Machine learning construction method of irradiation damage potential function in transition metal carbide high-entropy ceramic

Abstract

The application discloses a machine learning construction method of irradiation damage potential function of transition metal carbide high-entropy ceramics, relates to the field of potential function construction, and is suitable for constructing interatomic potential functions of material systems serving in irradiation environments such as nuclear power plants and aerospace. In order to solve the problems that the transition metal carbide high-entropy ceramics are various in types, the materials are difficult to be characterized after neutron irradiation, and large-scale screening cannot be performed through experiments, the application proposes a method for constructing irradiation damage potential functions of transition metal carbide high-entropy ceramics according to DPGEN software, is suitable for describing the irradiation damage behaviors of multi-component carbide high-entropy ceramics and single-component carbides formed by random arrangement and combination of eight transition metal elements, and provides a theoretical basis for mechanism research of irradiation damage of the carbide high-entropy ceramic system and molecular dynamics simulation of other mechanical and thermal properties. The method can perform preliminary screening at low cost and high efficiency, and provide theoretical guidance for experiments.

Description

Technical Field

[0001] This invention relates to the field of potential function construction, and specifically to a machine learning method for constructing the irradiation damage potential function in high-entropy transition metal carbide ceramics. Background Technology

[0002] Transition metal carbide ceramics possess high hardness, high elastic modulus, low coefficient of thermal expansion, and good radiation resistance; however, their stability is poor, and under high-temperature, high-dose irradiation conditions, they are prone to phase transformation, elemental segregation, and other phenomena. The compositional complexity and severe lattice distortion of high-entropy materials can effectively slow down defect migration, increase the recombination rate of irradiated defects, and improve the radiation resistance of the materials. Therefore, transition metal carbide high-entropy ceramics are expected to become candidate materials for advanced nuclear energy systems. Currently, research on radiation resistance mainly focuses on high-entropy alloys, while research on high-entropy ceramics started later and progressed slowly. Only three systems—(ZrTaNbTi)C4, (WTiVNbTa)C5, and (WTiVNbTa)C5—have been reported to exhibit excellent radiation resistance. No phase transformation or amorphization was observed after ion irradiation, and the resistance to radiation swelling was significantly improved. Current experimental results demonstrate the feasibility of applying carbide ceramics in the field of radiation resistance. However, high-entropy ceramics are diverse, neutron sources are limited, and irradiated materials are difficult to characterize, making it challenging to screen for systems with good radiation resistance on a large scale through experiments. Therefore, researchers are attempting to use molecular dynamics to simulate the deformation behavior of materials after irradiation, thereby screening for systems with excellent radiation resistance. Traditional interatomic interaction potential functions are insufficient to accurately describe the interactions between atoms in multi-component systems after irradiation; therefore, research on the irradiation potential function of high-entropy ceramics has not yet been reported.

[0003] In recent years, the rapid development of machine learning potential field models has provided a possibility for solving this problem. Zhang Linfeng, Wang Han, and others have developed the deep potential energy generators DeepMD-Kit and DPGEN. Scholars have successfully constructed machine learning potential functions for the (ZrHfTiNbTa)C5 and (TiZrHfNbTa)B2 systems using this software. These functions can reproduce first-principles calculations with high accuracy and predict the thermal properties of the materials. Therefore, it is feasible to construct irradiation damage potential functions for high-entropy transition metal carbide ceramics using machine learning methods. The successful establishment of such potential functions is of great significance for molecular dynamics simulation studies of irradiation damage behavior in carbide ceramics and for the study of irradiation mechanisms in the field of high-entropy ceramics. Summary of the Invention

[0004] This invention addresses the challenge of the diverse types of high-entropy carbide ceramics and the difficulty in characterizing the radiation emitted after neutron irradiation, hindering large-scale experimental screening. Based on the DPGEN software, this invention proposes a method for constructing the irradiation damage potential function of transition metal carbide high-entropy ceramics. This method is applicable to describing the irradiation damage behavior of multi-component and single-component high-entropy carbide ceramics formed by random combinations of eight transition metal elements (Zr, Ti, Ta, Mo, W, V, Cr, Nb).

[0005] The machine learning method for constructing the irradiation damage potential function in high-entropy transition metal carbide ceramics of the present invention is carried out according to the following steps:

[0006] Step 1: Prepare initial data and ZBL potential function

[0007] ① Establishing a model

[0008] A disordered solid solution model of (ZrVNbCrTiTaMoW)C8 was established, and based on this model, a liquid phase structure model of (ZrVNbCrTiTaMoW)C8 and a disordered solid solution model of (ZrVNbCrTiTaMoW)C8 containing point defects were established.

