration is its thermodynamic equilibrium concentration, and the initial value of the bubble order parameter is 0; the grain order parameter is initialized as follows: first, the size of the simulation area is determined to be Nx×Ny, where Nx and Ny are both positive integers, the simulation area is randomly divided into a number of polygons, each polygon represents a grain, p grain orientation order parameters are randomly assigned to a number of grains, and only one specific grain orientation order parameter in each grain is 1, and the remaining grain orientation order parameters are 0; the initial value of the atomic concentration of the metal fuel component is the Zr atomic concentration in the metal fuel, and the distribution of the Zr atomic concentration is non-uniform. Based on the phase field method, the migration behavior of Zr atoms in the metal fuel under the combined action of chemical potential, temperature gradient and volume diffusion is calculated to obtain the distribution of Zr atomic concentration in the metal fuel at different positions, and the initial value of the atomic concentration of the metal fuel component is obtained;

[0009] Step S4: solving the phase field variable evolution equation in the phase field model of the polycrystalline multiphase microstructure evolution of the metal fuel under irradiation conditions in step S2. The phase field variable evolution equation is a differential equation. First, the differential equation is converted into a difference equation. The difference equation of the phase field variable evolution equation is solved by using a semi-implicit Fourier spectrum method to obtain a numerical solution of the phase field variable. The boundary condition of the difference equation is a periodic zero flux boundary. The initial value of the phase field variable in the difference equation is obtained in step S3.

[0010] Step S5: Visualize the numerical solutions of the phase field variables obtained in step S4 to obtain the irradiated microstructure: first, save all the numerical solutions of the phase field variables as data in .vtk format, then import the data file in .vtk format into Paraview software, and output a two-dimensional image of size Nx×Ny. The color distribution information in the two-dimensional image reflects the size of the numerical solution of the phase field variables. Through visualization, the distribution information of vacancy concentration, gas atom concentration and metal fuel component atom concentration can be intuitively obtained, and the distribution information of the polycrystalline multiphase microstructure of the metal fuel under irradiation conditions can also be obtained, including grain distribution, bubble distribution and metal fuel matrix phase region distribution.

[0011] Step S6: Calculate the size and distribution of the irradiated structure inside the metal fuel at different burnup, including bubble size distribution and bubble porosity, metal fuel matrix phase volume ratio, average vacancy concentration, average gas atom concentration, and grain boundary fraction;

[0012] Step S7: Based on the irradiated tissue morphology obtained in step S5 and the size and distribution of the irradiated tissue inside the metal fuel at different burnups statistically obtained in step S6, the metal fuel performance at different burnups is calculated, including the thermal conductivity, swelling and stress inside the fuel, to obtain the variation pattern of the metal fuel performance with burnup.

[0013] Preferably, the specific process of correcting the diffusion coefficient using the radiation accelerated diffusion theory in step S1 is as follows:

[0014] According to the radiation accelerated diffusion theory, the vacancies generated during the irradiation process will accelerate the diffusion of substances. The accelerating effect of vacancies on the diffusion of substances is related to the vacancy concentration. The total vacancy concentration during the irradiation process is expressed as c v , the thermodynamic equilibrium concentration of the space-time without irradiation is for:

[0015]

[0016] Where: Vacancy formation energy, k B is the Boltzmann constant, T represents the temperature, and the relationship between the total vacancy concentration during irradiation and the thermodynamic equilibrium concentration of vacancies before irradiation is expressed as:

[0017]

[0018] Where: Γ is the ratio of the total vacancy concentration to the thermodynamic equilibrium concentration after irradiation. This ratio is used to correct the vacancy diffusion coefficient, gas atomic diffusion coefficient, and metal fuel component atomic diffusion coefficient to obtain the metal fuel related diffusion coefficient under irradiation conditions. The corrected vacancy diffusion coefficient is:

[0019]

[0020] Where: is the spatial diffusion coefficient without irradiation;

[0021] The corrected gas atomic diffusion coefficient is:

[0022]

[0023] Where: is the diffusion coefficient of gas atoms without irradiation;

[0024] The corrected atomic diffusion coefficient of the metal fuel component is:

[0025]

[0026] Where: is the atomic diffusion coefficient of the metal fuel component without irradiation.

[0027] Preferably, the evolution equation of the phase field variables defined in step S2 is specifically expressed as:

[0028] The vacancy concentration evolution equation is expressed as:

[0029]

[0030] Where: t represents time, M v represents the vacancy mobility, F represents the free energy expression of the phase field model of the polycrystalline multiphase structure evolution of metal fuel under irradiation conditions, and P v is the vacancy source term, S v represents the absorption term of vacancies by grain boundaries;

[0031] The gas atom concentration evolution equation is:

[0032]

[0033] Where: M g is the mobility of gas atoms, P g is the gas atom source term;

[0034] The atomic concentration evolution equation of metal fuel components is:

[0035]

[0036] Where: M s is the mobility of the atoms of the metal fuel component, which is related to the atoms of the metal fuel component under irradiation conditions

[0037] Bubble order parameter evolution equation:

[0038]

[0039] Where: L η is the bubble interface mobility;

[0040] The grain order parameter evolution equation is:

[0041]

[0042] Where: L φ is the grain boundary mobility, and p is the total number of grain orientations;

[0043] In the phase field model of the evolution of the polycrystalline and multiphase microstructure of metal fuel under irradiation conditions, the polycrystals come from two different matrix phases. The relationship between the grain orientation and the phase region is as follows:

[0044] Divide the p grain orientations into two categories. The first category of grain orientations includes the 1st to the rth grain orientations, where r < p. The grains belonging to the first category of grain orientations come from phase region 1, and the second category of grain orientations includes the (r + 1)th to the pth grain orientations. The grains belonging to the second category of grain orientations come from phase region 2;

[0045] The free energy expression of the phase field model of the evolution of the polycrystalline and multiphase microstructure of metal fuel under irradiation conditions constructed in step S2 is:

[0046] F = ∫ V {h(η)f m + j(η)f b + ωf poly + f chem + f grad + f elas}d 3 In formula (17), h(η) = (1 - η) 2 and j(η) = η 2 are interpolation functions, respectively describing the proportions of the matrix phase and the bubble phase; f m is the free energy density of the matrix phase, f b is the free energy density of the bubble phase, f poly is the free energy density of the polycrystalline and multiphase interaction, ω is the energy height of the free energy density of the polycrystalline and multiphase interaction, f chem is the chemical energy density, fgrad is the gradient energy density, f elas is the elastic energy density;

[0047] The free energy density of the matrix phase is:

[0048] f m =θ1f1+ θ2f2 (18) Where θ1 and θ2 are the proportion functions of phase region 1 and phase region 2 respectively, expressed as:

[0049]

[0050] f1 and f2 represent the free energy density of phase region 1 and phase region 2 respectively, and the specific expression is:

[0051]

[0052] Where: c v0,1 、c v0,2 are the equilibrium concentrations of vacancies in phase region 1 and phase region 2, respectively, and c g0,1 、c g0,2 represent the equilibrium concentrations of gas atoms in phase region 1 and phase region 2 respectively;

[0053] The free energy density of polycrystalline multiphase interaction is expressed as:

[0054]

[0055] Where: a gb is the grain boundary energy coefficient, a s It represents the interface energy coefficient. The last term on the right side of the equal sign is introduced to satisfy the condition that the minimum value of the polycrystalline multiphase interaction energy density is 0;

[0056] Considering the relationship between grains and phase regions, the third term on the right side of equation (23) is specifically expressed as:

[0057]

[0058] Where: represents the grain boundary energy coefficient between grains in phase region 1, represents the grain boundary energy coefficient between phase region 1 and phase region 2, represents the grain boundary energy coefficient between grains in phase region 2;

[0059] The fourth term on the right side of the equal sign in formula (23) is specifically expressed as:

[0060]

[0061] Where: and are the surface energy coefficients of the bubbles in phase region 1 and phase region 2, respectively;

[0062] The chemical energy density is expressed as:

[0063]

[0064] Where: c s0,1 and c s0,2 are the equilibrium concentrations of metal fuel component atoms in phase region 1 and phase region 2, respectively, and A is the energy height;

[0065] The gradient energy density is expressed as:

[0066]

[0067] Where: and denote the gradient energy coefficients of vacancies, gas atoms, and solute atoms, respectively, and κ η and κ φi represent the gradient energy coefficients of the bubble order parameter and the grain order parameter, respectively.

[0068] Preferably, the specific process of initializing the grain order parameter in step S3 is:

[0069] The size of the simulation area is Nx×Ny. The simulation area is evenly divided into Nx×Ny grids. The size of each grid is 1×1. The coordinates of the grid points are positive integers. The simulation area is randomly divided into 100 polygons. Each polygon corresponds to a grain with a specific orientation. The method is:

[0070] Randomly select 100 points, whose coordinates are represented as (x1, y1), (x2, y2), ..., (x 100 ,y 100 ), each point is randomly assigned a grain orientation, and then the distance from each point in the simulation area to the above 100 random points is calculated, and the random point corresponding to the minimum distance from each point in the simulation area to the above 100 random points is obtained. The grain orientation of each point in the simulation area is the same as the grain orientation of the random point closest to it. In this way, 100 polygons are obtained, and the grain orientation inside each polygon is the same. There is only one grain orientation in each polygon that takes the value of 1, and the values ​​of other grain orientations are all 0.

