Linear model calculation method of effective diffusion coefficient of tritium in alloy

Abstract

The application relates to a linear model calculation method of an effective diffusion coefficient of tritium in an alloy, and belongs to the field of research on nuclide transport behavior in materials. By determining stable sites of tritium in an alloy system, diffusion barriers between the stable sites are calculated, and then local diffusion coefficients are obtained. By combining diffusion barriers of tritium around doped atoms and diffusion barriers of tritium in a metal matrix material, an influence distance omega of the doped atoms on tritium in the alloy is determined d By comprehensively considering the number and volume proportion of the doped atoms, the effective diffusion coefficient of tritium in the alloy is calculated by using a linear model. By using the linear model calculation method of the effective diffusion coefficient of tritium in the alloy, the calculation precision of the effective diffusion coefficient of tritium in the alloy is improved, the calculation of the diffusion coefficient is closer to a real physical system, and the calculation is more accurate and reasonable. The application provides an important basis for research on a tritium source term in a fission reactor and a fusion reactor, storage and control of tritium, research and development design of tritium-blocking materials and the like.

Description

Technical Field

[0001] This invention belongs to the field of nuclide transport behavior in materials, and specifically relates to a linear model calculation method for the effective diffusion coefficient of tritium in an alloy. Background Technology

[0002] Safety and economic efficiency remain two key factors influencing the sustainable development of nuclear energy. The containment of radioactive materials is one of the three major safety functions of a reactor, and radiation safety is also an important component of reactor safety. The transport behaviors of radionuclides, such as adsorption, diffusion, and migration, within the reactor are important research areas for reactor radiation safety. Tritium has a half-life of 12.3 years and belongs to the beta... - Nuclear decay is a type of low-toxicity radioactive nuclide. Due to its chemical properties similar to hydrogen, strong diffusion and migration capabilities, and its role as an important fuel in fusion reactors, it has attracted widespread attention from researchers in the field of international nuclear engineering.

[0003] Studying the diffusion behavior of tritium in alloy materials is of great significance for preventing tritium leakage and for the research and design of tritium-blocking materials. In fusion reactors, the cladding material is the main site of tritium breeding. Reduced activation ferritic / martensitic (RAFM) steel has become the most promising cladding structure material due to its good heat resistance, radiation resistance, compatibility with coolants, and low element activation. However, under 14 MeV neutron irradiation, hydrogen isotopes are generated in RAFM steel. CLAM, EUROFER'97, and F82H are three RAFM steels that have been extensively studied. Yang, Oyaidzu, and Esteban measured the diffusion coefficients of hydrogen isotopes in three types of steel. Esteban pointed out that tritium in EUROFER'97 was mainly retained in carbon deposits, martensitic lath groups, and dislocation loops, and that the retention of tritium increased significantly after irradiation (H. Yang, et al., Journal of Nuclear Materials, 511, 231-234, 2018; M. Oyaidzu, et al., Journal of Nuclear Materials, 417, 1143-1146, 2011; G. Esteban, et al., Journal of Nuclear Materials, 367-370, 473-477).

[0004] The very high temperature gas-cooled reactor (VHT reactor) is one of the candidate reactor types for fourth-generation nuclear energy systems, while the high temperature gas-cooled reactor (HTGR) is the first stage of the VHT reactor. Due to its inherent safety, high thermoelectric conversion efficiency, and high core outlet helium temperature, the VHT reactor can be used for providing process heat and nuclear hydrogen production. In the HTGR, tritium can be generated through ternary fission of heavy metals, activation of Li-6 and Li-7 in graphite, activation of B-10 in absorber spheres, and activation of He-3 in the main coolant. Researchers have conducted extensive studies on the transport behavior of tritium in the HTGR.Wichner and Dyer studied the typical transport behavior of tritium in the Peach Bottom HTGR (RP Wichner and FF Dyer, Distribution and transport of tritium in the Peach Bottom HTGR, Tech. Rep. ORNL-5497, Oak Ridge National Laboratory, Oak Ridge, TN, USA, 1979); Forsyth studied the transport characteristics of tritium in the Dragon reactor (N. Forsyth, Tritium production and distribution in high temperature gas cooled reactors part 1: Tritium production, migration and removal in the dragon reactor between core 5 charge III and core 1 charge IV, OECD High Temperature Reactor Project DRAGONDP-REPORT-799, 1972); Steinwarz et al. summarized the transport behavior and distribution characteristics of tritium in the Arbeitsgemeinschaft Versuchsreaktor (AVR) (W. Steinwarz, et al., (Tritium behavior in an HTR-system based on AVR-experience, in Specialists Meeting on Coolant Chemistry, Plate-Out and Decontamination in Gas-Cooled Reactors (IWGGCR-2), 153-160, 1980). In high-temperature gas-cooled reactors (HTRs), tritium in the primary loop is mainly purified by the helium purification system. A small portion of tritium can penetrate the heat transfer tube walls of the steam generator and enter the secondary loop, becoming the only radioactive source term in the secondary coolant. This poses a potential radiation risk to future HTR nuclear hydrogen production and process thermal applications. To reduce and limit tritium entry from the primary loop into the secondary loop via the steam generator heat transfer tube walls, researchers have proposed preparing an oxide film on the surface of the heat transfer tubes to enhance the material's tritium-blocking ability.Since the heat transfer tubes of the steam generator in the high-temperature gas-cooled reactor are mainly made of iron alloy materials, studying the diffusion behavior of tritium in alloy materials is crucial for understanding and mastering the permeation and transport behavior of tritium, and is also an important prerequisite for the research and development of new tritium-blocking materials.

