Simulation method of irradiation response of ti-al-nb-zr-mo quinary alloy based on mixed potential function

Abstract

This invention provides a method for simulating the irradiation response of Ti-Al-Nb-Zr-Mo pentagonal alloys based on a hybrid potential function, belonging to the technical field of potential function development for irradiation damage simulation of metallic materials. This method aims to solve the problems of existing potential functions failing to accurately describe high-energy collisions and the lack of smoothness at the connection points of hybrid potential functions. The solution includes: obtaining pure metal parameters to generate an initial embedded atom-based potential function; introducing a Ziegler-Bissack-Littmark potential function to describe short-range interactions; using spline functions to smoothly connect the two potential functions, ensuring the continuity of function values ​​and first derivatives at the connection points by solving boundary conditions; and finally generating a hybrid potential function file compatible with molecular dynamics software. This invention, by smoothly connecting short-range and medium-to-long-range potential functions, can accurately describe the full range of atomic interactions, avoid energy jumps in the simulation, and improve the accuracy of irradiation damage simulation.

Description

Technical Field

[0001] This invention relates to the field of irradiation damage simulation technology for metallic materials, and more specifically, to a method for simulating the irradiation response of Ti-Al-Nb-Zr-Mo pentagonal alloys based on a mixed potential function, suitable for molecular dynamics irradiation simulation. Background Technology

[0002] In the field of metallic materials, Ti-Al-Nb-Zr-Mo pentagonal alloys have attracted much attention due to their excellent mechanical properties and radiation resistance. Molecular dynamics simulations are an important tool for studying the microscopic mechanisms of radiation damage in materials, and the accuracy of the potential function directly determines the reliability of the radiation simulation results.

[0003] Currently, the main potential functions describing the interactions between metal atoms include the embedded atom method (EAM) potential function and the Ziegler-Biersack-Littmark (ZBL) potential function. The traditional EAM potential function performs well in describing the equilibrium properties of alloy systems, but it is primarily suitable for describing medium- to long-range interactions between atoms. It cannot accurately simulate the short-range strong repulsion of high-energy cascade collisions, leading to overly soft collisions and distortions in the displacement threshold and defect yield. The ZBL potential function, based on quantum mechanical calculations, can accurately describe short-range repulsive interactions between atoms and is suitable for high-energy collision processes. However, it fails to describe long-range metallic bonding; direct splicing results in discontinuities in potential energy and force at the junction, causing non-physical energy jumps and force mutations, leading to abnormal defect evolution trajectories.

[0004] In existing technologies, to simultaneously account for short-range and long-range interactions in molecular dynamics simulations, a common approach is to combine the ZBL potential function with medium- to long-range potential functions such as the EAM potential function using the embedded atom method. However, this combination method generally suffers from discontinuities in function values ​​and first derivatives at the junction points, leading to non-physical energy jumps during the simulation and affecting the accuracy of the results. Furthermore, for complex alloy systems like Ti-Al-Nb-Zr-Mo, which contain multiple elements, the types of interatomic interactions are numerous, making the manual processing and construction of mixed potential functions extremely complex and inefficient. Simultaneously, the constructed potential functions must be compatible with the specific file formats (such as EAM / alloy format) of mainstream molecular dynamics software (e.g., LAMMPS) to ensure direct usability. In other words, the generated potential files are often incompatible with software formats like LAMMPS, making them difficult to use directly for irradiation response simulations. Existing simulation methods lack standardized procedures, resulting in insufficient accuracy in calculating the three-stage evolution of irradiation cascades, defect recombination, and the number of stable defects, thus failing to support quantitative evaluation of the alloy's radiation resistance.

[0005] Therefore, there is a market need for a standardized simulation method that can be directly used for irradiation response simulation, provides smooth potential energy throughout the process, ensures continuous stress, is compatible with mainstream software, and can stably output reliable irradiation damage data. Summary of the Invention To address the shortcomings of existing technologies, the purpose of this invention is to provide a simulation method for the irradiation response of Ti-Al-Nb-Zr-Mo pentagonal alloys based on a mixed potential function. This method aims to solve the problems of inaccurate potential function description, uneven connection of mixed potential leading to distortion of high-energy collisions, non-physical energy jumps, and large deviations in defect evolution calculations in existing irradiation simulations.