[0071] Preferably, in step S4, the phase field variable evolution equation is converted from a differential equation to a difference equation, and the specific process is as follows:

[0072] The differential equation for the vacancy concentration evolution equation is:

[0073]

[0074] Where: t represents time, M vrepresents the mobility of vacancies, F represents the free energy expression of the phase field model of the evolution of polycrystalline and multiphase microstructure of metal fuel under irradiation conditions, and P v is the vacancy source term, S v represents the absorption term of vacancies by grain boundaries;

[0075] Convert the differential equation of the vacancy concentration evolution equation into a difference equation:

[0076]

[0077] Where: is the vacancy concentration value at the n+1th moment, is the vacancy concentration value at the nth moment, n is the number of time steps, Δt is the time step length, represents the derivative of the free energy expression of the phase field model of the polycrystalline multiphase structure evolution of the metal fuel under irradiation conditions at the nth moment with respect to the vacancy concentration, is the vacancy source term at the nth moment, represents the absorption term of vacancies by grain boundaries at the nth moment;

[0078] The differential equation for the evolution of gas atom concentration is:

[0079]

[0080] Where: M g is the mobility of gas atoms, P g is the gas atom source term;

[0081] Convert the differential equation of the gas atom concentration evolution equation into a difference equation:

[0082]

[0083] Where: is the gas atom concentration value at the n+1th moment, is the gas atom concentration value at the nth moment, It represents the derivative of the free energy expression of the phase field model of the evolution of the polycrystalline multiphase structure of the metal fuel under irradiation conditions at the nth moment with respect to the gas atomic concentration, is the gas atom source term at the nth moment,

[0084] The differential equation for the evolution of the atomic concentration of metal fuel components is:

[0085]

[0086] Where: M s is the mobility of the metal fuel component atoms;

[0087] Convert the differential equation of the evolution equation of the atomic concentration of metal fuel components into a difference equation:

[0088]

[0089] Where: is the gas atom concentration value at the n+1th moment, is the gas atom concentration value at the nth moment, It represents the derivative of the free energy expression of the phase field model of the evolution of the polycrystalline and multiphase microstructure of the metal fuel under the irradiation condition at the nth moment with respect to the atomic concentration of the metal fuel component;

[0090] The differential equation of the bubble order parameter evolution equation is:

[0091]

[0092] Where: L η is the bubble interface mobility;

[0093] Convert the differential equation of the bubble order parameter evolution equation into a difference equation:

[0094]

[0095] Where: η n+1 is the bubble order parameter value at the n+1th moment, η n is the bubble order parameter value at the nth moment, It represents the derivative of the free energy expression of the phase field model of the evolution of the polycrystalline multiphase structure of the metal fuel under the irradiation condition at the nth moment with respect to the bubble order parameter;

[0096] The differential equation of the grain order parameter evolution equation is:

[0097]

[0098] Where: L φ is the grain boundary mobility;

[0099] Convert the differential equation of the grain order parameter evolution equation into a difference equation:

[0100]

[0101] Where: is the grain order parameter value at the n+1th moment, is the grain order parameter value at the nth moment, It represents the derivative of the free energy expression of the phase field model of the evolution of the polycrystalline multiphase structure of metal fuel under irradiation conditions at the nth moment with respect to the grain order parameter.

[0102] Preferably, the difference equation for solving the phase field variable evolution equation using the semi-implicit Fourier spectrum method in step S4 is specifically as follows:

[0103] The vacancy concentration in Fourier space at the n+1th moment is:

[0104]

[0105] Where: is the vacancy concentration value in Fourier space at the n+1th moment, is the vacancy concentration value in Fourier space at the nth moment, k is the Fourier space coordinate, represents the derivative of the free energy expression of the phase field model of the polycrystalline multiphase microstructure evolution of metal fuel under irradiation conditions in Fourier space at the nth moment with respect to the vacancy concentration, represents the vacancy concentration gradient energy coefficient, represents the vacancy source term in Fourier space at the nth moment, represents the absorption term of the grain boundary to the vacancy in Fourier space at the nth moment;

[0106] The gas atom concentration in Fourier space at the n+1th moment is:

[0107]

[0108] Where: is the gas atom concentration value in Fourier space at the n+1th moment, is the gas atom concentration value in Fourier space at the nth moment, It represents the derivative of the free energy expression of the phase field model of the polycrystalline multiphase structure evolution of metal fuel under irradiation conditions in Fourier space at the nth moment with respect to the gas atomic concentration, represents the gas atomic concentration gradient energy coefficient, represents the gas atom source term in Fourier space at the nth moment;

[0109] The atomic concentration of the metal fuel component in Fourier space at the n+1th moment is:

[0110]

[0111] Where: is the atomic concentration value of the metal fuel component in the Fourier space at the n+1th moment, is the atomic concentration value of the metal fuel component in Fourier space at the nth moment, It represents the derivative of the free energy expression of the phase field model of the polycrystalline multiphase structure evolution of metal fuel under irradiation conditions in Fourier space at the nth moment with respect to the atomic concentration of the metal fuel component, Represents the energy coefficient of the atomic concentration gradient of the metal fuel component;

[0112] The value of the bubble order parameter in Fourier space at the n+1th moment is:

[0113]

[0114] Where: is the value of the bubble order parameter in Fourier space at the n+1th moment, is the value of the bubble order parameter in Fourier space at the nth moment, k represents the derivative of the free energy expression of the phase field model of the evolution of the polycrystalline multiphase structure of the metal fuel under irradiation conditions in Fourier space at the nth moment with respect to the bubble order parameter, η represents the gradient energy coefficient of the bubble order parameter;

[0115] The value of the grain order parameter in Fourier space at the n+1th moment is:

[0116]

[0117] Where: is the grain order parameter value in Fourier space at the n+1th moment, is the grain order parameter value in Fourier space at the nth moment, k represents the derivative of the free energy expression of the phase field model of the evolution of the polycrystalline multiphase structure of the metal fuel under irradiation conditions in Fourier space at the nth moment with respect to the grain order parameter, φ represents the gradient energy coefficient of grain order parameter;

[0118] The inverse Fourier transform is performed on the phase field variable value in the Fourier space to obtain the value of the phase field variable in the actual space and obtain the numerical solution of the phase field variable.

[0119] Preferably, the process of calculating the size and distribution of the irradiated structure inside the metal fuel at different burnup in step S6 is as follows:

[0120] Calculation of bubble porosity:

[0121] The simulation area size is Nx×Ny, which contains Nx×Ny grid points. Set a variable n η , the bubble order parameter value at each grid point is cyclically counted. When η>0.8, the grid point is considered to be inside the bubble. η =1, otherwise, this grid point is outside the bubble, n η =0, therefore, the total number of grid points occupied by bubbles is:

[0122]

[0123] The expression of bubble porosity is:

[0124]

[0125] Grain boundary fraction calculation:

[0126] The grain boundary fraction is defined as follows: Set a variable nΦ , Φ is a function that distinguishes grain boundaries from grains, Assume that when Φ < 0.8, it is determined that this grid point is on the grain boundary n Φ = 1, conversely, this grid point is inside the grain n Φ = 0. Therefore, the total number of grid points occupied by grain boundaries is counted as:

[0127]

[0128] Then the grain boundary fraction expression is:

[0129]

[0130] The average vacancy concentration is:

[0131]

[0132] In the formula: c v (i,j) represents the vacancy concentration at coordinates (i,j);

[0133] The average concentration of gas atoms is:

[0134]

[0135] In the formula: c g (i,j) represents the gas atom concentration at coordinates (i,j);

[0136] In the phase field model of the evolution of the polycrystalline and multiphase microstructure of metal fuel under irradiation conditions, the polycrystals come from two different matrix phases. The relationship between the grain orientation and the phase region is as follows:

[0137] Divide the p grain orientations into two categories. The first category of grain orientations includes the 1st to the rth grain orientations, r < p. The grains belonging to the first category of grain orientations come from phase region 1. The second category of grain orientations includes the (r + 1)th to the pth grain orientations. The grains belonging to the second category of grain orientations come from phase region 2;

[0138] The volume fraction of phase region 1 is:

[0139]

[0140] The volume fraction of phase region 2 is:

[0141]

[0142] The process of counting the bubble size and number is as follows:

[0143] Set a new variable ra(Nx,Ny), with all initial values being 0. The entire simulation area is cycled sequentially from bottom to top and from left to right. For n η= 1, the horizontal coordinate is i, and the vertical coordinate is j. Each grid point is judged as follows:

[0144] If the left adjacent grid point ra(i-1,j)=0 and the lower adjacent grid point ra(i,j-1)=0, then ra(i,j)=k for this point, and k is accumulated by 1, and the initial value of k is 0. If only the left adjacent grid point ra(i-1,j)=0, then ra(i,j)=ra(i,j-1). If only the lower adjacent grid point ra(i,j-1)=0, then ra(i,j)=ra(i-1,j). If the left adjacent grid point ra(i-1,j)≠0 and the lower adjacent grid point ra(i,j-1)≠0, then ra(i,j)=ra(i,j-1). After one cycle, the variable ra at each grid point inside the bubble takes the same value, and this value is the number of the bubble. The total number of grid points with the variable ra=i is counted, i=1,2,3,…,nn is the number of bubbles, and the area of ​​the i-th bubble can be calculated. The bubble radius is calculated using the circular area formula.