[0009] Establish disordered solid solution models for five-element high-entropy ceramic carbides, six-element high-entropy ceramic carbides, and seven-element high-entropy ceramic carbides;

[0010] A monocomponent crystal structure model is established; the monocomponent crystal structure model is a NaCl-type monocomponent model.

[0011] The established (ZrVNbCrTiTaMoW)C8 disordered solid solution model, (ZrVNbCrTiTaMoW)C8 disordered solid solution model with point defects, pentagonal high-entropy ceramic carbide disordered solid solution model, hexaagonal high-entropy ceramic carbide disordered solid solution model, and heptagonal high-entropy ceramic carbide disordered solid solution model are crystal structure models.

[0012] The five-element high-entropy ceramic carbide disordered solid solution model is multiple and ensures that the model covers the eight elements Zr, V, Nb, Cr, Ti, Ta, Mo and W.

[0013] The six-element high-entropy ceramic carbide disordered solid solution model is multiple and ensures that the model covers the eight elements Zr, V, Nb, Cr, Ti, Ta, Mo and W;

[0014] The seven-element high-entropy ceramic carbide disordered solid solution model is multiple and ensures that the model covers the eight elements Zr, V, Nb, Cr, Ti, Ta, Mo and W;

[0015] ② Perform structural optimization and ab initio molecular dynamics relaxation on the (ZrVNbCrTiTaMoW)C8 disordered solid solution model, (ZrVNbCrTiTaMoW)C8 disordered solid solution model with point defects, (ZrVNbCrTiTaMoW)C8 liquid phase structure model, pentagonal high-entropy ceramic carbide disordered solid solution model, hexaagonal high-entropy ceramic carbide disordered solid solution model, heptagonal high-entropy ceramic carbide disordered solid solution model, and single-component crystal structure model established in step ① to obtain initial data as training potential functions;

[0016] ③ Calculate the short-range interaction energy of the dimer according to the ZBL formula, create a table of the close-range repulsion potentials of equally spaced atoms, and obtain the ZBL potential function;

[0017] Step 2: Training the potential function

[0018] The initial data obtained in step one is input into the DeePMD-kit package in the DPGEN software. After the DeePMD-kit package converts the data format, the starting and ending values ​​of the search radius for the distance between adjacent atoms are selected and input into the potential function network built by the TensorFlow framework in DPGEN for training, thus initializing the deep potential energy model, i.e., the DP (DeepPotential) model. The interpolation range is selected so that the DP model and the ZBL potential function can be smoothly connected using the DP-ZBL model included in the DPGEN software. Then, several DP-ZBL models are generated using different random number seeds. The principle for selecting the interpolation range is to enable a smooth connection between the DP model and the ZBL potential function and to accurately reflect the short-range interaction forces between atoms.

[0019] The initial value of the adjacent atom distance search radius is less than The cutoff value is the distance between the atom and its third nearest neighbor atom; the principle for selecting the initial value of the search radius for the distance between adjacent atoms is to be able to describe the short-distance interactions between atoms;

[0020] Step 3: Verify the accuracy of the potential function

[0021] The DP-ZBL model trained in step two was provided to the LAMMPS software to perform irradiation simulation on the (ZrVNbCrTiTaMoW)C8 crystal model.

[0022] If the DP-ZBL model can correctly simulate the thermal spike and steady-state stage of the material after irradiation, then a DP-ZBL model that can accurately describe the interatomic interaction potential in high-entropy carbide ceramics is obtained. Training is stopped. The DP-ZBL model that can accurately describe the interatomic interaction potential in high-entropy carbide ceramics is the potential function that can characterize the irradiation performance.

[0023] If a DP-ZBL model that can accurately describe the interatomic interaction potential in high-entropy carbide ceramics is not obtained, proceed to step four.

[0024] Step 4: Exploration and Labeling of Potential Function Models

[0025] Several DP-ZBL models from step two are used as interatomic interaction potentials to simultaneously perform molecular dynamics simulations on one or more crystal structure models constructed in step one, obtaining the maximum force deviation value of the atomic force of the model. The simulation temperature and pressure are set, and the range of predicted deviation values ​​of the DP-ZBL models is set as the upper and lower limits of the error criterion. Models with deviation values ​​within the upper and lower limits of the error criterion are selected as models that are expected to be improved, and these models are labeled. The labeled models are then calculated using DFT (Density Functional Theory) and added to the training dataset. Steps two and three are then performed until a potential function that can characterize the irradiation performance is obtained.