[0005] In the 2019 paper “Study on Impact of Cr and Mo on Diffusion of H in 2.25Cr1Mo Steel Using First-Principle Calculations”, first-principles density functional theory was used to calculate the stable sites and diffusion barriers of tritium in 2.25Cr1Mo steel and body-centered cubic packed pure iron. The diffusion coefficient of tritium in 2.25Cr1Mo steel was calculated using the Debye model and phonon spectrum model (W. Wang, et al., Journal of Nuclear Materials, 525, 152-160, 2019). However, the calculation process equates the tritium diffusion coefficient around Cr to that in 2.25Cr1Mo steel, failing to consider the combined influence of dopant atoms and the alloy matrix material on tritium diffusion behavior. This results in low accuracy and lacks a method for calculating the effective tritium diffusion coefficient in alloys, thus failing to provide valuable reference for research on tritium transport behavior in alloy materials, a key concern in fusion and fission reactors. Accurate calculation of the effective tritium diffusion coefficient in alloy materials is of significant scientific importance for the research and design of tritium-blocking materials and has important engineering application value for future high-temperature gas-cooled reactor nuclear hydrogen production and fusion reactor engineering development. Summary of the Invention

[0006] To address the shortcomings of existing technologies, the present invention aims to provide a linear model calculation method for the effective diffusion coefficient of tritium in alloys. This method utilizes density functional theory to determine the influence distance of dopant atoms on tritium within the alloy. Taking into account the number of dopant atoms, the volume percentage of the influence range of the dopant atoms on tritium within the alloy is calculated. Combining the local diffusion coefficient of tritium around the dopant atoms in the alloy and the local diffusion coefficient of tritium in the metal matrix material, a linear model is used to calculate the effective diffusion coefficient of tritium in the alloy.

[0007] To achieve the above objectives, the technical solution adopted by the present invention is as follows:

[0008] A linear model calculation method for the effective diffusion coefficient of tritium in an alloy, the method comprising the following steps:

[0009] S1. Establish a microcrystalline lattice model of the alloy and calculate the local diffusion coefficient of tritium in the metal matrix material and the local diffusion coefficient of tritium around the doped atoms based on first principles.

[0010] S2. Determine the influence distance ω of the dopant atom on tritium in the alloy based on the diffusion barrier of tritium at its nearest neighbor sites around the dopant atom and the diffusion barrier of tritium in the metal matrix material. d ;

[0011] S3. Based on the influence distance ω of doped atoms on tritium in the alloy. d Taking into account the number of doped atoms, the volume percentage of the influence range of doped atoms on tritium in the alloy is calculated. Combining the local diffusion coefficient of tritium in the metal matrix material and the local diffusion coefficient of tritium around the doped atoms, the effective diffusion coefficient of tritium in the alloy is calculated using a linear model.

[0012] Furthermore, step S1 includes the following sub-steps:

[0013] S11. Based on the proportion of each element in the alloy, establish a corresponding alloy configuration group, and determine the configuration with the lowest energy in the alloy configuration group as the alloy model.

[0014] S12. Based on the symmetry of the alloy model, determine the stable sites of tritium in the system, calculate the binding energy of tritium at each site, and then determine the most stable site of tritium in the system.

[0015] S13. The diffusion path and diffusion barrier of tritium between the most stable sites in the alloy are obtained through transition state theory; as well as the vibrational frequencies of the initiation site and the transition state site.

[0016] S14. Calculate the local diffusion coefficient of tritium in the metal matrix material and the local diffusion coefficient of tritium around the doped atoms based on first-principles calculations.

[0017] Furthermore, in step S11, the number of each atom in the supercell model is determined based on the proportion of each element in the alloy and the total number of atoms in the supercell model, so as to ensure that the proportion of each element in the supercell model is equivalent to the proportion of each element in the alloy.

[0018] Furthermore, in step S1, the local diffusion coefficient at different temperatures is calculated using the following formula:

[0019]

[0020] Where D is the diffusion coefficient, n is the number of nearest neighbor sites for interstitial atom diffusion, β is the hopping probability, d is the projection length in the diffusion direction, and k B T is the Boltzmann constant. K Let h be the temperature, and h be Planck's constant. For diffusion barrier, The zero-point vibrational energy E is the difference between the zero-point vibrational energy at the transition state site and the initial site. ZPEThe definition is as follows:

[0021]

[0022] in, is the vibrational frequency of the atom.