[0145] Compared with the prior art, the present invention has the following advantages:

[0146] 1) Through the present invention, a strong coupling effect between the metal fuel phase distribution and the fission bubble can be achieved, the influence of various objective conditions on the phase distribution and bubble evolution is fully considered, and the model of the metal fuel fission bubble evolution is expanded;

[0147] 2) The physical parameters of metal fuels were modified through the radiation accelerated diffusion theory, making the phase field model of metal fuel polycrystalline multiphase structure evolution closer to the actual irradiation physical process;

[0148] 3) Based on the phase field method, the migration behavior of component atoms in metal fuels under the combined effects of chemical potential, temperature gradient and bulk diffusion was calculated, and the initial distribution of component atoms and phase regions that is more in line with physical reality was obtained;

[0149] 4) The semi-implicit Fourier method is used to solve the phase field evolution equation, which improves the calculation efficiency and accuracy;

[0150] 5) The phase field model of the evolution of polycrystalline and multiphase structure of metal fuel takes into account the interaction between bubbles and different phase regions, realizes the evolution of bubbles in different phase regions and at phase boundaries, and makes the evolution of bubbles in metal fuel more in line with actual physical phenomena;

[0151] 6) The present invention is implemented by self-programming through Fortran language, and data processing is performed with the help of software such as Matlab and Paraview, which has good expansibility and flexibility. BRIEF DESCRIPTION OF THE DRAWINGS

[0152] Figure 1The figure is a flow chart of the method of the present invention.

[0153] Figure 2 The distribution of Zr atoms, α phase, β phase and γ phase at the radial position of the fuel at 3.6% atomic burnup.

[0154] Figure 3 This is the morphology of the irradiated structure inside the fuel at 5% atomic burnup. The dense black particles are bubbles, and the regular polygons are two different matrix phase structures (γ1-γ2).

[0155] Figure 4 for Figure 3 The size and distribution of bubbles in two different phase regions, where (a) is the size and distribution of bubbles in the γ1 phase, and (b) is the size and distribution of bubbles in the γ2 phase.

[0156] Figure 5 is the change of fuel swelling with fuel consumption. DETAILED DESCRIPTION

[0157] The present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0158] The main ideas of the present invention are as follows:

[0159] like Figure 1 As shown in the figure, molecular dynamics and first principles are used to obtain the relevant physical property parameters of metal fuel under unirradiated conditions, and then the diffusion coefficient is corrected using the radiation accelerated diffusion theory to obtain the physical property parameters under irradiated conditions; a phase field model for the evolution of polycrystalline and multiphase microstructure of metal fuel under irradiated conditions is established. The phase field variables required in this phase field model include the vacancy concentration c v , gas atomic concentration c g , the atomic concentration of metal fuel components c s , bubble order parameter η, grain order parameter φ with different orientations i, i=1,2,…,p, p is the total number of grain orientations, and the evolution equation of the phase field variables is determined; the initial values ​​of the phase field variables are calculated, the initial values ​​of the vacancy concentration and the gas atom concentration are their thermodynamic equilibrium concentrations, the initial value of the bubble order parameter is 0, and the Zr atomic concentration distribution in the metal fuel is calculated using the phase field method. The Zr atomic concentration distribution is the initial value of the atomic concentration of the metal fuel component. The grain order parameter is initialized as follows: first determine the size of the simulation area to be Nx×Ny, Nx, Ny are both positive integers, randomly divide the simulation area into several polygons, each polygon represents a grain, and the p grain orientation order parameters are The quantity is randomly distributed to several grains, and only one specific grain orientation order parameter in each grain takes the value of 1, and the orientation order parameters of the other grains take the value of 0; the phase field variable evolution equation is solved by Fourier spectrum method to obtain the numerical solution of the phase field variables; the numerical solution of the phase field variables is visualized to obtain the morphology of the polycrystalline and multiphase structure of the metal fuel; the size and distribution of the irradiated structure inside the metal fuel are calculated to obtain the evolution law of the irradiated structure with fuel consumption; the thermal conductivity, swelling and stress of the metal fuel are calculated by using the size and distribution of the irradiated structure inside the metal fuel to obtain the change law of the metal fuel performance with fuel consumption.

[0160] In order to make the purpose, technical solution and advantages of the present invention clearer, the present invention is further described in detail below in conjunction with the accompanying drawings and examples. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not limited to the present invention.

[0161] like Figure 1 As shown, the method for determining the irradiation microstructure evolution and performance change of metal fuel multiphase structure of the present invention comprises the following steps:

[0162] Step S1: using the first principles and molecular dynamics methods to calculate the physical properties of polycrystalline multiphase metal fuel under unirradiated conditions, including vacancy formation energy, migration energy and diffusion coefficient, gas atom formation energy, migration energy and diffusion coefficient, metal fuel component atomic diffusion coefficient and mutual diffusion coefficient, metal fuel grain boundary energy and interface energy, metal fuel grain boundary mobility and phase boundary mobility; using the radiation accelerated diffusion theory to correct the diffusion coefficient, and obtain the metal fuel related diffusion coefficient under irradiated conditions, including the vacancy diffusion coefficient, gas atomic diffusion coefficient and metal fuel component atomic diffusion coefficient;

[0163] Step S2: Establish a phase field model for the evolution of polycrystalline multiphase microstructure of metal fuel under irradiation conditions. First, define the phase field variables required in the phase field model, including the vacancy concentration c v , gas atomic concentration c g , the atomic concentration of metal fuel components c s , bubble order parameter η, grain order parameter φ with different orientations i, i=1,2,…,p, p is the total number of grain orientations; then determine the above phase field variable evolution equations, where the vacancy concentration, gas atom concentration and metal fuel component atom concentration evolution equations are Cahn-Hilliard equations, and the bubble order parameter and different orientation grain order parameter evolution equations are Allen-Cahn equations; construct a free energy expression of the metal fuel polycrystalline multiphase microstructure evolution phase field model under irradiation conditions, the free energy expression is a function of all phase field variables, and the free energy expression is also related to temperature and external macroscopic stress;

[0164] Step S3: obtaining the initial values ​​of the phase field variables in the phase field model of the polycrystalline multiphase microstructure evolution of the metal fuel under irradiation conditions in step S2, wherein the initial value of the vacancy concentration is its thermodynamic equilibrium concentration, the initial value of the gas atom concentration is its thermodynamic equilibrium concentration, and the initial value of the bubble order parameter is 0; the grain order parameter is initialized as follows: first, the size of the simulation area is determined to be Nx×Ny, where Nx and Ny are both positive integers, the simulation area is randomly divided into a number of polygons, each polygon represents a grain, p grain orientation order parameters are randomly assigned to a number of grains, and only one specific grain orientation order parameter in each grain is 1, and the remaining grain orientation order parameters are 0; the initial value of the atomic concentration of the metal fuel component is the Zr atomic concentration in the metal fuel, and the distribution of the Zr atomic concentration is non-uniform. Based on the phase field method, the migration behavior of Zr atoms in the metal fuel under the combined action of chemical potential, temperature gradient and volume diffusion is calculated to obtain the distribution of Zr atomic concentration in the metal fuel at different positions, and the initial value of the atomic concentration of the metal fuel component is obtained;

[0165] Step S4: solving the phase field variable evolution equation in the phase field model of the polycrystalline multiphase microstructure evolution of the metal fuel under irradiation conditions in step S2. The phase field variable evolution equation is a differential equation. First, the differential equation is converted into a difference equation. The difference equation is solved using a semi-implicit Fourier spectrum method to calculate the numerical solution of the phase field variable. The boundary condition of the difference equation is a periodic zero flux boundary. The initial value of the phase field variable in the difference equation is obtained in step S3.

[0166] Step S5: Visualize the numerical solutions of the phase field variables obtained in step S4 to obtain the irradiated microstructure: first, save all the numerical solutions of the phase field variables as data in .vtk format, then import the data file in .vtk format into Paraview software, and output a two-dimensional image of size Nx×Ny. The color distribution information in the two-dimensional image reflects the size of the numerical solution of the phase field variables. Through visualization, the distribution information of vacancy concentration, gas atom concentration and metal fuel component atom concentration can be intuitively obtained, and the distribution information of the polycrystalline multiphase microstructure of the metal fuel under irradiation conditions can also be obtained, including grain distribution, bubble distribution and metal fuel matrix phase region distribution.

[0167] Step S6: Calculate the size and distribution of the irradiated structure inside the metal fuel at different burnup, including bubble size distribution and bubble porosity, metal fuel matrix phase volume ratio, average vacancy concentration, average gas atom concentration, and grain boundary fraction;

[0168] Step S7: Based on the irradiated tissue morphology obtained in step S5 and the size and distribution of the irradiated tissue inside the metal fuel at different burnups statistically obtained in step S6, the metal fuel performance at different burnups is calculated, including the thermal conductivity, swelling and stress inside the fuel, to obtain the variation pattern of the metal fuel performance with burnup.