[0026] The beneficial effects of this invention are:

[0027] 1. This invention provides a method for training the irradiation potential function of high-entropy transition metal carbide ceramics, solving the problems of high cost and time consumption of first-principles calculation methods. It also addresses the difficulty of traditional potential functions in describing interatomic interactions in multi-component systems, particularly multi-component ceramic systems. This provides a feasible method for training the irradiation potential function of high-entropy ceramic materials, suitable for constructing interatomic potential functions for material systems used in irradiated environments such as nuclear power plants and aerospace.

[0028] 2. This invention can describe the behavior of internal atoms in a system after irradiation, such as close-range collisions, local melting, recrystallization, generation, migration, and recombination, at the atomic scale. It provides a theoretical basis for the study of the mechanism of irradiation damage in carbide high-entropy ceramic systems and the molecular dynamics simulation of other mechanical and thermal properties.

[0029] 3. Due to the wide variety of high-entropy transition metal carbide ceramics, and the difficulty in characterizing the radiation emitted after neutron irradiation, it is challenging to conduct large-scale experimental screening of systems with good radiation resistance. This invention can describe the interatomic interaction forces in a series of multi-element high-entropy transition metal carbide ceramic systems using a trained potential function, simulating the material irradiation damage process. This allows for low-cost and high-efficiency preliminary screening without the need for large-scale experimental screening, and provides theoretical guidance for experiments. Attached Figure Description

[0030] Figure 1 The graph shows the change in the number of Frenkel pairs generated after irradiation of the (ZrVNbCrTiTaMoW)C8 system in Example 1 as a function of irradiation time. Detailed Implementation

[0031] The technical solution of the present invention is not limited to the specific embodiments listed below, but also includes any reasonable combination of the specific embodiments.

[0032] Specific Implementation Method 1: The machine learning method for constructing the irradiation damage potential function in high-entropy transition metal carbide ceramics in this implementation method is carried out according to the following steps:

[0033] Step 1: Prepare initial data and ZBL potential function

[0034] ① Establishing a model

[0035] A disordered solid solution model of (ZrVNbCrTiTaMoW)C8 was established, and based on this model, a liquid phase structure model of (ZrVNbCrTiTaMoW)C8 and a disordered solid solution model of (ZrVNbCrTiTaMoW)C8 containing point defects were established.

[0036] Establish disordered solid solution models for five-element high-entropy ceramic carbides, six-element high-entropy ceramic carbides, and seven-element high-entropy ceramic carbides;

[0037] A monocomponent crystal structure model is established; the monocomponent crystal structure model is a NaCl-type monocomponent model.

[0038] The established (ZrVNbCrTiTaMoW)C8 disordered solid solution model, (ZrVNbCrTiTaMoW)C8 disordered solid solution model with point defects, pentagonal high-entropy ceramic carbide disordered solid solution model, hexaagonal high-entropy ceramic carbide disordered solid solution model, and heptagonal high-entropy ceramic carbide disordered solid solution model are crystal structure models.

[0039] The five-element high-entropy ceramic carbide disordered solid solution model is multiple and ensures that the model covers the eight elements Zr, V, Nb, Cr, Ti, Ta, Mo and W.

[0040] The six-element high-entropy ceramic carbide disordered solid solution model is multiple and ensures that the model covers the eight elements Zr, V, Nb, Cr, Ti, Ta, Mo and W;

[0041] The seven-element high-entropy ceramic carbide disordered solid solution model is multiple and ensures that the model covers the eight elements Zr, V, Nb, Cr, Ti, Ta, Mo and W;

[0042] ② Perform structural optimization and ab initio molecular dynamics relaxation on the (ZrVNbCrTiTaMoW)C8 disordered solid solution model, (ZrVNbCrTiTaMoW)C8 disordered solid solution model with point defects, (ZrVNbCrTiTaMoW)C8 liquid phase structure model, pentagonal high-entropy ceramic carbide disordered solid solution model, hexaagonal high-entropy ceramic carbide disordered solid solution model, heptagonal high-entropy ceramic carbide disordered solid solution model, and single-component crystal structure model established in step ① to obtain initial data as training potential functions;

[0043] ③ Calculate the short-range interaction energy of the dimer according to the ZBL formula (Ziegler-Biersack-Littmark, universal short-range repulsion potential), create a table of short-range repulsion potentials with equal atomic spacing, and obtain the ZBL potential function;

[0044] Step 2: Training the potential function

[0045] Input the initial data obtained in step one into the DeePMD-kit package in the DPGEN software. After the DeePMD-kit package converts the data format, select the starting and ending values ​​of the search radius for the distance between adjacent atoms and input them into the potential function network built by the TensorFlow framework in DPGEN for training, and initialize the deep potential energy model, i.e., the DP model. Select the interpolation range so that the DP model and the ZBL potential function can be smoothly connected using the DP-ZBL model that comes with the DPGEN software. Then, generate several DP-ZBL models using different random number seeds.