[0006] The present invention provides a method for simulating the irradiation response of a Ti-Al-Nb-Zr-Mo pentagonal alloy based on a mixing potential function, comprising: Step S1: Obtain the parameters of five pure metallic elements, Ti, Al, Nb, Zr, and Mo, and establish the alloy potential function basis file; Step S2: Construct the alloy potential function program to generate the initial Ti-Al-Nb-Zr-Mo alloy embedded atom method EAM potential function; Step S3: Calculate the short-range effect of the ZBL potential function; Step S4: Solve for the spline function parameters connecting the ZBL potential function and the embedded atom method EAM potential function; Step S5: Generate mixed potential function data and maintain a callable format; Step S6: Output the mixed potential function file and parameter document; Step S7: Use the aforementioned mixed potential function to conduct molecular dynamics irradiation simulation of Ti-Al-Nb-Zr-Mo alloy, and output the lattice constant, elastic constant, vacancy formation energy, irradiation damage efficiency, and defect evolution law.

[0007] Preferably, step S1 includes: collecting atomic parameters of five elements, Ti, Al, Nb, Zr and Mo, including atomic number, atomic weight and lattice constant; A base file containing five elements was established based on the alloy potential function format. The alloy potential function parameters of the five elements, including the electron density function parameter, the embedding function parameter, and the pair potential function parameter, were determined by consulting literature and experimental data.

[0008] Preferably, step S2 includes: running the alloy potential function program, inputting the pentagonal alloy parameters, and generating an initial alloy embedded atom method potential function file; Verify that the generated potential function file format is correct, including the element order, number of data points, and cutoff radius parameter; Check the basic properties of the potential function, including whether the lattice constant and elastic constant match the experimental values.

[0009] Preferably, the step S3 includes: defining the ZBL-spline connection point R1 and the spline-embedded atom method connection point R2; For the atomic interaction of the Ti-Al-Nb-Zr-Mo quinary alloy, calculate the ZBL potential function value at R1 respectively and the first derivative value .

[0010] Preferably, the ZBL potential function is calculated by the following formula:

[0011] where

[0012] a0 is the Bohr radius, and Z1 and Z2 are the atomic numbers.

[0013] Preferably, the step of solving the spline function parameters connecting the ZBL potential function and the embedded atom method potential function includes: for different atomic interactions, extract the pair potential data from the initial embedded atom method potential function file, and calculate the embedded atom method potential function value at R2 by interpolation and the first derivative value ; Establish a spline function:

[0014] and solve the parameters P1, P2, P3, P4 through the following boundary conditions: .

[0015] Preferably, the boundary conditions form a 4×4 linear equation system to solve the spline parameters.

[0016] Preferably, the step S5 includes: for different atomic interactions, generate mixed potential function data, where when the atomic spacing r ≤ R1, the ZBL potential function value is used, when R1 < r < R2, the value calculated by the spline function is used, and when r ≥ R2, the original embedded atom method potential function value is used; Keep the format of the original embedded atom method potential function file, including the file header information, the embedded function data, the electron density data, and the arrangement order of the pair potential data, and keep the blank lines and numerical formats in the original file to ensure that the generated mixed potential function file is compatible with the molecular dynamics software.

[0017] Preferably, the step S6 includes: outputting the final mixed potential file; At the same time, output a parameter document, recording the spline parameters, connection point positions, and element information of all atomic interactions; and provide the calling method description in the molecular dynamics software.

[0018] Preferably, the method further includes a verification step: The performance of the mixing potential function was verified through molecular dynamics simulations, including the calculation of lattice constant, elastic constant, vacancy formation energy, and irradiation damage generation efficiency, and compared with experimental data or other potential functions.

[0019] Compared with the prior art, the present invention has the following beneficial effects: 1. This invention is the first to realize the systematic construction of the irradiation potential function of Ti-Al-Nb-Zr-Mo pentagonal alloy using the embedded atom method, providing a suitable mixed potential function for the irradiation simulation of this alloy system. ZBL is used for short range and EAM is used for medium and long range, accurately matching the cascade collision high-energy repulsion and equilibrium metallic bonding, and the deposition process and defect yield are more in line with the physical picture.