[0169] The specific process of correcting the diffusion coefficient using the radiation accelerated diffusion theory in step S1 is as follows:

[0170] According to the radiation accelerated diffusion theory, the vacancies generated during the irradiation process will accelerate the diffusion of substances. The accelerating effect of vacancies on the diffusion of substances is related to the vacancy concentration. The total vacancy concentration during the irradiation process is expressed as c v , the thermodynamic equilibrium concentration of the space-time without irradiation is for:

[0171]

[0172] Where: Vacancy formation energy, k B is the Boltzmann constant, T represents the temperature, and the relationship between the total vacancy concentration during irradiation and the thermodynamic equilibrium concentration of vacancies before irradiation is expressed as:

[0173]

[0174] Where: Γ is the ratio of the total vacancy concentration to the thermodynamic equilibrium concentration after irradiation. This ratio is used to correct the vacancy diffusion coefficient, gas atomic diffusion coefficient, and metal fuel component atomic diffusion coefficient to obtain the metal fuel related diffusion coefficient under irradiation conditions. The corrected vacancy diffusion coefficient is:

[0175]

[0176] Where: is the spatial diffusion coefficient without irradiation;

[0177] The corrected gas atomic diffusion coefficient is:

[0178]

[0179] Where: is the diffusion coefficient of gas atoms without irradiation;

[0180] The corrected atomic diffusion coefficient of the metal fuel component is:

[0181]

[0182] Where: is the atomic diffusion coefficient of the metal fuel component without irradiation.

[0183] The evolution equation of the phase field variables defined in step S2 is specifically expressed as:

[0184] The vacancy concentration evolution equation is expressed as:

[0185]

[0186] Where: t represents time, M v represents the vacancy mobility, F represents the free energy expression of the phase field model of the polycrystalline multiphase structure evolution of metal fuel under irradiation conditions, and P v is the vacancy source term, S v represents the absorption term of vacancies by grain boundaries;

[0187] The relationship between the vacancy mobility and the vacancy diffusion coefficient under irradiation conditions is expressed as:

[0188]

[0189] Where: D v is the vacancy diffusion coefficient under irradiation conditions, V m is the reference molar molecular volume of the metal fuel, R is the ideal gas constant, and T represents the temperature;

[0190] New vacancies will be generated during the irradiation process, and the vacancy source term expression is:

[0191]

[0192] Where: η is the bubble order parameter, R1 and R2 are random numbers between 0 and 1, V G represents the maximum value of vacancies added due to cascade collisions, P casc represents the probability of cascade collisions occurring per unit volume per unit time. The expression of the vacancy source term shows that new vacancies can only appear in the matrix, and no vacancies are generated in the bubbles.

[0193] Grain boundaries have an absorption effect on vacancy atoms. The absorption term of grain boundaries on vacancies is expressed as:

[0194]

[0195] Where: represents the absorption factor, which indicates the absorption intensity of the grain boundary to the vacancy, Φ is a coefficient related to the crystal structure, is the thermodynamic equilibrium concentration of the space-time without irradiation;

[0196] The gas atom concentration evolution equation is:

[0197]

[0198] Where: M g is the mobility of gas atoms, P g is the gas atom source term;

[0199] The relationship between the mobility of gas atoms and the diffusion coefficient of gas atoms under irradiation conditions is expressed as:

[0200]

[0201] Where: D g is the diffusion coefficient of gas atoms under irradiation conditions;

[0202] The gas atom source term generated during the irradiation process is expressed as:

[0203] P g =(1-η) 2 ΛV m f r R3 (12) Where: Λ is a constant, f r is the fission rate, R3 is a random number between 0 and 2;

[0204] The atomic concentration evolution equation of metal fuel components is:

[0205]

[0206] Where: M s is the mobility of the metal fuel component atoms, and its relationship with the diffusion coefficient of the metal fuel component atoms under irradiation conditions is expressed as:

[0207]

[0208] Where: D s is the atomic diffusion coefficient of metal fuel components under irradiation conditions;

[0209] Bubble order parameter evolution equation:

[0210]

[0211] Where: L η is the bubble interface mobility;

[0212] The grain order parameter evolution equation is:

[0213]

[0214] Where: L φis the grain boundary mobility, and p is the total number of grain orientations;

[0215] In the phase field model of the evolution of the polycrystalline and multiphase microstructure of metallic fuel under irradiation conditions, the polycrystals come from two different matrix phases. The relationship between the grain orientation and the phase region is as follows:

[0216] Divide the p grain orientations into two categories. The first category of grain orientations includes the 1st to the rth grain orientations, where r < p. The grains belonging to the first category of grain orientations come from phase region 1, and the second category of grain orientations includes the (r + 1)th to the pth grain orientations. The grains belonging to the second category of grain orientations come from phase region 2;

[0217] The free energy expression of the phase field model of the evolution of the polycrystalline and multiphase microstructure of metallic fuel under irradiation conditions constructed in step S2 is:

[0218] F = ∫ V {h(η)f m + j(η)f b + ωf poly + f chem + f grad + f elas}d 3 In equation (17): h(η) = (1 - η) 2 and j(η) = η 2 are interpolation functions, respectively describing the proportions of the matrix phase and the bubble phase; f m is the free energy density of the matrix phase, f b is the free energy density of the bubble phase, f poly is the free energy density of the polycrystalline and multiphase interaction, ω is the energy height of the free energy density of the polycrystalline and multiphase interaction, f chem is the chemical energy density, f grad is the gradient energy density, f elas is the elastic energy density;

[0219] The free energy density of the matrix phase is:

[0220] f m = θ1f1 + θ2f2. In equation (18): θ1 and θ2 are the proportion functions of phase region 1 and phase region 2 respectively, and the expression forms are:

[0221]

[0222] f1 and f2 respectively represent the free energy densities of phase region 1 and phase region 2, and the specific expression forms are:

[0223]

[0224] In the formula: c v0,1 、c v0,2are the equilibrium concentrations of vacancies in phase region 1 and phase region 2, respectively, and c g0,1 、c g0,2 represent the equilibrium concentrations of gas atoms in phase region 1 and phase region 2 respectively;

[0225] The free energy density of the bubble phase is expressed as:

[0226]

[0227] Where: n Q is the quantum concentration, V a is the volume of gas atoms, b is the van der Waals constant, and the second term on the right side of the equal sign is to ensure that the bubble phase remains c v +c g =1.0 is a parabolic function of the vacancy and gas atom concentration, taking the factor k p =6.4×10 11 J / m 3 ;

[0228] The free energy density of polycrystalline multiphase interaction is expressed as:

[0229]

[0230] Where: a gb is the grain boundary energy coefficient, a s It represents the interface energy coefficient. The last term on the right side of the equal sign is introduced to satisfy the condition that the minimum value of the polycrystalline multiphase interaction energy density is 0;

[0231] Considering the relationship between grains and phase regions, the third term on the right side of equation (23) is specifically expressed as:

[0232]

[0233] Where: represents the grain boundary energy coefficient between grains in phase region 1, represents the grain boundary energy coefficient between phase region 1 and phase region 2, represents the grain boundary energy coefficient between grains in phase region 2;

[0234] The fourth term on the right side of the equal sign in formula (23) is specifically expressed as:

[0235]

[0236] Where: and are the surface energy coefficients of the bubbles in phase region 1 and phase region 2, respectively;

[0237] The chemical energy density is expressed as:

[0238]

[0239] Where: c s0,1 and c s0,2 are the equilibrium concentrations of metal fuel component atoms in phase region 1 and phase region 2, respectively, and A is the energy height;

[0240] The gradient energy density is expressed as:

[0241]

[0242] Where: and denote the gradient energy coefficients of vacancies, gas atoms, and solute atoms, respectively, and κ η and represent the gradient energy coefficients of bubble order parameter and grain order parameter respectively;

[0243] The elastic energy density is expressed as:

[0244]

[0245] Where: C ijkl is the elastic modulus in tensor form, ε ij is the strain; the strain has the following expression:

[0246]

[0247] Where: is uniform strain, δε ij is the non-uniform strain, is the intrinsic strain; the uniform strain is expressed as:

[0248]

[0249] Where: is the inverse of the elastic modulus tensor, is the applied stress;

[0250] The non-uniform strain is expressed as:

[0251]

[0252] Where: u i is the displacement component.

[0253] The initial value of the vacancy concentration in step S3 is its thermodynamic equilibrium concentration.

[0254]

[0255] Where: is the vacancy formation energy, k B is the Boltzmann constant, T represents the temperature;

[0256] The initial value of the gas atom concentration is its thermodynamic equilibrium concentration.