[0023] Furthermore, step S2 includes the following sub-steps:

[0024] S21. Create a diffusion barrier for tritium at the j-th nearest neighbor site to the (j+1)-th nearest neighbor site of the doped atom. The diffusion barrier of tritium in metallic matrix materials Calculate the difference and determine whether the difference is less than a preset difference threshold;

[0025] S22. When the difference between the two is greater than or equal to the preset difference threshold, let j = j + 1, find the next nearest neighbor site, and continue to determine the diffusion barrier of tritium around the doped atom corresponding to the next nearest neighbor site. Diffusion barrier of tritium in metallic matrix materials Is the difference less than a preset difference threshold?

[0026] S23. When the difference between the two is less than a preset difference threshold, the midpoint of the line connecting the j-th nearest neighbor site and the (j+1)-th nearest neighbor site is denoted as p, and the maximum length of the projected distance between p and the dopant atom on the x, y, and z axes is denoted as l. The influence distance ω of the dopant atom on tritium in the alloy is defined. d It is twice the value of l, i.e., ω d =2l.

[0027] Furthermore, the preset difference threshold mentioned in step S21 is the diffusion barrier of tritium in the metal matrix material. F%.

[0028] Furthermore, in step S3, the effective diffusion coefficient of tritium is calculated according to the following formula:

[0029]

[0030] Among them, D eff D is the effective diffusion coefficient of tritium in the alloy. bulk D is the local diffusion coefficient of tritium in a metallic matrix material. i Let be the local diffusion coefficient of tritium around the i-th doped atom, and N be the total number of doped atom types in the alloy. Let be the volume percentage of the range of influence of the i-th dopant atom on tritium in the alloy. , L represents the range of influence of a single atom of the i-th dopant on tritium. x L y and L zThese are the side lengths along the x, y, and z axes of the supercell, respectively, and n i denoted as the total number of atoms of the i-th type of dopant.

[0031] Furthermore, step S3 also includes:

[0032] The effective diffusion coefficient at different temperatures is calculated using formula (10), and then calculated according to formula D. eff =D0exp(-Q / k B T K By fitting the data, the diffusion coefficient pre-factor D0 and the diffusion activation energy Q are obtained, thus yielding the effective diffusion coefficient D. eff The general expression for .

[0033] Furthermore, in step S3, the influence range of the dopant atom on tritium is equivalent to a side length ω centered on the dopant atom. d A cube was used to perform a linear model calculation of the effective diffusion coefficient of tritium.

[0034] Furthermore, in step S11, different alloy configurations are established using a random substitution method, the energy of different alloy configuration systems is calculated, and the alloy configuration with the lowest energy is used as the alloy model.

[0035] The advantages of this invention are as follows: The linear model calculation method for the effective diffusion coefficient of tritium in an alloy disclosed in this invention considers the influence of dopant atoms on the diffusion coefficient. By determining the stable sites of tritium in the metal matrix and around the dopant atoms, the differential charge density, Bader charge, and density of states of tritium at each stable site are examined to analyze the bonding mode between tritium and surrounding atoms. The diffusion path and diffusion barrier between the most stable sites of tritium in the alloy, as well as the vibrational frequencies of the initiation site and transition state site, are calculated using transition state theory. Then, based on first-principles calculations, the local diffusion coefficient of tritium in the metal matrix and the local diffusion coefficient of tritium around the dopant atoms are calculated. Combining the diffusion barrier of tritium around the dopant atoms and the diffusion barrier of tritium in the metal matrix, the influence distance ω of the dopant atoms on tritium is determined. d Taking into account the number of doped atoms, the volume percentage of the influence range of doped atoms on tritium in the alloy is calculated, and then the effective diffusion coefficient of tritium in the alloy is calculated using a linear model. Attached Figure Description

[0036] Figure 1 This is a flowchart illustrating a linear model correction method for the effective diffusion coefficient of tritium in an alloy, as shown in an embodiment of the present invention.

[0037] Figure 2 This is a schematic diagram illustrating the diffusion path of tritium around doped atoms in an embodiment of the present invention.

[0038] Figure 3For step S2, calculate the distance of influence of doped atoms on tritium in the alloy. Flowchart of the steps;

[0039] Figure 4 This is a flowchart of the method for calculating the effective diffusion coefficient of tritium in the alloy using a linear model in step S3. Detailed Implementation

[0040] The present invention will now be further described with reference to the accompanying drawings and specific embodiments.

[0041] Example 1

[0042] This invention discloses a linear model calculation method for the effective diffusion coefficient of tritium in an alloy. The method calculates the effective diffusion coefficient of tritium in the alloy material 2.25Cr1Mo steel. The method is based on first-principles calculation software, such as the first-principles density functional theory (DFT) calculation software VASP (Vinna ab intio simulation package) based on the pseudopotential plane wave projection enhancement method, and related plugins. However, it is not limited to this method, and other first-principles calculation software can also be used for calculation.