[0046] The initial value of the adjacent atom distance search radius is less than The cutoff value is the distance between the atom and its third nearest neighbor atom;

[0047] Step 3: Verify the accuracy of the potential function

[0048] The DP-ZBL model trained in step two was provided to the LAMMPS software to perform irradiation simulation on the (ZrVNbCrTiTaMoW)C8 crystal model.

[0049] If the DP-ZBL model can correctly simulate the thermal spike and steady-state stage of the material after irradiation, then a DP-ZBL model that can accurately describe the interatomic interaction potential in high-entropy carbide ceramics is obtained. Training is stopped. The DP-ZBL model that can accurately describe the interatomic interaction potential in high-entropy carbide ceramics is the potential function that can characterize the irradiation performance.

[0050] If a DP-ZBL model that can accurately describe the interatomic interaction potential in high-entropy carbide ceramics is not obtained, proceed to step four.

[0051] Step 4: Exploration and Labeling of Potential Function Models

[0052] Several DP-ZBL models from step two are used as interatomic interaction potentials to simultaneously perform molecular dynamics simulations on one or more crystal structure models constructed in step one, obtaining the maximum force deviation value of the atomic force of the model; the simulation temperature and pressure are set, and the range of predicted deviation values ​​of the DP-ZBL models is set as the upper and lower limits of the error criterion. Models with deviation values ​​within the upper and lower limits of the error criterion are selected as models with potential for improvement, and these models are labeled. After DFT calculation of the labeled models, they are added to the training dataset, and steps two and three are performed until a potential function that can characterize the irradiation performance is obtained.

[0053] This embodiment has the following beneficial effects:

[0054] 1. This embodiment provides a method for training the irradiation potential function of high-entropy transition metal carbide ceramics, which solves the problems of high cost and high time consumption of first-principles calculation methods. At the same time, it solves the problem that traditional potential functions are difficult to describe the interatomic interaction potential in multi-component systems, especially multi-component ceramic systems, and provides a feasible method for training the irradiation potential function of high-entropy ceramic materials.

[0055] 2. This implementation method can describe the behavior of internal atoms in a system after irradiation, such as close-range collisions, local melting, recrystallization, generation, migration, and recombination, at the atomic scale. It provides a theoretical basis for the study of the mechanism of irradiation damage in carbide high-entropy ceramic systems and the molecular dynamics simulation of other mechanical and thermal properties.

[0056] 3. Due to the wide variety of high-entropy transition metal carbide ceramics, and the difficulty in characterizing the radiation emitted after neutron irradiation, it is challenging to conduct large-scale experimental screening of systems with good radiation resistance. This implementation method can describe the interatomic interaction forces in a series of multi-element high-entropy transition metal carbide ceramic systems using a trained potential function, simulating the material irradiation damage process. This allows for low-cost and high-efficiency preliminary screening without the need for large-scale experimental screening, and provides theoretical guidance for experiments.

[0057] Specific Implementation Method Two: This implementation method differs from Specific Implementation Method One in that: the monocomponent crystal structure model mentioned in step one ① is a NaCl type monocomponent model, including ZrC, VC, NbC, CrC, TiC, TaC, MoC, and WC.

[0058] Specific Implementation Method 3: This implementation method differs from Specific Implementation Method 1 or 2 in that: the (ZrVNbCrTiTaMoW)C8 disordered solid solution model, the five-element high-entropy ceramic carbide disordered solid solution model, the six-element high-entropy ceramic carbide disordered solid solution model, and the seven-element high-entropy ceramic carbide disordered solid solution model mentioned in step 1① are established using the SQS module in ATAT software; the (ZrVNbCrTiTaMoW)C8 disordered solid solution model with point defects, the (ZrVNbCrTiTaMoW)C8 liquid phase structure model, and the single-component crystal structure model are established using VASP software.

[0059] Specific Implementation Method Four: This implementation method differs from one of the specific implementation methods one to three in that the structural optimization described in step one ② uses the init_bulk module in the DPGEN software.

[0060] Specific Implementation Method Five: This implementation method differs from Specific Implementation Methods One to Four in that the initial data mentioned in Step One ② includes the coordinates of the atoms, the energy of the atoms, the force, and the virial information.