[0257]

[0258] Where: is the formation energy of gas atoms;

[0259] The specific process of initializing the grain order parameters is as follows:

[0260] The size of the simulation area is Nx×Ny. The simulation area is evenly divided into Nx×Ny grids. The size of each grid is 1×1. The coordinates of the grid points are positive integers. The simulation area is randomly divided into 100 polygons. Each polygon corresponds to a grain with a specific orientation. The method is:

[0261] Randomly select 100 points, whose coordinates are represented as (x1, y1), (x2, y2), ..., (x 100 ,y 100 ), each point is randomly assigned a grain orientation, and then the distance from each point in the simulation area to the above 100 random points is calculated, and the random point corresponding to the minimum distance from each point in the simulation area to the above 100 random points is obtained. The grain orientation of each point in the simulation area is the same as the grain orientation of the random point closest to it, so 100 polygons are obtained, and the grain orientation inside each polygon is the same. There is only one grain orientation in each polygon with a value of 1, and the other grain orientations are all 0;

[0262] In step S3, the initial value of the atomic concentration of the metal fuel component is the Zr atomic concentration in the metal fuel. The distribution of the Zr atomic concentration in the metal fuel is calculated using the phase field method. The specific process is as follows:

[0263] The main matrix phases of metal fuel are α phase, β phase and γ phase, among which the chemical mobility of components in α phase and β phase is:

[0264]

[0265] Where: c Zr represents the Zr atomic concentration in the metal fuel, and Q i represent the interdiffusion coefficient factor and activation energy of U atoms and Zr atoms in α phase and β phase, respectively;

[0266] The temperature mobility of the components in the α phase and the β phase is expressed as:

[0267]

[0268] Where: is the transport heat in the α phase and the β phase;

[0269] The chemical mobility of the components in the γ phase is expressed as:

[0270]

[0271] Where: β U and β Zr represent the diffusion coefficients of U atoms and Zr atoms in the γ phase, respectively;

[0272] The temperature mobility of the components in the γ phase is expressed as:

[0273]

[0274] Where: and is the transfer heat of U atoms and Zr atoms in the γ phase;

[0275] According to Fick's second law, the time evolution equation of Zr atoms in metal fuel is:

[0276]

[0277] Where: c Zr represents the Zr atomic concentration, t represents the time, is the diffusion flux of Zr atoms under the action of chemical potential, F re is the Gibbs free energy per unit volume of the metal fuel, is the diffusion flux of Zr atoms under the action of temperature gradient, then the evolution equation of Zr atoms in metal fuel over time is:

[0278]

[0279] Where: M c represents the chemical mobility of Zr atoms, M c represents the temperature mobility of Zr atoms;

[0280] The Gibbs free energy per unit volume of metal fuel is expressed as:

[0281]

[0282] Where: V m is the reference molar molecular volume of the metal fuel, is the interpolation function of the γ phase ratio, η γ is the γ phase sequence parameter, f αβ and f γ denote the free energy density in the α-β phase and the free energy density in the γ phase, respectively. is the double potential well function, W is the barrier height, is the gradient energy coefficient of Zr atoms, κ γ is the gradient energy coefficient of the γ phase sequence parameter;

[0283] The free energy density in the α-β phase is expressed as:

[0284]

[0285] Where: and are the intrinsic free energies of U atoms and Zr atoms in the α-phase and β-phase, respectively;

[0286] The free energy density in the γ phase is expressed as:

[0287]

[0288] Where: and are the intrinsic free energies of U and Zr atoms in the γ phase, respectively;

[0289] The evolution equation controlling the γ phase sequence parameter is expressed as:

[0290]

[0291] Where: L γ is the interfacial mobility of the γ phase, expressed in Arrhenius form:

[0292]

[0293] Where: L0 is the pre-factor, Q γ is the activation energy of the interfacial migration of the γ phase;

[0294] The distribution of Zr atomic concentration in metal fuel is calculated by calculating the evolution equation of Zr atoms in metal fuel with time and the evolution equation of γ phase sequence parameter. The Zr atomic concentration in metal fuel is the initial value of the atomic concentration of metal fuel components in the phase field model of polycrystalline and multiphase microstructure evolution of metal fuel under irradiation conditions.

[0295] Figure 2 In order to calculate the Zr atomic concentration, α phase, β phase and γ phase distribution in radial position in the metal fuel at 3.6% atomic burnup using the phase field method, the Zr atomic concentration distribution is the initial value of the atomic concentration of the metal fuel component in the phase field model of the evolution of the polycrystalline multiphase structure of the metal fuel. Figure 2 It can be seen that the concentration of Zr atoms varies greatly at different positions in the metal fuel. Therefore, the initial value of the atomic concentration of the metal fuel component must correspond to the concentration of Zr atoms at the corresponding position. At the same time, it is necessary to use the phase field method to calculate the distribution of Zr atomic concentration in the metal fuel to ensure accurate input for the phase field model of the evolution of the polycrystalline and multiphase microstructure of the metal fuel.

[0296] In step S4, the phase field variable evolution equation is converted from a differential equation to a difference equation. The specific process is as follows:

[0297] The differential equation for the vacancy concentration evolution equation is:

[0298]

[0299] Where: t represents time, M v represents the mobility of vacancies, F represents the free energy expression of the phase field model of the evolution of polycrystalline and multiphase microstructure of metal fuel under irradiation conditions, and P v is the vacancy source term, S v represents the absorption term of vacancies by grain boundaries;

[0300] Convert the differential equation of the vacancy concentration evolution equation into a difference equation:

[0301]

[0302] Where: is the vacancy concentration value at the n+1th moment, is the vacancy concentration value at the nth moment, n is the number of time steps, Δt is the time step length, represents the derivative of the free energy expression of the phase field model of the polycrystalline multiphase structure evolution of the metal fuel under irradiation conditions at the nth moment with respect to the vacancy concentration, is the vacancy source term at the nth moment, represents the absorption term of vacancies by grain boundaries at the nth moment;

[0303] The differential equation for the evolution of gas atom concentration is:

[0304]

[0305] Where: M g is the mobility of gas atoms, P g is the gas atom source term;

[0306] Convert the differential equation of the gas atom concentration evolution equation into a difference equation:

[0307]

[0308] Where: is the gas atom concentration value at the n+1th moment, is the gas atom concentration value at the nth moment, It represents the derivative of the free energy expression of the phase field model of the evolution of the polycrystalline multiphase structure of the metal fuel under irradiation conditions at the nth moment with respect to the gas atomic concentration, is the gas atom source term at the nth moment,

[0309] The differential equation for the evolution of the atomic concentration of metal fuel components is:

[0310]

[0311] Where: M s is the mobility of the metal fuel component atoms;

[0312] Convert the differential equation of the evolution equation of the atomic concentration of metal fuel components into a difference equation:

[0313]

[0314] Where: is the gas atom concentration value at the n+1th moment, is the gas atom concentration value at the nth moment, It represents the derivative of the free energy expression of the phase field model of the evolution of the polycrystalline and multiphase microstructure of the metal fuel under the irradiation condition at the nth moment with respect to the atomic concentration of the metal fuel component;

[0315] The differential equation of the bubble order parameter evolution equation is:

[0316]

[0317] Where: L η is the bubble interface mobility;

[0318] Convert the differential equation of the bubble order parameter evolution equation into a difference equation:

[0319]

[0320] Where: η n+1 is the bubble order parameter value at the n+1th moment, η n is the bubble order parameter value at the nth moment, It represents the derivative of the free energy expression of the phase field model of the evolution of the polycrystalline multiphase structure of the metal fuel under the irradiation condition at the nth moment with respect to the bubble order parameter;

[0321] The differential equation of the grain order parameter evolution equation is:

[0322]

[0323] Where: L φ is the grain boundary mobility;

[0324] Convert the differential equation of the grain order parameter evolution equation into a difference equation:

[0325]

[0326] Where: is the grain order parameter value at the n+1th moment, is the grain order parameter value at the nth moment, It represents the derivative of the free energy expression of the phase field model of the evolution of the polycrystalline multiphase structure of the metal fuel under the irradiation condition at the nth moment with respect to the grain order parameter;

[0327] The difference equation of the phase field variable evolution equation is solved using the semi-implicit Fourier spectrum method. The vacancy concentration value in the Fourier space at the n+1th moment is:

[0328]

[0329] Where: is the vacancy concentration value in Fourier space at the n+1th moment, is the vacancy concentration value in Fourier space at the nth moment, k is the Fourier space coordinate, represents the derivative of the free energy expression of the phase field model of the polycrystalline multiphase microstructure evolution of metal fuel under irradiation conditions in Fourier space at the nth moment with respect to the vacancy concentration, represents the vacancy concentration gradient energy coefficient, represents the vacancy source term in Fourier space at the nth moment, represents the absorption term of the grain boundary to the vacancy in Fourier space at the nth moment;

[0330] The gas atom concentration in Fourier space at the n+1th moment is:

[0331]

[0332] Where: is the gas atom concentration value in Fourier space at the n+1th moment, is the gas atom concentration value in Fourier space at the nth moment, It represents the derivative of the free energy expression of the phase field model of the polycrystalline multiphase structure evolution of metal fuel under irradiation conditions in Fourier space at the nth moment with respect to the gas atomic concentration, represents the gas atomic concentration gradient energy coefficient, represents the gas atom source term in Fourier space at the nth moment;

[0333] The atomic concentration of the metal fuel component in Fourier space at the n+1th moment is:

[0334]

[0335] Where: is the atomic concentration value of the metal fuel component in the Fourier space at the n+1th moment, is the atomic concentration value of the metal fuel component in Fourier space at the nth moment, It represents the derivative of the free energy expression of the phase field model of the polycrystalline multiphase structure evolution of metal fuel under irradiation conditions in Fourier space at the nth moment with respect to the atomic concentration of the metal fuel component, Represents the energy coefficient of the atomic concentration gradient of the metal fuel component;

[0336] The value of the bubble order parameter in Fourier space at the n+1th moment is:

[0337]

[0338] Where: is the value of the bubble order parameter in Fourier space at the n+1th moment, is the value of the bubble order parameter in Fourier space at the nth moment, k represents the derivative of the free energy expression of the phase field model of the evolution of the polycrystalline multiphase structure of the metal fuel under irradiation conditions in Fourier space at the nth moment with respect to the bubble order parameter, η represents the gradient energy coefficient of the bubble order parameter;

[0339] The value of the grain order parameter in Fourier space at the n+1th moment is:

[0340]

[0341] Where: is the grain order parameter value in Fourier space at the n+1th moment, is the grain order parameter value in Fourier space at the nth moment, k represents the derivative of the free energy expression of the phase field model of the evolution of the polycrystalline multiphase structure of the metal fuel under irradiation conditions in Fourier space at the nth moment with respect to the grain order parameter, φ represents the gradient energy coefficient of grain order parameter;

[0342] The inverse Fourier transform is performed on the phase field variable value in the Fourier space to obtain the value of the phase field variable in the actual space and obtain the numerical solution of the phase field variable.