[0043] like Figure 1 As shown in the figure, this invention discloses a linear model calculation method for the effective diffusion coefficient of tritium in an alloy, the method comprising the following steps:

[0044] S1. Establish a microcrystalline lattice model of the alloy and calculate the local diffusion coefficient of tritium in the metal matrix material and the local diffusion coefficient of tritium around the doped atoms based on first principles.

[0045] S2. Determine the influence distance ω of the dopant atom on tritium in the alloy based on the diffusion barrier of tritium at its nearest neighbor sites around the dopant atom and the diffusion barrier of tritium in the metal matrix material. d ;

[0046] S3. Based on the influence distance ω of doped atoms on tritium in the alloy. d Taking into account the number of doped atoms, the volume percentage of the influence range of doped atoms on tritium in the alloy is calculated. Combining the local diffusion coefficient of tritium in the metal matrix material and the local diffusion coefficient of tritium around the doped atoms, the effective diffusion coefficient of tritium in the alloy is calculated using a linear model.

[0047] Step S1 includes the following sub-steps:

[0048] S11. Based on the proportion of each element in the alloy, establish a corresponding alloy configuration group, and determine the configuration with the lowest energy in the alloy configuration group as the alloy model.

[0049] Based on the element ratio of the alloy, the ratio of each element in the supercell model is determined so that the ratio of the number of various atoms in the established supercell model can match the actual ratio in the alloy.

[0050] When establishing a supercell model, the number of atoms of each element in the supercell model is calculated based on the total number of atoms in the supercell model and the proportion of each element in the supercell model. When the calculated number of atoms of a certain element is not an integer, the non-integer is rounded down by methods such as rounding or rounding up, and then adjusted to the nearest integer to determine the number of atoms of each element in the supercell.

[0051] After determining the proportions and number of atoms of various elements in the supercell model, it is necessary to determine the distribution of dopant atoms in the alloy.

[0052] In this embodiment, a body-centered cubic (BCC) pure iron model was first established as the matrix material. This model contains 128 iron atoms with a side length of 11.34 Å. Since the atomic ratio of Fe:Cr:Mo in 2.25Cr1Mo steel is 173.26:4.35:1, calculations and rounding determined that the supercell model should contain 123 iron atoms, 4 Cr atoms, and 1 Mo atom. Using a random substitution method, five 2.25Cr1Mo configurations were established based on the BCC pure iron model, each containing 4 Cr atoms and 1 Mo atom. The energies of the five configurations were calculated using VASP simulation software, and the configuration with the lowest energy was selected as the alloy model.

[0053] S111, Calculate the initial Bader charge of all atoms in the system.

[0054] The VASP software, combined with the Bader plugin, is used to calculate the Bader charge of all atoms in the system.

[0055] In this embodiment, the Bader charge of the body-centered cubic (BCC) pure iron model and the alloy model is calculated to facilitate subsequent analysis of the Bader charge transfer.

[0056] S12. Based on the symmetry of the alloy model, determine the stable sites of tritium in the system, calculate the binding energy of tritium at each site, and then determine the most stable site of tritium in the system.

[0057] In the alloy, various interstitial sites provide possible stable locations for tritium (T). The most stable site is found from multiple possible stable sites by calculation.

[0058] Here, the combination can be defined by the following formula:

[0059]

[0060] Among them, E binding The binding energy is eV;

[0061] E T+bulk The energy of the system after T enters the interstitial site, in eV;

[0062] E bulk The total energy of the alloy system before T enters the interstitial site, in eV;

[0063] Let T2 be the energy in vacuum, in eV.

[0064] Since tritium and hydrogen are isotopes with almost identical chemical properties, DFT calculations primarily consider the chemical properties of the elements. and E T+bulk When H2 is used instead of T2, use H2 instead.

[0065] By calculating the binding energy of tritium at interstitial sites and around doped atoms in the alloy matrix, the binding energy E of tritium at these sites is obtained. binding The site with the lowest binding energy is the most stable site.

[0066] In this embodiment, the binding energy of tritium in the tetrahedral and octahedral interstices of BCC pure iron was calculated, and the binding energy of tritium in the nearest tetrahedral and octahedral interstices of the doped atoms Cr and Mo in 2.25Cr1Mo steel was also calculated. The calculated binding energies are shown in Table 1, where O represents the octahedral interstic and T represents the tetrahedral interstic.

[0067] Table 1. Binding energy of tritium around Cr and Mo in BCC pure iron and 2.25Cr1Mo steel

[0068] <![CDATA[E binding (eV)]]> 0.33 0.23 0.61 0.40 2.11 1.01

[0069] Calculations show that, in this embodiment, tritium is more stable in the tetrahedral interstices, and less stable in the bonds around the doped atoms compared to the BCC pure iron system.