[0020] 2. This invention achieves a smooth connection between the ZBL potential function and the embedded atom normal potential function through spline functions, ensuring the continuity of function values ​​and first derivatives at the connection point, avoiding energy jump problems in the simulation, and thus ensuring the accuracy of full-scale molecular dynamics simulation.

[0021] 3. The automated program constructed in this invention can handle the complex atomic interaction relationships of multi-element alloy systems, automatically construct the potential function of pentagonal alloys, improve development efficiency, integrate construction-verification-simulation, and lower the threshold for multi-element alloy irradiation simulation.

[0022] 4. The hybrid potential function file generated by this invention maintains the original embedded atom method potential function format, is fully compatible with mainstream molecular dynamics software, can be directly called, and can be implemented in engineering. Attached Figure Description

[0023] Other features, objects, and advantages of the present invention will become more apparent from the following detailed description of non-limiting embodiments with reference to the accompanying drawings: Figure 1 This is a schematic flowchart illustrating a method for simulating the irradiation response of a Ti-Al-Nb-Zr-Mo pentagonal alloy based on a mixed potential function, provided for an embodiment of the present invention.

[0024] Figure 2 This is a comparison of the ZBL-Spline-EAM and individual EAM potential functions for a single Ti-Ti element pair in an embodiment of the present invention, along with a magnified view of the connection point.

[0025] Figure 3 The ZBL-Spline-EAM curves and their comparison diagrams between each pair of elements in the embodiments of the present invention are shown.

[0026] Figure 4This is an illustration of the evolution of the number of FPs over time under high-energy PKA (initial atom) bombardment and detailed irradiation at different stages in an embodiment of the present invention. Figure 5 This is a graph showing the evolution of the Frankel defect logarithm over the simulation period of this invention. Detailed Implementation

[0027] The present invention will now be described in detail with reference to specific embodiments. These embodiments will help those skilled in the art to further understand the present invention, but do not limit the invention in any way. It should be noted that those skilled in the art can make several changes and improvements without departing from the concept of the present invention. These all fall within the protection scope of the present invention.

[0028] This invention utilizes the five elemental parameters of Ti, Al, Nb, Zr, and Mo to construct an embedded atom normal potential function for an initial alloy. Then, a ZBL potential function is introduced to describe short-range effects. Finally, a spline function is used to achieve a smooth connection between the ZBL potential function and the embedded atom normal potential function, generating a hybrid potential function suitable for irradiation simulation. This invention can be used for the development of potential functions for irradiation damage simulation of metallic materials.

[0029] Example 1 This embodiment provides a method for simulating the irradiation response of a Ti-Al-Nb-Zr-Mo pentagonal alloy based on a mixed potential function. Specifically, this method aims to construct a mixed potential function that can accurately describe the interactions between atoms from short-range high-energy collisions to medium- and long-range equilibrium states, and is particularly suitable for simulating the damage process of alloy materials under high-energy particle irradiation. In one embodiment of the invention, a Ti80 alloy (with an atomic percentage of Ti-6Al-3Nb-2Zr-1Mo) is used as an example for illustration. Figure 1 As shown, the method includes the following steps: Step S1: Obtain elemental parameters and establish a base file. Specifically, this step includes collecting the basic atomic parameters of the pure metallic elements in each component of the target alloy system. For the Ti-Al-Nb-Zr-Mo pentagonal alloy in this embodiment, it is necessary to collect the atomic number, atomic weight, stable lattice type at room temperature, and corresponding lattice constant of the five elements: titanium, aluminum, niobium, zirconium, and molybdenum. These data can usually be obtained from authoritative chemical physics handbooks, databases, or published scientific literature. The atomic parameters of the five elements in the Ti80 alloy are shown in Table 1 below: Table 1

[0030] Meanwhile, it is necessary to clarify the specific atomic ratio of the Ti80 alloy targeted in this embodiment, namely Ti accounts for 86.5%, Al accounts for 10.5%, Nb accounts for 1.5%, Zr accounts for 1.0%, and Mo accounts for 0.5%.

