A prediction method for the villus growth mechanism during the helium bubble swelling process

Abstract

The present invention discloses a method for predicting the villus growth mechanism during the swelling process of helium bubbles. The method includes: First, constructing a prediction model; Second, determining the influence of the depth of unbroken He bubbles on the surface of the W substrate; Third, determining the influence of the rupture of He bubbles on the change of the surface morphology of the W substrate. By studying the influence of the depth of He bubbles on the surface of the W substrate when the He bubbles are unbroken and the influence of the rupture of He bubbles on the change of the surface morphology of the W substrate, the present invention obtains the situation of villus growth on the surface of the W substrate. The influence of the reactions in two cases of helium diffusion + aggregation and bubble expansion + rupture on the villus growth situation is of great significance for comprehensively evaluating the engineering application of nuclear reactor materials.

Description

Technical Field

[0001] The present invention belongs to the technical field of nuclear fusion, and in particular relates to a method for predicting the villus growth mechanism during the helium bubble swelling process. Background Technique

[0002] Nuclear power generation has characteristics such as cleanness and high efficiency. Among them, the stability and safety of the nuclear power system depend on the performance of the nuclear materials in the reactor. For example, in a nuclear fusion device, the plasma has a strong effect on the material, which requires the material to be able to withstand a more severe erosion environment (high temperature, high-flux particle irradiation, time-varying stress, and strong neutron irradiation). The structural materials of the nuclear reactor need to have excellent mechanical properties such as high strength, large ductility, and high fracture strength. Therefore, the performance inspection of traditional nuclear reactor materials after being irradiated by high-flux particles and strong neutrons, as well as the development and exploration of new nuclear reactor materials, have always attracted great attention from materials researchers.

[0003] Metallic tungsten (W) has attracted much attention as the first wall material of a fusion reactor. Experimental studies have shown that under helium (He) irradiation, a nano-structured organization is formed on the tungsten surface, which will seriously change the retention of hydrogen isotopes in the material of the fusion reactor and the sputtering behavior of the facing wall material, thus affecting the normal reaction operation of the core plasma. It was found in the experiment that there are villi on the W surface, but the growth mechanism is not clear; and studying the evolution of He bubbles under the W surface and their influence on the surface morphology has become the key to understanding the deterioration of the surface performance of the plasma-facing material. Therefore, it is crucial to improve the internal mechanism of villus growth on the W material surface from a microscopic perspective. Summary of the Invention

[0004] The technical problem to be solved by the present invention is to provide a method for predicting the villus growth mechanism during the helium bubble swelling process in view of the deficiencies in the above-mentioned prior art. By studying the influence of the depth of He bubbles on the W substrate surface before rupture and the influence of the rupture of He bubbles on the change of the W substrate surface morphology, the situation of villus growth on the W substrate surface is obtained. The influence of the reactions in two cases, namely helium diffusion + aggregation and bubble expansion + rupture, on the villus growth situation is of great significance for comprehensively evaluating the engineering application of nuclear reactor materials.

[0005] To solve the above technical problem, the technical solution adopted by the present invention is: a method for predicting the villus growth mechanism during the helium bubble swelling process, characterized in that: the method includes the following steps:

[0006] Step 1, constructing a prediction model: select multiple vacuum areas, fill a W matrix in each vacuum area, and the distance between the top surface of the W matrix and the top surface of the vacuum area is 10a0~15a0; dig a spherical cavity in each W matrix and fill it with multiple He atoms, and the proportion of He atoms filled in each W matrix is different, and the He atoms gather to form He bubbles; wherein the size of the W matrix is 30a0×30a0×40a0, a0 is the crystal lattice constant, which represents the interval between two adjacent atoms; the depth between the top surface of the He bubble in the W matrix and the top surface of the W matrix is D;

[0007] Step 2: Determine the effect of the depth of the He bubble on the surface of the W substrate when it is not broken. The process is as follows:

[0008] Step 201, select the system as the canonical ensemble NVT, and the maximum distance of movement within the time step is 0.05A as the simulation parameters of the prediction model constructed in step 1 to perform simulation calculation;

[0009] Step 202, selecting a potential function acting in the atomic collision process;