[0343] The process of calculating the size and distribution of the irradiated structure inside the metal fuel at different burnup in step S6 is as follows:

[0344] Calculation of bubble porosity:

[0345] The simulation area size is Nx×Ny, which contains Nx×Ny grid points. Set a variable n η , the bubble order parameter value at each grid point is cyclically counted. When η>0.8, the grid point is considered to be inside the bubble. η =1, otherwise, this grid point is outside the bubble, n η =0, therefore, the total number of grid points occupied by bubbles is:

[0346]

[0347] The expression for the bubble porosity is as follows:

[0348]

[0349] Calculation of the grain boundary fraction:

[0350] The definition of the grain boundary fraction is as follows: Set a variable n Φ , where Φ is a function that distinguishes grain boundaries and grains, Assume that when Φ < 0.8, it is determined that this grid point is on the grain boundary, n Φ = 1, otherwise, this grid point is inside the grain, n Φ = 0. Therefore, the total number of grid points occupied by grain boundaries is counted as:

[0351]

[0352] Then the expression for the grain boundary fraction is:

[0353]

[0354] The average concentration of vacancies is:

[0355]

[0356] In the formula: c v (i,j) represents the vacancy concentration at the coordinates (i,j);

[0357] The average concentration of gas atoms is:

[0358]

[0359] In the formula: c g (i,j) represents the gas atom concentration at the coordinates (i,j);

[0360] In the phase field model for the evolution of the polycrystalline and multiphase microstructure of metallic fuels under irradiation conditions, the polycrystals come from two different matrix phases. The relationship between the grain orientation and the phase region is as follows:

[0361] Divide the p grain orientations into two categories. The first category of grain orientations includes the 1st to the rth grain orientations, r < p. The grains belonging to the first category of grain orientations come from phase region 1. The second category of grain orientations includes the (r + 1)th to the pth grain orientations. The grains belonging to the second category of grain orientations come from phase region 2;

[0362] The volume fraction of phase region 1 is:

[0363]

[0364] The volume fraction of phase region 2 is:

[0365]

[0366] The bubble size and number statistics process is as follows:

[0367] Set a new variable ra(Nx, Ny) with all initial values ​​0. The entire simulation area is cycled from bottom to top and from left to right. η = 1, the horizontal coordinate is i, and the vertical coordinate is j. Each grid point is judged as follows:

[0368] If the left adjacent grid point ra(i-1,j)=0 and the lower adjacent grid point ra(i,j-1)=0, then ra(i,j)=k for this point, and k is accumulated by 1, and the initial value of k is 0. If only the left adjacent grid point ra(i-1,j)=0, then ra(i,j)=ra(i,j-1). If only the lower adjacent grid point ra(i,j-1)=0, then ra(i,j)=ra(i-1,j). If the left adjacent grid point ra(i-1,j)≠0 and the lower adjacent grid point ra(i,j-1)≠0, then ra(i,j)=ra(i,j-1). After one cycle, the variable ra at each grid point inside the bubble takes the same value, and this value is the number of the bubble. The total number of grid points with the variable ra=i is counted, i=1,2,3,…,nn is the number of bubbles, and the area of ​​the i-th bubble can be calculated. The bubble radius is calculated using the circular area formula.

[0369] The calculation process of thermal conductivity in step S7 is as follows:

[0370] First, the steady-state heat transfer equation of metal fuel is established, and the equation expression is:

[0371]

[0372] Where: T is temperature, κ m is the local thermal conductivity, which is related to the local microstructure and is specifically expressed as:

[0373] κ m =h(η)(κ0Φ+κ gb (1-Φ))+j(η)κ b (69) Where: h(η)=(1-η) 2 and j(η)=η 2 is an interpolation function, describing the proportion of matrix phase and bubble phase respectively, κ0 is the thermal conductivity of the perfect crystal inside the matrix, Φ is the function to distinguish grain boundaries and grains, When Φ>0.8, Φ=1 indicates grain boundary, and when Φ<0.8, Φ=0 indicates grain boundary, κ gb is the thermal conductivity at the grain boundary, κ bis the thermal conductivity at the bubble;

[0374] The specific expression of thermal conductivity of a perfect crystal inside the matrix is:

[0375] κ0=(0.0375+2.165 × 10 -4 T) -1 +4.715 × 10 9 T -2 exp(-1.41 / k B T) (70) Where: k B is the Boltzmann constant;

[0376] Considering the specific expression of the thermal conductivity of the bubble containing gas Xe and gas Kr, it is:

[0377] κ gas =0.1(8.247×10 -5 T 0.8363 )+0.9(4.351×10 -5 T 0.8616 ) (71)

[0378] The boundary conditions of the steady-state heat transfer equation for metal fuel are: a fixed temperature is set at the left boundary of the simulation area; a fixed heat flux j is set at the right boundary of the simulation area Q ; The effect of temperature on thermal conductivity is studied by changing the temperature of the left boundary; after obtaining the temperature distribution of the simulation area, the effective thermal conductivity of the simulation area is obtained by calculating the average temperature drop of the left and right boundaries. The specific expression is:

[0379]

[0380] Where: l x represents the length of the simulation area along the x direction; T l and T r Represent the average temperatures of the left and right boundaries, respectively.

[0381] The internal swelling of the fuel and the internal stress of the fuel in step S7 are specifically calculated as follows:

[0382] The swelling inside the metal fuel caused by fission bubbles is the bubble porosity:

[0383] S w =ρ η (73)

[0384] Where: η is the bubble porosity;

[0385] The internal stress of the fuel is obtained by solving the mechanical equilibrium equation. Assuming that the fuel is in a static equilibrium state in each time step, the mechanical field control equation is as follows:

[0386]

[0387] Where: σ is the Cauchy stress tensor; F v Unit volume force / N·kg -1 .

[0388] Based on the linear elastic model, the Cauchy stress tensor is calculated as follows:

[0389] σ=[C]·[ε] (75)

[0390] Where: [C] represents the material tensor; [ε] represents the strain tensor. In the linear elastic model, the strain tensor only considers the swelling strain of gas fission products, so:

[0391] ε=S w (76)

[0392] The Cauchy stress tensor inside the fuel is:

[0393] σ=[C]·[S w ] (77)

[0394] The internal stress of the fuel, i.e., the force per unit volume, is:

[0395]

[0396] In this embodiment, the calculated numerical solution is saved as a .vtk file, which gives the two-dimensional or three-dimensional coordinates of the simulation area, and each coordinate corresponds to a corresponding value; the obtained .vtk file is input into the Paraview software for visualization, which facilitates the observation of the morphology distribution and size of the specific organization during the irradiation of the metal fuel, as well as the concentration distribution of vacancies and gas atoms in different organizations; the distribution of bubbles and phase regions is shown in Figure 3 As shown in the figure, the dense circular particles are fission bubbles, and the regular polygons represent two different phase regions. Figure 3 It can be seen that the phase field model of the evolution of polycrystalline and multiphase microstructure of metal fuels can simulate bubbles in different phase regions and reflect the morphological characteristics of bubbles at the phase interface.

[0397] The bubble sizes in different phase regions (γ1-γ2) are counted. The statistical results are as follows: Figure 4As shown in (a) and (a), (a) represents the bubble size and distribution in the γ1 phase. From (a), it can be seen that the bubble size peak in the γ1 phase is between 12nm-24nm, and the bubbles have more counts, indicating that the γ1 phase has a larger porosity. (b) represents the bubble size and distribution in the γ2 phase. From (b), it can be seen that the bubble size peak in the γ2 phase is between 4nm-10nm, and the bubbles have fewer counts, indicating that the γ2 phase has a smaller porosity.

[0398] Figure 5 represents the change of swelling caused by pores in the simulation area with the combustion consumption, from Figure 5 It can be seen that the change of swelling caused by bubbles with fuel consumption can be divided into two stages. In the first stage, the fuel matrix hardly swells. This is because the gas atoms are diffused in the matrix and bubbles have not yet formed, so there is no swelling. In the second stage, the swelling begins to increase with fuel consumption because the gas atoms are saturated in the matrix and bubbles begin to form, causing the matrix to swell.