[0061] Specific Implementation Method Six: This implementation method differs from Specific Implementation Methods One through Five in that: the embedded neural network in the deep potential energy model in step two has three layers, with the number of nodes in the three layers being 25, 50, and 100 respectively; the fitting neural network also has three layers, with the number of nodes in the three layers being 240, 240, and 240 respectively. The learning rate decays exponentially, and the starting learning rate, stopping learning rate, and decay step size are set to 0.001, 3.51e, and so on. -8 And 50.

[0062] Specific Implementation Method Seven: This implementation method differs from Specific Implementation Methods One through Six in that: in step two, four DP models are trained simultaneously using different random seeds for 800,000 steps.

[0063] Specific Implementation Method Eight: This implementation method differs from one of the specific implementation methods one to seven in that: in step four, molecular dynamics simulation is performed using lammps molecular dynamics software in the NVT ensemble or NPT ensemble.

[0064] Specific Implementation Method Nine: This implementation method differs from Specific Implementation Methods One to Eight in that the simulated temperature set in step four is 100K, 200K, 300K, 400K, 500K, 600K, 700K, 800K, 900K, or 1000K.

[0065] Specific Implementation Method 10: This implementation method differs from Specific Implementation Methods 1 to 9 in that the simulated pressure in step 4 is set to 1 standard atmosphere.

[0066] Example 1:

[0067] The machine learning method for constructing the irradiation damage potential function in transition metal carbide high-entropy ceramics in this embodiment is carried out according to the following steps:

[0068] Step 1: Prepare initial data and ZBL potential function

[0069] ① Establishing a model

[0070] A disordered solid solution model of (ZrVNbCrTiTaMoW)C8 was established, and based on this model, a liquid phase structure model of (ZrVNbCrTiTaMoW)C8 and a disordered solid solution model of (ZrVNbCrTiTaMoW)C8 containing point defects were established.

[0071] Establish disordered solid solution models for five-element high-entropy ceramic carbides, six-element high-entropy ceramic carbides, and seven-element high-entropy ceramic carbides;

[0072] A monocomponent crystal structure model is established; the monocomponent crystal structure model is a NaCl-type monocomponent model.

[0073] The established (ZrVNbCrTiTaMoW)C8 disordered solid solution model, (ZrVNbCrTiTaMoW)C8 disordered solid solution model with point defects, pentagonal high-entropy ceramic carbide disordered solid solution model, hexaagonal high-entropy ceramic carbide disordered solid solution model, and heptagonal high-entropy ceramic carbide disordered solid solution model are crystal structure models.

[0074] The five-element high-entropy ceramic carbide disordered solid solution model is multiple and ensures that the model covers the eight elements Zr, V, Nb, Cr, Ti, Ta, Mo and W.

[0075] The six-element high-entropy ceramic carbide disordered solid solution model is multiple and ensures that the model covers the eight elements Zr, V, Nb, Cr, Ti, Ta, Mo and W;

[0076] The seven-element high-entropy ceramic carbide disordered solid solution model is multiple and ensures that the model covers the eight elements Zr, V, Nb, Cr, Ti, Ta, Mo and W;

[0077] Step 1① The (ZrVNbCrTiTaMoW)C8 disordered solid solution model, the five-element high-entropy ceramic carbide disordered solid solution model, the six-element high-entropy ceramic carbide disordered solid solution model, and the seven-element high-entropy ceramic carbide disordered solid solution model were established using the SQS module in ATAT software; the (ZrVNbCrTiTaMoW)C8 disordered solid solution model with point defects, the (ZrVNbCrTiTaMoW)C8 liquid phase structure model, and the single-component crystal structure model were established using VASP software.

[0078] The monocomponent crystal structure model is a NaCl-type monocomponent model, including ZrC, VC, NbC, CrC, TiC, TaC, MoC, and WC.

[0079] ② Perform structural optimization and ab initio molecular dynamics relaxation on the (ZrVNbCrTiTaMoW)C8 disordered solid solution model, (ZrVNbCrTiTaMoW)C8 disordered solid solution model with point defects, (ZrVNbCrTiTaMoW)C8 liquid phase structure model, pentagonal high-entropy ceramic carbide disordered solid solution model, hexaagonal high-entropy ceramic carbide disordered solid solution model, heptagonal high-entropy ceramic carbide disordered solid solution model, and single-component crystal structure model established in step ① to obtain initial data as training potential functions;

[0080] The structural optimization was performed using the init_bulk module in the DPGEN software.