[0010] Step 203: According to the formula P = -(σ 11 +σ 22 +σ 33 ) / 3, calculate the pressure P of each atom, and combine the potential function to obtain that in each W matrix with different He atomic ratios, when the He bubble is not broken, at a distance of D = 5a0, the He bubble appears droplet-shaped, and makes the surface of the W matrix uneven, producing a fuzzy structure; where σ ii (i∈x,y,z) is the atomic stress tensor, representing the normal stress in the x, y, and z directions; σ 11 is the normal stress in the x direction, σ 22 is the normal stress in the y direction, σ 33 is the normal stress in the z direction;

[0011] Step 3: Determine the effect of He bubble rupture on the surface morphology of the W substrate. The process is as follows:

[0012] Step 301, observing each W matrix in step 1, and obtaining that in the W matrix filled with He with a He / V ratio of 3.7, He bubbles become unstable and break after 1.35 ps;

[0013] Step 302: After the He bubble ruptures, a separation channel is formed between the center of the He bubble and the surface of the W substrate, and the separation channel cannot be restored after the W substrate structure is stabilized; after the W atoms are stabilized, they are randomly stacked at the connection between the separation channel and the surface of the W substrate to form an island structure;

[0014] In the process of irradiating the W substrate in step 303, new He atoms are continuously generated. The new He atoms merge and grow, and the newly formed He bubbles continuously accumulate in the island-like structure. After the He bubbles rupture, pits are formed, and W atoms accumulate at the edges of the pits, and the height of the pits is higher than the surface of the W substrate.

[0015] In the process of continuously irradiating the W substrate in step 304, repeat step 303 to obtain a villous structure formed on the surface of the W substrate when the He bubbles rupture.

[0016] The above method for predicting the villus growth mechanism during the helium bubble swelling process is characterized in that: in step one, the radius of the He bubble is 3a0 to 5a0; the He / V ratios of He filled in multiple W substrates are 3, 3.1,..., 5 respectively, and the difference in the proportion of He filled in adjacent two W substrates is 0.1.

[0017] The above method for predicting the villus growth mechanism during the helium bubble swelling process is characterized in that: in step 202, the potential function between W atoms is selected as the Ackland - Thetford (AT) potential function of the many - body Finnis - Sinclair type; the potential function between He atoms at short distances is selected as the Ziegler - Biersack - Littmark (ZBL) potential function.

[0018] The above method for predicting the villus growth mechanism during the helium bubble swelling process is characterized in that: in step 203, where p, m, and Ω are the momentum, mass, and Voronoi volume of the atom respectively, is the mutual force between atom α and atom β, is the distance between atom α and atom β.

[0019] The above method for predicting the villus growth mechanism during the helium bubble swelling process is characterized in that: in steps 303 and 304, the stacking position of the He bubbles is judged. Since the overall structure of the W substrate tends to the state of minimum energy, the He bubbles continuously accumulate in the surface convex structures of the W substrate. After the He bubbles rupture on the surface convex of the W substrate, new convexes will be formed, forming a villous structure.

[0020] The beneficial effect of the present invention is to obtain the villus growth situation on the surface of the W substrate by studying the influence of the depth of the He bubble on the surface of the W substrate before rupture and the influence of the He bubble rupture on the surface morphology change of the W substrate. The influence of the reactions in the two cases of helium diffusion + aggregation and bubble expansion + rupture on the villus growth situation is of great significance for comprehensively evaluating the engineering application of nuclear reactor materials.

[0021] The technical solution of the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. Description of the Drawings

[0022] Figure 1 It is a comparison diagram of the atomic volume and pressure distribution in He bubbles at different depths in the present invention.

[0023] Figure 2 It is a schematic diagram of the state of generating a villous structure in the present invention.

[0024] Figure 3 It is a schematic diagram of the model structure at different depths between the He bubble and the surface protrusion in the present invention.

[0025] Figure 4 It is a flowchart of the method of the present invention. Detailed Embodiments

[0026] As Figures 1 to 4 shown, a method for predicting the villus growth mechanism during the swelling process of helium bubbles, the method comprising the following steps:

[0027] Step 1: Construct a prediction model: Select a plurality of vacuum regions, and fill a W matrix in each vacuum region, and the distance between the top surface of the W matrix and the top surface of the vacuum region is 10a0 to 15a0; Dig out a spherical cavity in each W matrix and fill it with a plurality of He atoms, and the proportion of He atoms filled in each W matrix is different, and the He atoms aggregate to form He bubbles; wherein, the size of the W matrix is 30a0×30a0×40a0, a0 is the crystal lattice constant, which represents the interval between adjacent two atoms; the depth between the top surface of the uppermost He bubble in the W matrix and the top surface of the W matrix is D;

[0028] In Step 1, a0 is the crystal lattice constant, which represents the interval between adjacent two atoms, and a0 varies slightly with temperature; wherein, the is the unit of length.