Claims

1. A method for determining the irradiation microstructural evolution and performance changes of a metal fuel multiphase structure, characterized in that: The following steps are involved: Step S1: using the first principles and molecular dynamics methods to calculate the physical properties of polycrystalline multiphase metal fuel under unirradiated conditions, including vacancy formation energy, migration energy and diffusion coefficient, gas atom formation energy, migration energy and diffusion coefficient, metal fuel component atomic diffusion coefficient and mutual diffusion coefficient, metal fuel grain boundary energy and interface energy, metal fuel grain boundary mobility and phase boundary mobility; using the radiation accelerated diffusion theory to correct the diffusion coefficient, and obtain the metal fuel related diffusion coefficient under irradiated conditions, including the vacancy diffusion coefficient, gas atomic diffusion coefficient and metal fuel component atomic diffusion coefficient; Step S2: Establish a phase field model for the evolution of polycrystalline multiphase microstructure of metal fuel under irradiation conditions. First, define the phase field variables required in the phase field model, including the vacancy concentration c v , gas atomic concentration c g , the atomic concentration of metal fuel components c s , bubble order parameter η, grain order parameter φ with different orientations i , i=1,2,…,p, p is the total number of grain orientations; then the above phase field variable evolution equation is determined, wherein the evolution equations of vacancy concentration, gas atom concentration and metal fuel component atom concentration are Cahn-Hilliard equations, and the evolution equations of bubble order parameters and grain order parameters with different orientations are Allen-Cahn equations; Construct a free energy expression for the phase field model of the evolution of polycrystalline and multiphase microstructure of metal fuel under irradiation conditions. This free energy expression is a function of all phase field variables and is also related to temperature and external macroscopic stress. Step S3: obtaining the initial values ​​of the phase field variables in the phase field model of the polycrystalline multiphase microstructure evolution of the metal fuel under irradiation conditions in step S2, wherein the initial value of the vacancy concentration is its thermodynamic equilibrium concentration, the initial value of the gas atom concentration is its thermodynamic equilibrium concentration, and the initial value of the bubble order parameter is 0; the grain order parameter is initialized as follows: first, the size of the simulation area is determined to be Nx×Ny, where Nx and Ny are both positive integers, the simulation area is randomly divided into a number of polygons, each polygon represents a grain, p grain orientation order parameters are randomly assigned to a number of grains, and only one specific grain orientation order parameter in each grain is 1, and the remaining grain orientation order parameters are 0; the initial value of the atomic concentration of the metal fuel component is the Zr atomic concentration in the metal fuel, and the distribution of the Zr atomic concentration is non-uniform. Based on the phase field method, the migration behavior of Zr atoms in the metal fuel under the combined action of chemical potential, temperature gradient and volume diffusion is calculated to obtain the distribution of Zr atomic concentration in the metal fuel at different positions, and the initial value of the atomic concentration of the metal fuel component is obtained; Step S4: solving the phase field variable evolution equation in the phase field model of the polycrystalline multiphase microstructure evolution of the metal fuel under irradiation conditions in step S2. The phase field variable evolution equation is a differential equation. First, the differential equation is converted into a difference equation. The difference equation of the phase field variable evolution equation is solved by using a semi-implicit Fourier spectrum method to obtain a numerical solution of the phase field variable. The boundary condition of the difference equation is a periodic zero flux boundary. The initial value of the phase field variable in the difference equation is obtained in step S3. Step S5: The irradiated tissue morphology obtained by visualizing the numerical solution of the phase field variables obtained in Step S4: First, save all the numerical solutions of the phase field variables as data in the.vtk format, and then import the.vtk format data file into the Paraview software to output a two-dimensional image with a size of Nx×Ny. The color distribution information in the two-dimensional image reflects the magnitude of the numerical solution of the phase field variables. Through visualization, the distribution information of the vacancy concentration, gas atom concentration, and metal fuel component atom concentration can be intuitively obtained. At the same time, the distribution information of the polycrystalline and multiphase microstructure of the metal fuel under irradiation conditions can also be obtained, including grain distribution, bubble distribution, and metal fuel matrix phase region distribution; Step S6: Calculate the size and distribution of the irradiated tissue inside the metal fuel at different burnups, including bubble size distribution, bubble porosity, metal fuel matrix phase volume ratio, average vacancy concentration, average gas atom concentration, and grain boundary fraction; Step S7: According to the irradiated tissue morphology obtained in Step S5 and the size and distribution of the irradiated tissue inside the metal fuel at different burnups statistically obtained in Step S6, calculate the performance of the metal fuel at different burnups, including thermal conductivity, swelling, and stress inside the fuel, and obtain the variation law of the metal fuel performance with burnup.

2. The method for determining the irradiation microstructural evolution and performance change of metal fuel multiphase structure according to claim 1, characterized in that: The specific process of correcting the diffusion coefficient using the irradiation-accelerated diffusion theory in Step S1 is as follows: According to the radiation accelerated diffusion theory, the vacancies generated during the irradiation process will accelerate the diffusion of substances. The accelerating effect of vacancies on the diffusion of substances is related to the vacancy concentration. The total vacancy concentration during the irradiation process is expressed as c v , the thermodynamic equilibrium concentration of the space-time without irradiation is for: Where: Vacancy formation energy, k B is the Boltzmann constant, T represents the temperature, and the relationship between the total vacancy concentration during irradiation and the thermodynamic equilibrium concentration of vacancies before irradiation is expressed as: In the formula: Γ is the ratio of the total vacancy concentration after irradiation to the thermodynamic equilibrium concentration. This ratio is used to correct the vacancy diffusion coefficient, gas atom diffusion coefficient, and metal fuel component atom diffusion coefficient to obtain the relevant diffusion coefficients of the metal fuel under irradiation conditions. The corrected vacancy diffusion coefficient is: Where: is the spatial diffusion coefficient without irradiation; The corrected gas atom diffusion coefficient is: Where: is the diffusion coefficient of gas atoms without irradiation; The corrected metal fuel component atom diffusion coefficient is: Where: is the atomic diffusion coefficient of the metal fuel component without irradiation.

3. The method for determining the irradiation microstructural evolution and performance change of metal fuel multiphase structure according to claim 1, characterized in that: The specific expression of the evolution equation of the phase field variables defined in Step S2 is: The evolution equation of the vacancy concentration is expressed as: Where: t represents time, M v represents the vacancy mobility, F represents the free energy expression of the phase field model of the polycrystalline multiphase structure evolution of metal fuel under irradiation conditions, and P v is the vacancy source term, S v represents the absorption term of vacancies by grain boundaries; The evolution equation of the gas atom concentration is: Where: M g is the mobility of gas atoms, P g is the gas atom source term; The evolution equation of the metal fuel component atom concentration is: Where: M s is the mobility of the metal fuel component atoms, which is related to the metal fuel component atoms under irradiation conditions. The evolution equation of the bubble order parameter: Where: L η is the bubble interface mobility; The evolution equation of the grain order parameter is: Where: L φ is the grain boundary mobility, p is the total number of grain orientations; In the phase field model of the evolution of the polycrystalline and multiphase microstructure of the metal fuel under irradiation conditions, the polycrystals come from two different matrix phases. The relationship between the grain orientation and the phase region is as follows: Divide the p grain orientations into two categories. The first category of grain orientations includes the 1st to the rth grain orientations, where r < p. The grains belonging to the first category of grain orientations come from phase region 1. The second category of grain orientations includes the (r + 1)th to the pth grain orientations. The grains belonging to the second category of grain orientations come from phase region 2; The free energy expression of the phase field model of the evolution of the polycrystalline and multiphase microstructure of the metal fuel under irradiation conditions constructed in Step S2 is: F = ∫ V {h(η)f m +j(η)f b +ωf poly +f chem +f grad +f elas }d 3 r (17) where: h(η) = (1-η) 2 and j(η)=η 2 is the interpolation function, which describes the proportion of matrix phase and bubble phase respectively; f m is the free energy density of the matrix phase, f b is the free energy density of the bubble phase, f poly is the free energy density of polycrystalline multiphase interaction, ω is the energy height of the free energy density of polycrystalline multiphase interaction, and f chem is the chemical energy density, f grad is the gradient energy density, f elas is the elastic energy density; The free energy density of the matrix phase is: f m =θ1f1+ θ2f2 (18) Where θ1 and θ2 are the proportion functions of phase region 1 and phase region 2 respectively, expressed as: f1 and f2 respectively represent the free energy densities of phase region 1 and phase region 2, and the specific expression forms are: Where: c v0,1 、c v0,2 are the equilibrium concentrations of vacancies in phase region 1 and phase region 2, respectively, and c g0,1 、c g0,2 represent the equilibrium concentrations of gas atoms in phase region 1 and phase region 2 respectively; The free energy density of the polycrystalline and multiphase interaction is expressed as: Where: a gb is the grain boundary energy coefficient, a s It represents the interface energy coefficient. The last term on the right side of the equal sign is introduced to satisfy the condition that the minimum value of the polycrystalline multiphase interaction energy density is 0; Considering the relationship between the grains and the phase region, the third term on the right side of Equation (23) is specifically expressed as: Where: represents the grain boundary energy coefficient between grains in phase region 1, represents the grain boundary energy coefficient between phase region 1 and phase region 2, represents the grain boundary energy coefficient between grains in phase region 2; The fourth term on the right side of Equation (23) is specifically expressed as: Where: and are the surface energy coefficients of the bubbles in phase region 1 and phase region 2, respectively; The chemical energy density is expressed as: Where: c s0,1 and c s0,2 are the equilibrium concentrations of metal fuel component atoms in phase region 1 and phase region 2, respectively, and A is the energy height; The gradient energy density is expressed as: Where: and denote the gradient energy coefficients of vacancies, gas atoms, and solute atoms, respectively, and κ η and represent the gradient energy coefficients of the bubble order parameter and the grain order parameter, respectively.