[0081] The initial data includes the coordinates of the atoms, their energy, forces, and virial information.

[0082] ③ Calculate the short-range interaction energy of the dimer according to the ZBL formula, create a table of closely spaced repulsive potentials between atoms, and obtain the ZBL potential function; where the range of atomic pair spacing is selected is... Step size is

[0083] Step 2: Training the potential function

[0084] The initial data obtained in step one is input into the DeePMD-kit package in the DPGEN software. The DeePMD-kit package converts the data format, selects the starting and ending values ​​for the search radius of adjacent atom distances, and inputs them into the potential function network built using the TensorFlow framework in DPGEN for training, initializing the deep potential energy model, i.e., the DP model; the interpolation range is selected as... The DP model and ZBL potential function are smoothly connected using the DP-ZBL model built into the DPGEN software. Then, several DP-ZBL models are generated using different random number seeds. The initial value of the search radius for the distance between adjacent atoms is... The cutoff value is

[0085] The embedded neural network in the deep potential energy model has three layers with 25, 50, and 100 nodes respectively; the fitting neural network also has three layers with 240, 240, and 240 nodes respectively. The learning rate decays exponentially, with the initial learning rate, stopping learning rate, and decay step size set to 0.001, 3.51e, and so on. -8 And 50. Train 4 DP models simultaneously using different random seeds for 800,000 steps;

[0086] Step 3: Verify the accuracy of the potential function

[0087] The DP-ZBL model trained in step two was provided to the LAMMPS software to perform irradiation simulation on the (ZrVNbCrTiTaMoW)C8 crystal model.

[0088] If the DP-ZBL model can correctly simulate the thermal spike and steady-state stage of the material after irradiation, then a DP-ZBL model that can accurately describe the interatomic interaction potential in high-entropy carbide ceramics is obtained. Training is stopped. The DP-ZBL model that can accurately describe the interatomic interaction potential in high-entropy carbide ceramics is the potential function that can characterize the irradiation performance.

[0089] The method for judging whether the DP-ZBL model can correctly simulate the thermal spike and steady-state stage of the material after irradiation is as follows: After irradiating the (ZrVNbCrTiTaMoW)C8 crystal model with LAMMPS software, the change of the number of Frenkel pairs generated by irradiation with irradiation time is statistically analyzed. If the curve of the number of Frenkel pairs as a function of time first increases sharply and then decreases, and finally tends to stabilize, it is considered that the thermal spike and steady-state stage of the material after irradiation can be correctly simulated.

[0090] If a DP-ZBL model that can accurately describe the interatomic interaction potential in high-entropy carbide ceramics is not obtained, proceed to step four.

[0091] Step 4: Exploration and Labeling of Potential Function Models

[0092] Several DP-ZBL models from step two are used as interatomic interaction potentials to simultaneously perform molecular dynamics simulations on one or more crystal structure models constructed in step one, obtaining the maximum force deviation values ​​of the atomic forces in the models; the simulation temperature and pressure are set, and the range of predicted deviation values ​​of the DP-ZBL models is set as the upper and lower limits of the error criterion. Models with deviation values ​​within the upper and lower limits of the error criterion were selected as promising models for improvement, totaling 100. These models were then labeled, and the labeled models were added to the training dataset after DFT calculation. Steps two and three were then performed to obtain a potential function that can characterize the irradiation performance.

[0093] The molecular dynamics simulations were performed using LAMMPS molecular dynamics software in the NVT ensemble.

[0094] The simulated temperatures are set to 100K, 200K, 300K, 400K, 500K, 600K, 700K, 800K, 900K, and 1000K.

[0095] The simulated pressure is set to 1 standard atmosphere.

[0096] After multiple rounds of training, the calculation results of LAMMPS software and first-principles calculations were compared, as shown in Table 1. The lattice constants calculated by both methods were highly consistent, and the elastic constants were also very close, with the maximum relative error being less than 30%, which can correctly describe the interatomic interactions in high-entropy carbide ceramics. The error of the C-Frenkel pair of formation energy related to irradiation performance was only 0.13 eV, and it could correctly simulate the thermal spike and steady-state stage after material irradiation. Thus, the DP-ZBL model, which can accurately describe the interatomic interaction potential in high-entropy carbide ceramics, was obtained. Training was stopped, and a potential function characterizing the irradiation performance was obtained.

[0097] Table 1 shows the lattice constants, elastic constants, and Frenkel's DFT (first principles) and MD (LAMMPS molecular dynamics software) calculations of the formation energy for the ZrVNbCrTiTaMoW)C8 system.