[0029] Step 2: Determine the influence of the depth of the He bubble on the surface of the W matrix when the He bubble does not rupture, the process is as follows:

[0030] Step 201: Select the system as the canonical ensemble NVT, and the maximum distance of movement within the time step is used as the simulation parameter of the prediction model constructed in Step 1 for simulation calculation;

[0031] Step 202: Select the potential function acting in the atomic collision process;

[0032] Step 203: According to the formula P = -(σ 11 +σ 22 +σ33 ) / 3, calculate the pressure P of each atom, and combine the potential function to obtain that in each W matrix with different He atomic ratios, when the He bubble is not broken, at a distance of D = 5a0, the He bubble appears droplet-shaped, and makes the surface of the W matrix uneven, producing a fuzzy structure; where σ ii (i∈x,y,z) is the atomic stress tensor, representing the normal stress in the x, y, and z directions; σ 11 is the normal stress in the x direction, σ 22 is the normal stress in the y direction, σ 33 is the normal stress in the z direction;

[0033] Step 3: Determine the effect of He bubble rupture on the surface morphology of the W substrate. The process is as follows:

[0034] Step 301, observing each W matrix in step 1, and obtaining that in the W matrix filled with He with a He / V ratio of 3.7, He bubbles become unstable and break after 1.35 ps;

[0035] Step 302: After the He bubble ruptures, a separation channel is formed between the center of the He bubble and the surface of the W substrate, and the separation channel cannot be restored after the W substrate structure is stabilized; after the W atoms are stabilized, they are randomly stacked at the connection between the separation channel and the surface of the W substrate to form an island structure;

[0036] Step 303, during the irradiation of the W substrate, new He atoms are continuously generated, the new He atoms merge and grow, and the newly formed He bubbles are continuously accumulated on the island structure. After the He bubbles are broken, pits are formed, and W atoms are accumulated at the edges of the pits, and the height of the pits is higher than the surface of the W substrate;

[0037] Step 304: While the W substrate is continuously irradiated, step 303 is repeated, so that when the He bubble is broken, a fuzzy structure is formed on the surface of the W substrate.

[0038] In step 1, a spherical cavity is dug out in the W matrix to fill He atoms. This is because He atoms aggregate to form He bubbles, which are spherical structures. In order to accommodate the He bubbles, a spherical cavity needs to be dug out in the W matrix.

[0039] In step 201, a pure W substrate can be selected in the LAMMPS software for irradiation testing. In the displacement cascade occurrence part, when the system is the canonical ensemble NVT and the microcanonical ensemble NVE, the fix command in the LAMMPS software is combined to select different time steps and energies for analysis and comparison. The system of the prediction model is the canonical ensemble NVT, and the maximum distance of movement within the time step is

[0040] In actual use, it is divided into three parts along the direction perpendicular to the W matrix: the bottom 2 lattice layers are fixed to maintain the center of mass of the matrix; the middle 4 lattice layers are kept at a constant temperature by the Nosé–Hoover thermostat. First, a smaller parameter 0.0001a0 was selected for comparison and compared with the cases where the displacement cascade occurred using the canonical ensemble NVT (the middle part is the thermostat) and the microcanonical ensemble NVE (the middle part becomes NVE). In the LAMMPS software, when the PKA (primary knock-on atom) energies are 100 eV and 5000 eV respectively, the kinetic energy (corresponding to temperature) and potential energy of the top (except the middle and bottom) and the middle part of the system under the NVT ensemble are given. At different energies, the case with the time step parameter of 0.0001a0 is very similar to the case with the time step parameter of . When using the NVT ensemble, the total energy of the system is not conserved because there is an energy transfer process between the thermostat in the middle part and the upper part, and finally the temperatures of the two parts reach the same.

[0041] In step 203, as Figure 1 shown in the first layer, it represents the change in volume with the increase in depth D. The ones with color changes in the figure are He bubbles. As the depth D increases, the color of the He bubbles becomes darker. Corresponding to the leftmost vertical coordinate, as the depth D increases, the volume decreases; as Figure 1 shown in the second layer, it represents the change in pressure with the increase in depth D. The ones with color changes in the figure are He bubbles. As the depth D increases, the number of regions with darker colors in the He bubbles increases. Corresponding to the leftmost vertical coordinate, as the depth D increases, the pressure increases.