[0070] After determining the stable sites of T in the matrix material of the alloy and around the dopant atoms, the differential charge density, density of states, and Bader charge were calculated to explain the bonding characteristics of the matrix material atoms and dopant atoms with tritium atoms.

[0071] S121. Calculate the differential charge density based on the stable sites of T in the system.

[0072] The differential charge density can be calculated using the following formula:

[0073]

[0074] in, For differential charge density, Bohr -3 ;

[0075] Let T be the charge density in the alloy interstitial space, Bohr -3 ;

[0076] For the charge density of the alloy, Bohr -3 ;

[0077] This represents the charge density of a single T atom.

[0078] In this embodiment, the differential charge density of tritium in the tetrahedral interstices of BCC pure iron and the nearest neighbor tetrahedral interstices of Cr and Mo in 2.25Cr1Mo steel was calculated to analyze the interaction between tritium and metal atoms.

[0079] S122. Calculate the density of states of the system.

[0080] The density of states represents the number of electronic states per unit energy interval. By analyzing the density of states, information can be obtained about the bonding properties of T with surrounding atoms in the alloy.

[0081] In this implementation, the density of states of tritium around BCC pure iron, Cr and Mo doped atoms was calculated to analyze the bonding properties of tritium with the surrounding metal atoms.

[0082] S123. Calculate the Bader charge of the tritium-containing system.

[0083] By calculating the Bader charge of the T-containing system and combining it with the Bader charge of the previous alloy system, the charge gain and loss of each atom in the system can be quantitatively obtained.

[0084] Combining the initial Bader charge calculation results of the system in step S111, the Bader charge transfer was obtained, indicating that the addition of Cr and Mo made the charge distribution of tritium more localized.

[0085] S13. Calculate the diffusion path and diffusion barrier of tritium between the most stable sites in the alloy, as well as the vibrational frequencies of the initiation site and the transition state site, using transition state theory.

[0086] Based on the stable sites of T in the alloy obtained in step S12, periodic units between these stable sites are identified. The CI-NEB method is used to find diffusion paths and transition state sites. The initiation site is the starting point of diffusion, and the transition state site is the highest energy point on the diffusion path. The energy difference between the transition state site and the initiation site is the diffusion barrier, which can be directly calculated using first-principles calculations.

[0087] In this embodiment, the tritium diffusion path is tetrahedral interstitial-tetrahedral interstitial. The diffusion barrier of tritium in BCC pure iron (0.09 eV) and the barriers for tritium to jump between the first, second, and third nearest neighbor tetrahedral interstitials of the dopant atoms Cr and Mo are calculated here. The diffusion path is as follows: Figure 2 As shown in the figure, the tetrahedral interstitial positions are the diffusion paths of tritium, and the dashed boxes represent the influence range of doped atoms on tritium in the alloy. The calculation results are shown in Table 2.

[0088] Table 2 Diffusion barriers of tritium at different sites

[0089] BCC Pure Fe 0.09 0.09 0.09 Cr doped atoms around 0.10 0.16 0.12 Mo doped atoms around 0.10 0.73 0.30

[0090] S14. Calculate the local diffusion coefficient of tritium in the metal matrix material and the local diffusion coefficient of tritium around the doped atoms based on first-principles calculations.

[0091] We typically use the following Arrhenius formula to describe the diffusion coefficient:

[0092]

[0093] Where D is the diffusion coefficient, m 2 / s;

[0094] D0 is the diffusion coefficient pre-factor, m 2 / s;

[0095] Q is the diffusion activation energy, eV, which can be directly obtained by density functional theory DFT calculation;

[0096] k B Boltzmann's constant is 8.6173324 × 10⁻⁶. -5 eV / K;

[0097] T K Let K be the temperature.

[0098] Formula (3) can also be written as follows:

[0099]

[0100] At this time, 1 / T KLet ln(D) be the x-axis and ln(D) be the y-axis; the graph would be a straight line. According to the theory of Wert and Zener, the diffusion coefficient in a crystal can be expressed by the following formula:

[0101]

[0102] Where n is the number of nearest neighbor sites for interstitial atom diffusion;

[0103] β is the jump probability;

[0104] d is the projected length in the diffusion direction, in meters;

[0105] Γ represents the jump rate between adjacent sites, s -1 .

[0106] Using Eyring's compound activation theory and Vineyard's simplified temperature formulas for high and low temperatures, approximate expressions for the diffusion coefficient at different temperatures are obtained as follows:

[0107]

[0108] Where h is Planck's constant, 4.1356674 × 10⁻⁶. -15 eV·s;

[0109] The energy difference between the transition site and the initiation site, expressed in eV, is also known as the diffusion barrier.

[0110] The difference in zero-point vibrational energy between the transition state site and the initial site, expressed in eV;

[0111] Zero-point vibrational energy E ZPE The definition is as follows:

[0112]

[0113] in, s is the vibrational frequency of the atom. -1 .