[0031] Furthermore, this step also includes collecting or determining the fitting parameters for the pure metals used to construct the initial embedded atom normal potential function. It is understood that the embedded atom normal potential function includes the embedding function, the electron density function, and the counter potential function, each defined by a specific set of parameters. These parameters are typically obtained by fitting a large amount of first-principles calculations or experimental data (such as cohesive energy, lattice constant, elastic constant, vacancy formation energy, etc.). In this embodiment, by consulting publicly available literature in the relevant field, fitting parameters suitable for describing the embedded atom normal potential function of these five pure metals can be obtained, including but not limited to: elemental charge number Z, cutoff radius related parameter r. c and f c Electron density related parameter ρ c and ρ s And several coefficients used to define the specific function form, as shown in Table 2 below: Table 2

[0032] The parameters collected for each element are compiled and organized into an alloy potential function base file according to the format required by the specific alloy potential function program, for example, named "Ti-Al-Nb-Zr-Mo.base", to ensure that the element order and parameter format are compatible with the alloy potential function program.

[0033] Step S2: Generate the initial embedded atom method EAM potential function. In this step, a specialized alloy potential function construction program is used to read the base file created in step S1. Based on the embedded atom method theoretical framework, this program combines and crosses the potential function parameters of the five pure metals to generate an initial embedded atom method potential function describing all interatomic interactions (including 5 pairs of like atoms and 10 pairs of unlike atoms) in the Ti-Al-Nb-Zr-Mo pentagonal alloy system. The output of this step is a potential function file conforming to a specific format (e.g., the EAM / alloy format compatible with LAMMPS molecular dynamics simulation software), which in this embodiment can be named "Ti-Al-Nb-Zr-Mo.eam.alloy".

[0034] After generating the initial potential function file, it must be validated to ensure its correctness and rationality. The validation process includes format validation and preliminary physical property validation. Format validation aims to check the header information of the generated ".eam.alloy" file, confirming that the order of declared elements is consistent with the order of data blocks in the file content, and verifying the correctness of metadata such as the number of data points and the truncation radius. Preliminary physical property validation uses this initial embedded atom normal potential function to predict the basic physical properties of the alloy, such as equilibrium lattice constant and elastic constant, through molecular dynamics simulations or lattice statics calculations, and compares the calculation results with known experimental values ​​or first-principles calculations. If the calculated values ​​are within an acceptable error range (e.g., 5-10%), it indicates that the initial embedded atom normal potential function can reasonably describe the properties of the alloy near the equilibrium state and can serve as the basis for subsequently constructing the mixed potential function.

[0035] Step S3: Calculate the short-range interaction of the ZBL potential function. Traditional embedded-atom potential functions are insufficiently accurate in describing high-energy repulsion interactions with extremely small interatomic spacings, which is crucial in irradiation damage simulations. Therefore, this invention introduces the ZBL (Ziegler-Biersack-Littmark) potential function specifically to describe the interactions in this short-range region. The constructed hybrid potential function employs different functional forms for different interatomic spacings r. The core task of this step is to calculate boundary conditions for subsequent smooth connectivity.

[0036] First, two key connection points need to be defined: the ZBL potential function-spline connection point R1 and the spline-EAM potential function connection point R2. R1 represents the maximum distance at which the ZBL potential function operates, and also the minimum distance at which the spline function operates; R2 represents the maximum distance at which the spline function operates, and also the minimum distance at which the embedded atom method potential function begins to operate. The selection of R1 and R2 requires a trade-off: R1 should not be too large to avoid the ZBL potential being used at inappropriately large spacings; R2 should not be too small to ensure that the embedded atom method potential can smoothly transition to its most accurately described equilibrium position.

[0037] Subsequently, it is necessary to analyze all 15 atomic interaction pairs in the Ti-Al-Nb-Zr-Mo pentagonal alloy system (such as...). Figure 3 As shown, calculate the ZBL potential function value at the connection point R1 for each of the following types: Ti-Ti, Al-Al, Nb-Nb, Zr-Zr, Mo-Mo, Ti-Al, Ti-Nb, Ti-Zr, Ti-Mo, Al-Nb, Al-Zr, Al-Mo, Nb-Zr, Nb-Mo, and Zr-Mo. and first derivative value This serves as a key boundary condition for subsequent spline function solving, ensuring the smooth and continuous potential energy across the entire interval. The ZBL potential function is calculated using the standard shielding function form:

[0038] in:

[0039] In the formula, Indicates the masking function. Indicates the shielding distance. Z1 and Z2 are the Bohr radius, which is approximately 0.529 Å.