4. The method for determining the irradiation microstructural evolution and performance change of metal fuel multiphase structure according to claim 1, characterized in that: In Step S3 The specific process of initializing the grain order parameter is: The size of the simulation region is Nx×Ny. The simulation region is evenly divided into Nx×Ny grids, and the size of each grid is 1×1. The coordinates of the grid points are positive integers. The simulation region is randomly divided into 100 polygons, and each polygon corresponds to a grain with a specific orientation. The method is as follows: Randomly select 100 points, whose coordinates are represented as (x1, y1), (x2, y2), ..., (x 100 ,y 100 ), each point is randomly assigned a grain orientation, and then the distance from each point in the simulation area to the above 100 random points is calculated, and the random point corresponding to the minimum distance from each point in the simulation area to the above 100 random points is obtained. The grain orientation of each point in the simulation area is the same as the grain orientation of the random point closest to it. In this way, 100 polygons are obtained, and the grain orientation inside each polygon is the same. There is only one grain orientation in each polygon that takes the value of 1, and the values ​​of other grain orientations are all 0.

5. The method for determining the irradiation microstructural evolution and performance change of metal fuel multiphase structure according to claim 1, characterized in that: In step S4, the phase field variable evolution equation is transformed from a differential equation into a difference equation. The specific process is as follows: The differential equation of the vacancy concentration evolution equation is: Where: t represents time, M v represents the mobility of vacancies, F represents the free energy expression of the phase field model of the polycrystalline multiphase structure evolution of metal fuel under irradiation conditions, and P v is the vacancy source term, S v represents the absorption term of vacancies by grain boundaries; Transform the differential equation of the vacancy concentration evolution equation into a difference equation: Where: is the vacancy concentration value at the n+1th moment, is the vacancy concentration value at the nth moment, n is the number of time steps, Δt is the time step length, represents the derivative of the free energy expression of the phase field model of the evolution of the polycrystalline multiphase microstructure of the metal fuel under irradiation conditions at the nth moment with respect to the vacancy concentration, P v n is the vacancy source term at the nth moment, represents the absorption term of vacancies by grain boundaries at the nth moment; The differential equation of the gas atom concentration evolution equation is: Where: M g is the mobility of gas atoms, P g is the gas atom source term; Transform the differential equation of the gas atom concentration evolution equation into a difference equation: Where: is the gas atom concentration value at the n+1th moment, is the gas atom concentration value at the nth moment, It represents the derivative of the free energy expression of the phase field model of the evolution of the polycrystalline multiphase structure of the metal fuel under irradiation conditions at the nth moment with respect to the gas atomic concentration, is the gas atom source term at the nth moment, The differential equation of the metal fuel component atom concentration evolution equation is: Where: M s is the mobility of the metal fuel component atoms; Transform the differential equation of the metal fuel component atom concentration evolution equation into a difference equation: Where: is the gas atom concentration value at the n+1th moment, is the gas atom concentration value at the nth moment, It represents the derivative of the free energy expression of the phase field model of the evolution of the polycrystalline and multiphase microstructure of the metal fuel under the irradiation condition at the nth moment with respect to the atomic concentration of the metal fuel component; The differential equation of the bubble order parameter evolution equation is: Where: L η is the bubble interface mobility; Transform the differential equation of the bubble order parameter evolution equation into a difference equation: Where: η n+1 is the bubble order parameter value at the n+1th moment, η n is the bubble order parameter value at the nth moment, It represents the derivative of the free energy expression of the phase field model of the evolution of the polycrystalline multiphase structure of the metal fuel under the irradiation condition at the nth moment with respect to the bubble order parameter; The differential equation of the grain order parameter evolution equation is: Where: L φ is the grain boundary mobility; Transform the differential equation of the grain order parameter evolution equation into a difference equation: Where: φ i n+1 is the grain order parameter value at the n+1th moment, φ i n is the grain order parameter value at the nth moment, It represents the derivative of the free energy expression of the phase field model of the evolution of the polycrystalline multiphase structure of metal fuel under irradiation conditions at the nth moment with respect to the grain order parameter.

6. The method for determining the irradiation microstructural evolution and performance change of metal fuel multiphase structure according to claim 1, characterized in that: In step S4, the difference equation of the phase field variable evolution equation is solved by the semi-implicit Fourier spectral method as follows: The value of the vacancy concentration in the Fourier space at the (n + 1)-th moment is: Where: is the vacancy concentration value in Fourier space at the n+1th moment, is the vacancy concentration value in Fourier space at the nth moment, k is the Fourier space coordinate, represents the derivative of the free energy expression of the phase field model of the polycrystalline multiphase microstructure evolution of metal fuel under irradiation conditions in Fourier space at the nth moment with respect to the vacancy concentration, represents the vacancy concentration gradient energy coefficient, represents the vacancy source term in Fourier space at the nth moment, represents the absorption term of the grain boundary to the vacancy in Fourier space at the nth moment; The value of the gas atom concentration in the Fourier space at the (n + 1)-th moment is: Where: is the gas atom concentration value in Fourier space at the n+1th moment, is the gas atom concentration value in Fourier space at the nth moment, It represents the derivative of the free energy expression of the phase field model of the polycrystalline multiphase structure evolution of metal fuel under irradiation conditions in Fourier space at the nth moment with respect to the gas atomic concentration, represents the gas atomic concentration gradient energy coefficient, represents the gas atom source term in Fourier space at the nth moment; The value of the metal fuel component atom concentration in the Fourier space at the (n + 1)-th moment is: Where: is the atomic concentration value of the metal fuel component in the Fourier space at the n+1th moment, is the atomic concentration value of the metal fuel component in Fourier space at the nth moment, It represents the derivative of the free energy expression of the phase field model of the polycrystalline multiphase structure evolution of metal fuel under irradiation conditions in Fourier space at the nth moment with respect to the atomic concentration of the metal fuel component, Represents the energy coefficient of the atomic concentration gradient of the metal fuel component; The value of the bubble order parameter in the Fourier space at the (n + 1)-th moment is: Where: is the value of the bubble order parameter in Fourier space at the n+1th moment, is the value of the bubble order parameter in Fourier space at the nth moment, k represents the derivative of the free energy expression of the phase field model of the evolution of the polycrystalline multiphase structure of the metal fuel under irradiation conditions in Fourier space at the nth moment with respect to the bubble order parameter, η represents the gradient energy coefficient of the bubble order parameter; The value of the grain order parameter in the Fourier space at the (n + 1)-th moment is: Where: is the grain order parameter value in Fourier space at the n+1th moment, is the grain order parameter value in Fourier space at the nth moment, k represents the derivative of the free energy expression of the phase field model of the evolution of the polycrystalline multiphase structure of the metal fuel under irradiation conditions in Fourier space at the nth moment with respect to the grain order parameter, φ represents the gradient energy coefficient of grain order parameter; Inverse Fourier transform the values of the phase field variables in the Fourier space to obtain the values of the phase field variables in the real space, and obtain the numerical solution of the phase field variables.

7. The method for determining the irradiation microstructural evolution and performance change of metal fuel multiphase structure according to claim 1, characterized in that: In step S6, the process of calculating the size and distribution of the irradiated microstructure inside the metal fuel at different burnups is as follows: Calculation of the bubble porosity: The simulation area size is Nx×Ny, which contains a total of Nx×Ny grid points. Set a variable n η , the bubble order parameter value at each grid point is cyclically counted. When η>0.8, the grid point is considered to be inside the bubble. η =1, otherwise, this grid point is outside the bubble, n η =0, therefore, the total number of grid points occupied by bubbles is: Then the expression of the bubble porosity is: Calculation of the grain boundary fraction: The grain boundary fraction is defined as follows: Set a variable n Φ , Φ is the function that distinguishes grain boundaries from grains, Assume that when Φ < 0.8, it is determined that this grid point is on the grain boundary. Φ =1, otherwise, this grid point is inside the grain n Φ =0, therefore, the total number of grid points occupied by grain boundaries is: Then the expression of the grain boundary fraction is: The average vacancy concentration is: Where: c v (i,j) represents the vacancy concentration at coordinate (i,j); The average gas atom concentration is: Where: c g (i,j) represents the concentration of gas atoms at coordinate (i,j); In the phase field model of the evolution of the polycrystalline and multiphase microstructure of metal fuel under irradiation conditions, the polycrystals come from two different matrix phases. The relationship between the grain orientation and the phase region is as follows: Divide the p grain orientations into two categories. The first category of grain orientations includes the 1st to the r-th grain orientations, r < p. The grains belonging to the first category of grain orientations come from phase region 1. The second category of grain orientations includes the (r + 1)-th to the p-th grain orientations. The grains belonging to the second category of grain orientations come from phase region 2; The volume fraction of phase region 1 is: The volume fraction of phase region 2 is: The process of counting the bubble size and number is as follows: Set a new variable ra(Nx, Ny) with all initial values ​​0. The entire simulation area is cycled from bottom to top and from left to right. η = 1, the horizontal coordinate is i, and the vertical coordinate is j. Each grid point is judged as follows: If the left adjacent grid point ra(i-1,j)=0 and the lower adjacent grid point ra(i,j-1)=0, then ra(i,j)=k for this point, and k is accumulated by 1, and the initial value of k is 0. If only the left adjacent grid point ra(i-1,j)=0, then ra(i,j)=ra(i,j-1). If only the lower adjacent grid point ra(i,j-1)=0, then ra(i,j)=ra(i-1,j). If the left adjacent grid point ra(i-1,j)≠0 and the lower adjacent grid point ra(i,j-1)≠0, then ra(i,j)=ra(i,j-1). After one cycle, the variable ra at each grid point inside the bubble takes the same value, and this value is the number of the bubble. The total number of grid points with the variable ra=i is counted, i=1,2,3,…,nn is the number of bubbles, and the area of ​​the i-th bubble can be calculated. The bubble radius is calculated using the circular area formula.

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