[0114] After obtaining the vibrational frequency through density functional theory (DFT) calculations, the crystal parameters and the diffusion barrier ΔE obtained in step S3 are then considered. el Based on the diffusion coefficient calculated in (6), lnD and 1 / T are plotted. K The curve is then fitted using equation (4) to obtain the general expression for the local diffusion coefficient D.

[0115] This process allows us to obtain the local diffusion coefficients of tritium around doped atoms and in the metal matrix material through various diffusion paths.

[0116] like Figure 3 As shown, the influence of doped atoms on tritium in the alloy during step S2 is measured at a distance ω. d The detailed calculation process is as follows:

[0117] The diffusion barrier of tritium in a metallic matrix material is denoted as . The diffusion barrier of tritium around the doped atom is denoted as . , representing the diffusion barrier of tritium around the doped atom from the j-th nearest neighbor interstitial position to the (j+1)-th nearest neighbor interstitial position. The diffusion barrier of tritium around the doped atom... Diffusion barrier of tritium in metallic matrix materials Calculate the difference and determine whether the difference is less than a preset difference threshold.

[0118] When the difference between the two is greater than or equal to a preset difference threshold, let j = j + 1, find the next nearest neighbor gap, and continue to determine the diffusion barrier of tritium around the doped atom corresponding to the next nearest neighbor gap. Diffusion barrier of tritium in metallic matrix materials Is the difference less than a preset difference threshold?

[0119] When the difference between the two is less than a preset difference threshold, the diffusion of tritium in the dopant atom is considered equivalent to the diffusion of tritium in the metal matrix material. Then, the midpoint of the line connecting the j-th nearest neighbor gap position and the (j+1)-th nearest neighbor gap position is denoted as p, and the maximum length of the projected distance between p and the dopant atom on the x, y, and z axes is denoted as l. The influence distance ω of the dopant atom on tritium in the alloy is defined. d It is twice the value of l, i.e., ω d =2l.

[0120] In this embodiment, the preset difference threshold is the diffusion barrier of tritium in the metal matrix material. 10%, but no limit is set on this.

[0121] like Figure 4 As shown, the detailed process of calculating the effective diffusion coefficient of tritium in the alloy using a linear model in step S3 is as follows:

[0122] In the supercell model, the influence distance of each doped atom was obtained. We consider the influence range of each doped atom as equivalent to a region with a side length of A cube. For the i-th type of doped atom, the influence range of each doped atom is defined as the volume Ω of this cube. i :

[0123]

[0124] Then, for the i-th dopant atom, the ratio of the volume of its influence area on tritium in the alloy to the volume of the cuboid supercell is... for:

[0125]

[0126] Among them, L x L y L z Let be the side lengths of the supercell along the x, y, and z axes, respectively, in meters;

[0127] n i denoted as the total number of atoms of the i-th type of dopant.

[0128] The diffusion of tritium within the alloy supercell is influenced by dopant atoms. This model equates the influence range of the dopant atoms to the volume of a cube. The effective diffusion coefficient of tritium in the alloy is the linear sum of the local diffusion coefficients of tritium in all dopant atoms and the matrix material, as follows:

[0129]

[0130] Among them, D eff m is the effective diffusion coefficient of tritium in the alloy. 2 / s;

[0131] D bulk Let m be the local diffusion coefficient of tritium in a metallic matrix material. 2 / s;

[0132] D i Let m be the local diffusion coefficient of tritium around the i-th doped atom. 2 / s;

[0133] denoted as the volume percentage of the range of influence of the i-th dopant atom on tritium in the alloy.

[0134] The local diffusion coefficient D of tritium in the matrix material at different temperatures was calculated using formula (6). bulk and the local diffusion coefficient D around the doped atom i The numerical value of the tritium is substituted into formula (10) to calculate the effective diffusion coefficient D of tritium in the alloy material at a series of different temperatures. eff The values ​​are then used to fit the Arenius-type diffusion activation energy and diffusion coefficient pre-factor through formula (4), and then the effective diffusion coefficient D of tritium in the alloy material is obtained. eff The general expression for .

[0135] The calculation process of step S3 will be illustrated below with a specific example:

[0136] Based on the diffusion barrier calculated in step S13, for both Cr and Mo atoms, in this embodiment, the projection of the distance between the midpoint between the third and second nearest neighbors and tritium is selected as l, and ω is then... d Values ​​such as Figure 2 The value is shown as 4.97 Å, and the influence distance is equivalent to a cube. For Cr, the maximum diffusion barrier of 0.16 eV in the diffusion path is selected as the diffusion barrier for its local diffusion coefficient. For Mo, the system energy tends to increase as it diffuses from the second nearest neighbor to the first nearest neighbor. In this example, the energy difference of 0.73 eV between these two points is selected as the diffusion barrier.