[0098] Table 1

[0099]

[0100] Using the same computer system and number of cores, and at the same temperature, first-principles molecular dynamics relaxation and MD relaxation using the DP-ZBL model were performed on the same octagonal crystal model. It was found that the computation time required for 1 fs of first-principles molecular dynamics relaxation was 108 seconds, while the computation time required for 1 fs of MD relaxation using the DP-ZBL model was only 0.0252 seconds, approximately four orders of magnitude faster than first-principles calculations. This fully demonstrates the superior efficiency of this invention compared to first-principles calculations.

[0101] Irradiation performance testing: The irradiation damage behavior of the (ZrVNbCrTiTaMoW)C8 system was simulated using LAMMPS software with a trained potential function. The Ti atom at the center of the crystal model was selected as the PKA atom, and the incident energy was set to 2 keV with the incident direction as follows. <001> Direction. Energy-imported PKA atoms collide short distances with atoms within the material, causing atomic displacement, disrupting the material's normal structure, and generating numerous point defects. Due to the excessively high local temperature in the cascade collision region, local melting occurs in this area, corresponding to the thermal spike stage of the cascade process. As irradiation time increases, unstable point defects migrate to lower energy locations, most interstitial atoms recombine with vacancies, the molten region recrystallizes, the number of point defects decreases significantly, and eventually stabilizes, reaching the steady-state stage of the cascade process. The change in the number of Frenkel pairs generated after irradiation with irradiation time is as follows: Figure 1As shown, the irradiation process exhibits both a thermal spike stage and a steady-state stage within the cascade collision process, verifying the accuracy of the potential function. The thermal spike stage is reached approximately 0.25 ps after irradiation, at which point the number of defect pairs peaks at approximately 10⁷. With prolonged irradiation time, vacancies and interstitial atoms recombine, leading to a significant decrease in the number of defect pairs, eventually stabilizing at approximately 30. Furthermore, small-sized defect clusters were observed in the irradiated model, but no dislocation loops were observed, indicating that the (ZrVNbCrTiTaMoW)C8 system possesses good radiation resistance.

Claims

1. A machine learning method for constructing the irradiation damage potential function in high-entropy transition metal carbide ceramics, characterized in that: The machine learning method for constructing the irradiation damage potential function in high-entropy transition metal carbide ceramics follows these steps: Step 1: Prepare initial data and ZBL potential function ① Establishing a model A disordered solid solution model of (ZrVNbCrTiTaMoW)C8 was established, and based on this model, a liquid phase structure model of (ZrVNbCrTiTaMoW)C8 and a disordered solid solution model of (ZrVNbCrTiTaMoW)C8 containing point defects were established. Establish disordered solid solution models for five-element high-entropy ceramic carbides, six-element high-entropy ceramic carbides, and seven-element high-entropy ceramic carbides; A monocomponent crystal structure model is established; the monocomponent crystal structure model is a NaCl-type monocomponent model. The established (ZrVNbCrTiTaMoW)C8 disordered solid solution model, (ZrVNbCrTiTaMoW)C8 disordered solid solution model with point defects, pentagonal high-entropy ceramic carbide disordered solid solution model, hexaagonal high-entropy ceramic carbide disordered solid solution model, and heptagonal high-entropy ceramic carbide disordered solid solution model are crystal structure models. The five-element high-entropy ceramic carbide disordered solid solution model is multiple and ensures that the model covers the eight elements Zr, V, Nb, Cr, Ti, Ta, Mo and W; The six-element high-entropy ceramic carbide disordered solid solution model is multiple and ensures that the model covers the eight elements Zr, V, Nb, Cr, Ti, Ta, Mo and W; The seven-element high-entropy ceramic carbide disordered solid solution model is multiple and ensures that the model covers the eight elements Zr, V, Nb, Cr, Ti, Ta, Mo and W; ② Perform structural optimization and ab initio molecular dynamics relaxation on the (ZrVNbCrTiTaMoW)C8 disordered solid solution model, (ZrVNbCrTiTaMoW)C8 disordered solid solution model with point defects, (ZrVNbCrTiTaMoW)C8 liquid phase structure model, pentagonal high-entropy ceramic carbide disordered solid solution model, hexaagonal high-entropy ceramic carbide disordered solid solution model, heptagonal high-entropy ceramic carbide disordered solid solution model, and single-component crystal structure model established in step ① to obtain initial data as training potential functions; ③ Calculate the short-range interaction energy of the dimer according to the ZBL formula, create a table of close-range repulsive potentials with equal atomic spacing, and obtain the ZBL potential function; Step 2: Training the potential function Input the initial data obtained in step one into the DeePMD-kit package in the DPGEN software. After the DeePMD-kit package converts the data format, select the starting and ending values ​​of the search radius for the distance between adjacent atoms and input them into the potential function network built by the TensorFlow framework in DPGEN for training, and initialize the deep potential energy model, i.e., the DP model. Select the interpolation range so that the DP model and the ZBL potential function can be smoothly connected using the DP-ZBL model that comes with the DPGEN software. Then, generate several DP-ZBL models using different random number seeds. The initial value of the adjacent atom distance search radius is less than The cutoff value is the distance between the atom and its third nearest neighbor atom; Step 3: Verify the accuracy of the potential function The DP-ZBL model trained in step two was provided to the LAMMPS software to perform irradiation simulation on the (ZrVNbCrTiTaMoW)C8 crystal model. If the DP-ZBL model can correctly simulate the thermal spike and steady-state stage of the material after irradiation, then a DP-ZBL model that can accurately describe the interatomic interaction potential in high-entropy carbide ceramics is obtained. Training is stopped. The DP-ZBL model that can accurately describe the interatomic interaction potential in high-entropy carbide ceramics is the potential function that can characterize the irradiation performance. If a DP-ZBL model that can accurately describe the interatomic interaction potential in high-entropy carbide ceramics is not obtained, proceed to step four. Step 4: Exploration and Labeling of Potential Function Models Several DP-ZBL models from step two are used as interatomic interaction potentials to simultaneously perform molecular dynamics simulations on one or more crystal structure models constructed in step one, obtaining the maximum force deviation value of the atomic force of the model; the simulation temperature and pressure are set, and the range of predicted deviation values ​​of the DP-ZBL models is set as the upper and lower limits of the error criterion. Models with deviation values ​​within the upper and lower limits of the error criterion are selected as models with potential for improvement, and these models are labeled. After DFT calculation of the labeled models, they are added to the training dataset, and steps two and three are performed until a potential function that can characterize the irradiation performance is obtained.