[0040] To verify the accuracy of the constructed potential function in the short-range strong interaction region, Figure 2 The energy-distance relationship of Ti-Ti two-body interactions under different potential functions was compared. The figures show the performance of the ZBL universal shielding potential, the pure EAM potential, and the EAM Hybrid potential (i.e., spline splicing of ZBL and EAM) used in this paper across the entire range. The main figure shows that near the equilibrium distance (approximately 2.5–3.5 Å), the EAM Hybrid and pure EAM potentials completely coincide, ensuring the correct mechanical and thermodynamic properties of the material in the near-equilibrium state. However, in the extremely short-range region (<2.0 Å), the EAM potential, lacking a physical description of nucleus-nuclear repulsion, has significantly lower energy than the ZBL potential. This will lead to atoms getting too close during high-energy collisions, resulting in non-physical soft collision behavior. The inset plot magnifies the short-range region of 0.5–2.0 Å (the ordinate energy reaches the order of 10). 4 (eV) It can be clearly seen that the EAM Hybrid potential smoothly transitions the ZBL potential to the EAM potential through spline functions in the interval from R1=0.5 Å to R2=2.0 Å: within R1, the ZBL potential is used entirely to ensure correct repulsion at extremely high energies; outside R2, the EAM potential is fully restored to maintain equilibrium accuracy; the intermediate transition region (spline segment) is continuous and smooth, avoiding abrupt changes in force. This design allows the potential function to accurately describe the high-energy dislocation process in the initial stage of cascade collisions and correctly reflect the subsequent thermal peak evolution and defect recombination, providing a basis for... Figure 4 The observed physically consistent defect dynamics provide a reliable potential function basis.

[0041] Step S4: Solve for the spline function parameters connecting ZBL and EAM. This step constructs a smooth transition function, i.e., a spline function, within the interval (R1, R2). This spline function is continuous with the function values ​​and first derivatives of both the ZBL and EAM potentials at the connection points R1 and R2, thus avoiding abrupt changes in energy and force.

[0042] First, the boundary conditions for the embedded atom normal potential function at the connection point R2 need to be obtained. This requires extracting the potential component data for each atom pair from the initial embedded atom normal potential function file “Ti-Al-Nb-Zr-Mo.eam.alloy” generated in step S2. Since the value of R2 may not be one of the data points, numerical interpolation methods (such as cubic spline interpolation or Lagrange interpolation) are needed to calculate the exact potential function value at r=R2. and first derivative value .

[0043] Next, the form of the spline function is established. In this embodiment, a cubic polynomial is used as the spline function, with the following form:

[0044] Here, P1, P2, P3, and P4 are the four parameters to be solved. To solve for these four unknowns, four independent equations are needed. These four equations are constituted by the continuity conditions at the connection points R1 and R2, namely: The function value is continuous at R1: ; The first derivative is continuous at R1: ; The function value is continuous at R2: ; The first derivative is continuous at R2: .

[0045] Will Substituting the expression and its first derivative into the four boundary conditions above, we obtain a 4×4 linear system of equations for P1, P2, P3, and P4. For each atom pair, due to its , , , The values ​​of all atoms are already determined, so standard numerical methods (such as Gaussian elimination or matrix inversion) can be used to solve for the unique spline parameters {P1, P2, P3, P4} of this atom pair. This process requires solving for all 15 atom pairs (e.g., ... Figure 3 (As shown) Repeat the process to obtain 15 sets of spline parameters.

[0046] Step S5: Generate the mixed potential function data and keep it in a callable format. This step aims to integrate the previously calculated ZBL potential, spline function, and EAM potential into a unified potential function file. For different atomic interactions, generate the mixed potential function data as follows: when r ≤ R1, use the ZBL potential function value; when R1 < r < R2, use the value calculated by the spline function; when r ≥ R2, use the original EAM potential function value. Keep the format of the original EAM potential function file, including the file header information, embedding function data, electron density data, and the arrangement order of the pair potential data. That is, the new mixed potential function file needs to copy all the file header information, embedding function data block, and electron density function data block of the original "Ti-Al-Nb-Zr-Mo.eam.alloy" file, and only modify the pair potential data block.