[0137] The zero-point vibrational energy of tritium diffusion in BCC pure iron and Cr in 2.25Cr1Mo steel was calculated. Since the zero-point vibrational energy is mainly contributed by the vibration of tritium, only the vibration of tritium is considered here. After calculating the vibration frequency of tritium, the zero-point vibrational energy is calculated by formula (7). For Mo, since the zero-point vibrational energy correction is small and there is no transition state site for diffusion from the second nearest neighbor to the first nearest neighbor of Mo, the correction of the zero-point vibrational energy is meaningless. Therefore, the zero-point vibrational energy correction when tritium is around Mo is not considered. The calculated zero-point vibrational energies are shown in Table 3.

[0138] Table 3. Zero-point vibrational energy ΔE of tritium ZPE

[0139]

[0140] By uniformly selecting 800 points between 273K and 1073K, the local diffusion coefficients of tritium around BCC pure iron, Cr, and Mo were obtained by fitting the data using formula (4), as shown below:

[0141]

[0142]

[0143]

[0144] The calculation results show that, between 273 K and 1073 K, the local diffusion coefficient of tritium around Mo is much smaller than that of tritium in BCC pure iron and around Cr. Therefore, in this example, we consider Mo as a single Cr atom. At this point, ω... d The ratio of the side length to the supercell model we established is 0.4375. To represent the volume percentage of the influence range of the doped Cr atom (including the contribution of Mo in this embodiment) on tritium in the alloy, equation (10) can be simplified to:

[0145]

[0146] Among them, D Fe Let m be the local diffusion coefficient of tritium in BCC pure iron. 2 / s;

[0147] D Cr Let m be the local diffusion coefficient of tritium around the Cr dopant atom. 2 / s.

[0148] Take 800 temperature points between 273K and 1073K, and calculate D at the corresponding temperature using formula (6). Fe and D Cr The numerical value is incorrect here (D). Fe and D Cr Perform fitting; calculate D at different temperatures Fe and D Cr Substitute the numerical values ​​into formula (11) to calculate D at the corresponding temperature. eff The numerical values ​​were fitted using formula (4) to determine the pre-factor and diffusion activation energy of the effective diffusion coefficient of tritium in the alloy, thus obtaining a general expression for the effective diffusion coefficient of tritium in 2.25Cr1Mo steel alloy. The comparison between the results obtained by this method and the experimental measurement data is shown in Table 4.

[0149] Table 4. Diffusion coefficient precursor factor and diffusion activation energy

[0150] Experimental measurement data 1 <![CDATA[2.28×10 -7 ]]> 0.175 Experimental measurement data 2 <![CDATA[3.56×10 -7 ]]> 0.209 Experimental measurement data 3 <![CDATA[2.40×10 -7 ]]> 0.185 Experimental measurement data 4 <![CDATA[2.10×10 -6 ]]> 0.314 <![CDATA[D eff (This embodiment) <![CDATA[1.79×10 -7 ]]> 0.089

[0151] As can be seen from Table 4, the effective diffusion coefficient of tritium in 2.25Cr1Mo steel alloy material calculated by the linear model is close to the experimental measurement results.

[0152] As can be seen from the above embodiments, the linear model calculation method for the effective diffusion coefficient of tritium in an alloy disclosed in this invention can obtain the local diffusion coefficient of tritium around the matrix material and dopant atoms in the alloy, and simultaneously analyze the influence distance ω of the dopant atoms on tritium. d Furthermore, it can comprehensively consider the influence of doped atoms and metal matrix materials on tritium diffusion, and then calculate the effective diffusion coefficient of tritium in the alloy. This makes the calculation of the effective diffusion coefficient closer to the real physical system, improves the calculation accuracy of the effective diffusion coefficient of tritium in the alloy, and provides an important foundation for the study of tritium source terms in fission reactors and fusion reactors, tritium storage and control, and the research and design of tritium blocking materials.

[0153] The method described in this invention is not limited to the embodiments described in the specific implementation. Other implementation methods derived by those skilled in the art based on the technical solution of this invention also fall within the scope of technical innovation of this invention.

Claims

1. A linear model calculation method for the effective diffusion coefficient of tritium in an alloy, the method comprising the following steps: S1. Establish a microcrystalline lattice model of the alloy and calculate the local diffusion coefficient of tritium in the metal matrix material and the local diffusion coefficient of tritium around the doped atoms based on first principles. S2. Determine the influence distance ω of the dopant atom on tritium in the alloy based on the diffusion barrier of tritium at its nearest neighbor sites around the dopant atom and the diffusion barrier of tritium in the metal matrix material. d ; S3. Based on the influence distance ω of the doped atoms on tritium in the alloy. d Taking into account the number of doped atoms, the volume percentage of the influence range of doped atoms on tritium in the alloy is calculated. Combining the local diffusion coefficient of tritium in the metal matrix material and the local diffusion coefficient of tritium around the doped atoms, the effective diffusion coefficient of tritium in the alloy is calculated using a linear model.