[0042] In step 301, based on step two, the W surface has been roughened, and the adsorbed atoms are orderly arranged above the original surface by one or two epitaxial layers. However, these alone are not enough as the dominant mechanism for the growth of "fluff". So next, it was studied that the rupture of helium bubbles would open a breakthrough for the growth mechanism of fluff.

[0043] In step 302, when D = 3a0, when the system reaches a stable structure after the He bubble ruptures, 289 adsorbed atoms gather on the surface, and 29 W atoms leave the surface and are sputtered out. When D = 4a0, except for 303 adsorbed atoms gathering on the surface, no W atoms leave the surface, that is, no sputtering phenomenon occurs.

[0044] By studying the influence of the depth of He bubbles on the W matrix surface before the He bubbles rupture and the influence of the rupture of He bubbles on the change of the W matrix surface morphology, the present invention obtains the growth situation of fluff on the W matrix surface. By studying the influence of the reaction on the growth situation of fluff in the two cases of helium diffusion + aggregation and bubble expansion + rupture, it has important significance for comprehensively evaluating the engineering application of nuclear reactor materials.

[0045] It should be noted that according to Step 3, the formation process of the nanostructure can be inferred as follows: After the rupture of the previous He bubble, the subsequent bubbles will diffuse into the new protrusions caused by the rupture (high temperature will accelerate this thermal activity process). The He bubbles continuously grow through the coalescence of bubbles or the addition of helium by irradiation, and when the critical pressure is reached or they are subjected to impact, they will rupture again. The rupture behavior will further raise the protrusions. This process is continuously repeated, causing the protrusions to evolve into fibers and leave the original surface, forming a villous structure.

[0046] Therefore, the generation of the villi involves both non-equilibrium thermodynamics processes and kinetic processes: The non-equilibrium thermodynamics process plays an important role in the diffusion of He, promoting the aggregation and migration of He to the surface. Once the pressure exceeds the critical value or is subjected to impact, the helium bubbles will rupture, further increasing the branched protrusions. The increase in temperature can enhance surface diffusion and strengthen these branches.

[0047] The villous structure on the W surface can be attributed to two processes of He bubble evolution: helium diffusion + aggregation, and bubble expansion + rupture. The presence of high temperature accelerates the diffusion and aggregation of He under the protrusion surface. Once the helium bubbles rupture (either spontaneous rupture when the bubble pressure exceeds the critical value or rupture due to external irradiation), the protrusion part on the surface will further grow and become the precursor of the villous structure. The continuous aggregation and subsequent rupture of He atoms constitute the recursive process of the growth of the protrusion part. In Step 3, there are two cases of He bubble rupture. One is that the He bubble ruptures due to excessive internal pressure, and the other is that irradiation will also induce the rupture of He bubbles. The effects on the change of the W matrix surface morphology in both cases are the same.

[0048] In particular, the prediction method mentioned in the present invention can also be applied to Mo.

[0049] In this embodiment, in Step 1, the radius of the He bubble is 3a0 to 5a0; the He / V ratios of He filled in the multiple W matrices are 3, 3.1,..., 5 respectively, and the difference in the ratio of He filled in adjacent two W matrices is 0.1.

[0050] In this embodiment, in Step 202, the potential function between W atoms is the many-body Finnis-Sinclair type Ackland-Thetford (AT) potential function; the potential function between He atoms at short distances is the Ziegler-Biersack-Littmark (ZBL) potential function.

[0051] In this embodiment, in Step 203, where p, m, and Ω are the momentum, mass, and Voronoi volume of the atom respectively, is the interaction force between atom α and atom β, is the distance between atom α and atom β.

[0052] In this embodiment, in steps 303 and 304, the stacking positions of He bubbles are judged. Since the W matrix structure as a whole tends to the state of minimum energy, He bubbles continuously accumulate in the surface convex structures of the W matrix. After the He bubbles rupture on the surface convex of the W matrix, new convexes will be formed, forming a villous structure.

[0053] In actual use, the LAMMPS software is used to select three models with different depths between He bubbles and surface convexes for comparison. As Figure 3 shown, the convex ones are W atoms, and the circular structures are He atoms. The system energy in a is 28 eV and 23 eV smaller than that in the cases shown in b and c respectively. Since the W matrix structure as a whole tends to the state of minimum energy, it indicates that the He bubbles are indeed pushed into the surface convexes.