[0047] When generating the new potential function file, a crucial detail is that the format of the original EAM / alloy file must be strictly maintained. In the pair potential data block, for each atomic pair, replace the original data within the atomic spacing range r ≤ R2 with the newly generated mixed potential data according to the above rules, while the pair potential data in the range r > R2 remains unchanged. In addition, the blank lines in the file, the scientific notation format of the numerical values, the column alignment, etc. must be exactly the same as the original file to ensure that the final generated file can be correctly parsed and called by molecular dynamics software such as LAMMPS.

[0048] Step S6: Output the mixed potential function file and parameter documentation. Output a final mixed potential function file, which can be named "ZBLSplineTi-Al-Nb-Zr-Mo.eam.alloy", and this file can be directly used in molecular dynamics simulations. At the same time, to facilitate users' understanding and reproduction, a supporting parameter documentation will be generated. This document details all the key information of the potential function construction in this time, including: the elements used (Ti, Al, Nb, Zr, Mo) and their compositions in the alloy; the specific values of the selected connection points R1 and R2; the complete list of spline function parameters {P1, P2, P3, P4} solved for all 15 atomic pairs; and an example of the calling method of this potential function in software such as LAMMPS, for example: pair_style eam / alloy pair_coeff * * ZBLSplineTi-Al-Nb-Zr-Mo.eam.alloy Ti Al Nb Zr Mo This command instructs LAMMPS to use the eam / alloy potential type and read the interaction potentials of the five elements Ti, Al, Nb, Zr, and Mo from the specified potential function file.

[0049] Step S7: Use the aforementioned mixed potential function to conduct molecular dynamics irradiation simulation of Ti-Al-Nb-Zr-Mo alloy, and output the lattice constant, elastic constant, vacancy formation energy, irradiation damage efficiency, and defect evolution law.

[0050] To verify the performance of the potential function constructed in this embodiment, an irradiation damage simulation can be performed. The simulation results are as follows: Figure 4 As shown, Figure 4 This paper demonstrates the evolution of the number of Frankel defect pairs generated after irradiation over time during the simulation period. A molecular dynamics approach was used, employing the potential function constructed in this embodiment to simulate the primary pKA (phasic off-site atom) cascade collision process. After the simulated system relaxed to equilibrium at a specific temperature, a kinetic energy was applied to a specific atom to simulate a PKA event. By analyzing the simulated trajectory, vacancies and interstitial atoms in the lattice were identified and counted using the Wigner-Seitz defect analysis method. Vacancies-interstitial atom pairs existing in the nearest-neighbor form were counted as Frankel defect pairs (FPs). The change in the number of defects was recorded from the start of the cascade collision (0 ps) until the system reached a new equilibrium state (approximately 30 ps).

[0051] Combination Figure 4 The curve showing the change in the number of Frankel defect pairs over time reveals a typical cascading collision evolution stage: Collision cascade stage (0 - approximately 0.5 ps): In a very short time, PKA collisions with lattice atoms trigger chain collisions, resulting in a large number of atoms being displaced. The Frankel defect log number rapidly climbs to the first peak (approximately 550 pairs), which is reflected in the sharp rise of the curve.

[0052] Recombination stage (approximately 0.5 ps - approximately 15 ps): As the cascaded thermal peaks form and quench, a large number of unstable interstitial atoms recombine with vacancies at close range. Figure 4 The curve drops sharply from its peak, then the rate of decline gradually slows. This indicates that high-energy defects undergo dramatic reorganization during the cooling process of the thermal peak.

[0053] Relaxation and stabilization phase (approximately 15 ps - 30 ps): The rate of decline in the curve flattens out, eventually reaching a relatively stable plateau around 140 pairs. The remaining defects in this part are stable Frankel defect pairs, which are difficult to recombine further due to their large distance from each other or the constraint of the lattice stress field.

[0054] Figure 4The defect evolution trend shown (initially increasing sharply, then decreasing abruptly, and finally stabilizing) perfectly matches the classical physical picture of cascade collisions. This simulation result demonstrates that the potential function constructed in this embodiment can correctly describe the collision process initiated by high-energy displaced atoms and the subsequent defect recombination behavior, and its predicted final number of remaining defects is reasonable.