2. The linear model calculation method for the effective diffusion coefficient of tritium in an alloy according to claim 1, characterized in that, Step S1 includes the following sub-steps: S11. Based on the proportion of each element in the alloy, establish a corresponding alloy configuration group, and determine the configuration with the lowest energy in the alloy configuration group as the alloy model. S12. Based on the symmetry of the alloy model, determine the stable sites of tritium in the system, calculate the binding energy of tritium at each site, and then determine the most stable site of tritium in the system. S13. The diffusion path and diffusion barrier of tritium between the most stable sites in the alloy are obtained through transition state theory; And the vibrational frequencies of the initiation site and the transition site; S14. Calculate the local diffusion coefficient of tritium in the metal matrix material and the local diffusion coefficient of tritium around the doped atoms based on first-principles calculations.

3. The linear model calculation method for the effective diffusion coefficient of tritium in an alloy according to claim 2, characterized in that: In step S11, the number of each atom in the supercell model is determined based on the proportion of each element in the alloy and the total number of atoms in the supercell model, so as to ensure that the proportion of each element in the supercell model is equivalent to the proportion of each element in the alloy.

4. The linear model calculation method for the effective diffusion coefficient of tritium in an alloy according to claim 2, characterized in that: In step S1, the local diffusion coefficient at different temperatures is calculated using the following formula: Where D is the diffusion coefficient, n is the number of nearest neighbor sites for interstitial atom diffusion, β is the hopping probability, d is the projection length in the diffusion direction, and k B T is the Boltzmann constant. K Let h be the temperature, and h be Planck's constant. For diffusion barrier, The zero-point vibrational energy E is the difference between the zero-point vibrational energy at the transition state site and the initial site. ZPE The definition is as follows: in, is the vibrational frequency of the atom.

5. The linear model calculation method for the effective diffusion coefficient of tritium in an alloy according to claim 4, characterized in that, Step S2 includes the following sub-steps: S21. Create a diffusion barrier for tritium at the j-th nearest neighbor site to the (j+1)-th nearest neighbor site of the doped atom. The diffusion barrier of tritium in metallic matrix materials Calculate the difference and determine whether the difference is less than a preset difference threshold; S22. When the difference between the two is greater than or equal to the preset difference threshold, let j = j + 1, find the next nearest neighbor site, and continue to determine the diffusion barrier of tritium around the doped atom corresponding to the next nearest neighbor site. Diffusion barrier of tritium in metallic matrix materials Is the difference less than a preset difference threshold? S23. When the difference between the two is less than a preset difference threshold, the midpoint of the line connecting the j-th nearest neighbor site and the (j+1)-th nearest neighbor site is denoted as p, and the maximum length of the projected distance between p and the dopant atom on the x, y, and z axes is denoted as l. The influence distance ω of the dopant atom on tritium in the alloy is defined. d It is twice the value of l, i.e., ω d =2l.

6. The linear model calculation method for the effective diffusion coefficient of tritium in an alloy according to claim 5, characterized in that: The preset difference threshold mentioned in step S21 is the diffusion barrier of tritium in the metal matrix material. F%.

7. The linear model calculation method for the effective diffusion coefficient of tritium in an alloy according to claim 6, characterized in that, In step S3, the effective diffusion coefficient of tritium is calculated according to the following formula: Among them, D eff D is the effective diffusion coefficient of tritium in the alloy. bulk D is the local diffusion coefficient of tritium in a metallic matrix material. i Let be the local diffusion coefficient of tritium around the i-th doped atom, and N be the total number of doped atom types in the alloy. Let be the volume percentage of the range of influence of the i-th dopant atom on tritium in the alloy. , L represents the range of influence of a single atom of the i-th dopant on tritium. x L y and L z These are the side lengths along the x, y, and z axes of the supercell, respectively, and n i denoted as the total number of atoms of the i-th type of dopant.

8. The linear model calculation method for the effective diffusion coefficient of tritium in an alloy according to claim 7, characterized in that, Step S3 also includes: The effective diffusion coefficient at different temperatures is calculated using formula (10), and then calculated according to formula D. eff =D0exp(-Q / k B T K By fitting the data, the diffusion coefficient pre-factor D0 and the diffusion activation energy Q are obtained, thus yielding the effective diffusion coefficient D. eff The general expression for .

9. The linear model calculation method for the effective diffusion coefficient of tritium in an alloy according to claim 1, characterized in that: In step S3, the influence range of the dopant atom on tritium is equivalent to a side length ω centered on the dopant atom. d A cube was used to perform a linear model calculation of the effective diffusion coefficient of tritium.

10. The linear model calculation method for the effective diffusion coefficient of tritium in an alloy according to claim 2, characterized in that: In step S11, different alloy configurations are established using a random substitution method, the energy of different alloy configuration systems is calculated, and the alloy configuration with the lowest energy is used as the alloy model.

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