[0054] The above are only the preferred embodiments of the present invention, and do not impose any limitations on the present invention. Any simple modifications, changes, and equivalent structural changes made to the above embodiments according to the technical essence of the present invention still fall within the protection scope of the technical solution of the present invention.

Claims

1. A method for predicting the villus growth mechanism during the helium bubble swelling process, characterized in that, The method includes the following steps: Step 1, construct a prediction model: Select multiple vacuum regions, fill a W matrix in each vacuum region, and the distance between the top surface of the W matrix and the top surface of the vacuum region is 10a0 to 15a0; dig out a spherical cavity in each W matrix and fill it with multiple He atoms, and the proportion of He atoms filled in each W matrix is different. After the He atoms aggregate, He bubbles are formed; wherein, the size of the W matrix is 30a0×30a0×40a0, and a0 is the crystal lattice constant, which represents the interval between two adjacent atoms; the depth between the top surface of the topmost He bubble in the W matrix and the top surface of the W matrix is D; Step 2, determine the influence of the depth of the unbroken He bubble on the surface of the W matrix, and the process is as follows: Step 201, select the system as the canonical ensemble NVT, and the maximum distance of movement within the time step is used as the simulation parameter of the prediction model constructed in Step 1 for simulation calculation, where is the length unit; Step 202, select the potential function acting in the atomic collision process; Step 203: According to the formula P = -(σ 11 +σ 22 +σ 33 ) / 3, calculate the pressure P of each atom, and combine the potential function to obtain that in each W matrix with different He atomic ratios, when the He bubble is not broken, at a distance of D = 5a0, the He bubble appears droplet-shaped, and makes the surface of the W matrix uneven, producing a fuzzy structure; where σ ii (i∈x,y,z) is the atomic stress tensor, representing the normal stress in the x, y, and z directions; σ 11 is the normal stress in the x direction, σ 22 is the normal stress in the y direction, σ 33 is the normal stress in the z direction; Step 3, determine the influence of the rupture of the He bubble on the change of the surface morphology of the W matrix, and the process is as follows: Step 301, observe each W matrix in Step 1, and it is obtained that in the W matrix with a He / V ratio of 3.7 of the filled He, the He bubble becomes unstable and ruptures after 1.35 ps; Step 302, after the He bubble ruptures, a detachment channel is formed between the center of the He bubble and the surface of the W matrix, and the detachment channel cannot be restored after the W matrix structure is stable; after the W atoms are stable, they are disorderly stacked at the connection between the detachment channel and the surface of the W matrix to form an island structure; Step 303, during the irradiation of the W matrix, new He atoms are continuously generated, the new He atoms merge and grow, and the newly formed He bubbles are continuously stacked in the island structure. After the He bubbles rupture, pits are formed, and the W atoms are stacked at the edge of the pits, and the height of the pits is higher than the surface of the W matrix; Step 304, during the continuous irradiation of the W matrix, repeat Step 303 to obtain that when the He bubble ruptures, a villous structure is formed on the surface of the W matrix.

2. The prediction method for the villus growth mechanism during the helium bubble swelling process according to claim 1, wherein: In Step 1, the radius of the He bubble is 3a0 to 5a0; the He / V ratios of the He filled in the multiple W matrices are 3, 3.1,..., 5 respectively, and the difference in the proportion of the He filled in two adjacent W matrices is 0.

1.

3. A method for predicting the villus growth mechanism during the helium bubble swelling process according to claim 1, characterized in that: In Step 202, the many-body Finnis-Sinclair type Ackland-Thetford (AT) potential function is selected for the potential function between W atoms; the Ziegler-Biersack-Littmark (ZBL) potential function is selected for the potential function between He atoms at short distances.

4. A method for predicting the villus growth mechanism during the helium bubble swelling process according to claim 1, characterized in that: In step 203, where p, m, and Ω are the momentum, mass, and Voronoi volume of the atom, respectively, is the interaction force between atom α and atom β, is the distance between atom α and atom β.

5. A method for predicting the villus growth mechanism during the helium bubble swelling process according to claim 1, characterized in that: In Step 303 and Step 304, judge the stacking position of the He bubble. Since the overall structure of the W matrix tends to the state of minimum energy, the He bubbles are continuously stacked in the surface convex structure of the W matrix. After the He bubbles rupture on the surface convex of the W matrix, new convexes will be formed to form a villous structure.

Images