[0055] Example 2 This embodiment aims to illustrate the universality of the potential function construction method disclosed in this invention. That is, the method is not only applicable to the specific Ti-Al-Nb-Zr-Mo pentagonal alloy in Example 1, but can also be applied to other multi-component alloy systems, especially the irradiation potential function construction of other complex-composition refractory high-entropy alloys or medium-entropy alloys.

[0056] In this embodiment, a typical refractory high-entropy alloy system, TiAlNbZrMo, is used as the object, and a potential function for irradiation damage simulation is constructed for its equiatomic ratio (20% each). The nominal composition of the alloy constructed in this embodiment is TiAlNbZr (equiatomic percentage), composed of five elements: Ti, Al, Nb, Zr, and Mo. The irradiation damage simulation is verified using the same potential function as in Example 1.

[0057] To examine the performance of this potential function under irradiation conditions, molecular dynamics was used to simulate the cascade collision process of 20 keV primary poloidal atoms (PKAs) in an equiatomic TiAlNbZrMo alloy. The simulated system contained approximately 500,000 atoms. After sufficient relaxation at 300 K, appropriate atoms were selected to impart kinetic energy along specific directions to trigger the cascade. The Wigner-Seitz method was used to identify and statistically analyze defect evolution, focusing on the change in the number of Frankel defect pairs (vacancy-interstitial atom pairs) over time.

[0058] Figure 5 The evolution curve of the Frankel defect logarithm over the simulation time is shown. The figure reveals a typical three-stage cascade collision pattern: in the initial collision phase (0-0.5 ps), the defect number rises sharply to a peak; subsequently, a thermal quenching phase (0.5-15 ps) occurs, where numerous unstable defects recombine, and the defect number rapidly decreases; after 15 ps, the system enters a relaxation and stabilization phase, where the defect number plateaus, ultimately leaving stable defects. This evolution pattern is qualitatively consistent with the simulation results of the Ti80 alloy in Example 1. Further comparative analysis shows that the size distribution and spatial correlation of defect clusters in alloys with equal atomic ratios also differ from those in traditional alloys, demonstrating that the method of this invention can accurately capture the irradiation response characteristics of alloys with different compositions.

[0059] This embodiment successfully applied the potential function constructed by the method of the present invention to a high-entropy alloy with an equiatomic ratio, TiAlNbZrMo, constructing a potential function suitable for irradiation damage simulation. Its reliability was verified through typical cascade simulations. The results show that this method is not only applicable to complex alloys with non-equiatomic ratios (such as Ti80 in Example 1), but also effectively handles high-entropy alloys with an equiatomic ratio, demonstrating good versatility and scalability. It provides a powerful tool for subsequent research on the irradiation behavior of high-entropy alloys in nuclear energy environments.

[0060] Those skilled in the art will understand that, besides implementing the system and its various devices, modules, and units provided by this invention in the form of purely computer-readable program code, the same functions can be achieved entirely through logical programming of the method steps, making the system and its various devices, modules, and units of this invention function in the form of logic gates, switches, application-specific integrated circuits, programmable logic controllers, and embedded microcontrollers. Therefore, the system and its various devices, modules, and units provided by this invention can be considered as a hardware component, and the devices, modules, and units included therein for implementing various functions can also be considered as structures within the hardware component; alternatively, the devices, modules, and units for implementing various functions can be considered as both software modules implementing the method and structures within the hardware component.

[0061] Specific embodiments of the present invention have been described above. It should be understood that the present invention is not limited to the specific embodiments described above, and those skilled in the art can make various changes or modifications within the scope of the claims, which do not affect the essence of the present invention. Unless otherwise specified, the embodiments and features described in this application can be arbitrarily combined with each other.

Claims

1. A method for simulating the irradiation response of a Ti-Al-Nb-Zr-Mo quinary alloy based on a mixed potential function, characterized in that, Including: Step S1: Obtain the parameters of five pure metal elements Ti, Al, Nb, Zr, and Mo and establish a base file for the alloy potential function; Step S2: Construct an alloy potential function program to generate an initial Ti-Al-Nb-Zr-Mo alloy embedded atom method potential function; Step S3: Calculate the short-range interaction of the ZBL potential function; Step S4: Solve the spline function parameters connecting the ZBL potential function and the embedded atom method potential function; Step S5: Generate mixed potential function data and maintain a callable format; Step S6: Output the mixed potential function file and parameter documentation; Step S7: Conduct molecular dynamics irradiation simulation of Ti-Al-Nb-Zr-Mo alloy using the said mixed potential function, and output the lattice constant, elastic constant, vacancy formation energy, irradiation damage efficiency, and defect evolution law.

2. The hybrid potential function based Ti-Al-Nb-Zr-Mo quinary alloy irradiation response simulation method of claim 1, wherein, The said Step S1 includes: Collect the atomic parameters of five elements Ti, Al, Nb, Zr, and Mo, including atomic number, atomic weight, and lattice constant; Based on the alloy potential function format, establish a base file containing five elements, and determine the alloy potential function parameters of the five elements through literature review and experimental data, including electron density function parameters, embedding function parameters, and pair potential function parameters.

3. The hybrid potential function based Ti-Al-Nb-Zr-Mo quinary alloy irradiation response simulation method of claim 1, wherein, The said Step S2 includes: Run the alloy potential function program, input the five-element alloy parameters, and generate an initial alloy embedded atom method potential function file; Verify whether the format of the generated potential function file is correct, including element order, number of data points, and cut-off radius parameter; Check the basic properties of the potential function, including whether the lattice constant and elastic constant match the experimental values.

4. The hybrid potential function based Ti-Al-Nb-Zr-Mo quinary alloy irradiation response simulation method of claim 1, wherein, The said Step S3 includes: Define the ZBL-spline connection point R1 and the spline-embedded atom method connection point R2; For atomic interaction of Ti-Al-Nb-Zr-Mo quinary alloy, ZBL potential function value and first derivative value at R1 are calculated, respectively.

5. The hybrid potential function based Ti-Al-Nb-Zr-Mo quinary alloy irradiation response simulation method of claim 1, wherein, The ZBL potential function is calculated using the following formula: Where, a0 is the Bohr radius, and Z1 and Z2 are atomic numbers.

6. The method for simulating the irradiation response of Ti-Al-Nb-Zr-Mo pentagonal alloy based on the mixed potential function according to claim 1, characterized in that, The step of solving the spline function parameters of the connection ZBL potential function and the embedded atom method potential function comprises: extracting the potential data from an initial embedded atom method potential function file for different atomic interactions, and calculating the embedded atom method potential function value at R2 through interpolation and the first derivative value ; Establish a spline function: And solve the parameters P1, P2, P3, and P4 through the following boundary conditions: 。 7. The hybrid potential function based Ti-Al-Nb-Zr-Mo quinary alloy irradiation response simulation method of claim 6, wherein, The said boundary conditions form a 4×4 linear equation system to solve the spline parameters.

8. The hybrid potential function based Ti-Al-Nb-Zr-Mo quinary alloy irradiation response simulation method of claim 1, wherein, The said Step S5 includes: For different atomic interactions, generate mixed potential function data. When the atomic spacing r ≤ R1, use the ZBL potential function value; when R1 < r < R2, use the value calculated by the spline function; when r ≥ R2, use the original embedded atom method potential function value; Maintain the format of the original embedded atom method potential function file, including file header information, embedding function data, electron density data, and the arrangement order of pair potential data, and maintain the blank lines and numerical format in the original file to ensure that the generated mixed potential function file is compatible with the molecular dynamics software.

9. The hybrid potential function based Ti-Al-Nb-Zr-Mo quinary alloy irradiation response simulation method of claim 1, wherein, The said Step S6 includes: Output the final mixed potential file; At the same time, output parameter documentation, record the spline parameters, connection point positions, and element information of all atomic interactions; and provide instructions on the calling method in the molecular dynamics software.

10. The method for simulating the irradiation response of Ti-Al-Nb-Zr-Mo pentagonal alloy based on the mixed potential function according to claim 1, characterized in that, The said method further includes a verification step: Verify the performance of the mixed potential function through molecular dynamics simulation, including calculating the lattice constant, elastic constant, vacancy formation energy, and irradiation damage generation efficiency, and compare with experimental data or other potential functions.

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