2. The machine learning method for constructing the irradiation damage potential function in high-entropy transition metal carbide ceramics according to claim 1, characterized in that: Step 1① The monocomponent crystal structure model is a NaCl type monocomponent model, including ZrC, VC, NbC, CrC, TiC, TaC, MoC, and WC.

3. The machine learning method for constructing the irradiation damage potential function in high-entropy transition metal carbide ceramics according to claim 1, characterized in that: Step 1① The (ZrVNbCrTiTaMoW)C8 disordered solid solution model, the five-element high-entropy ceramic carbide disordered solid solution model, the six-element high-entropy ceramic carbide disordered solid solution model, and the seven-element high-entropy ceramic carbide disordered solid solution model were established using the SQS module in ATAT software; the (ZrVNbCrTiTaMoW)C8 disordered solid solution model with point defects, the (ZrVNbCrTiTaMoW)C8 liquid phase structure model, and the single-component crystal structure model were established using VASP software.

4. The machine learning method for constructing the irradiation damage potential function in high-entropy transition metal carbide ceramics according to claim 1, characterized in that: Step 1② describes structural optimization using the init_bulk module in the DPGEN software.

5. The machine learning method for constructing the irradiation damage potential function in high-entropy transition metal carbide ceramics according to claim 1, characterized in that: The initial data mentioned in step one ② includes the coordinates of the atoms, their energy, force, and virial information.

6. The machine learning method for constructing the irradiation damage potential function in high-entropy transition metal carbide ceramics according to claim 1, characterized in that: In step two, the embedded neural network in the deep potential energy model has three layers with 25, 50, and 100 nodes respectively; the fitting neural network also has three layers with 240, 240, and 240 nodes respectively. The learning rate decays exponentially, with the initial learning rate, stopping learning rate, and decay step size set to 0.001, 3.51e, and so on. -8 And 50.

7. The machine learning method for constructing the irradiation damage potential function in high-entropy transition metal carbide ceramics according to claim 1, characterized in that: Step 2: Train 4 DP models simultaneously using different random seeds for 800,000 steps.

8. The machine learning method for constructing the irradiation damage potential function in high-entropy transition metal carbide ceramics according to claim 1, characterized in that: Step 4: Perform molecular dynamics simulations using LAMMPS molecular dynamics software in the NVT or NPT ensemble.

9. The machine learning method for constructing the irradiation damage potential function in high-entropy transition metal carbide ceramics according to claim 1, characterized in that: Step four describes setting the simulated temperature to 100K, 200K, 300K, 400K, 500K, 600K, 700K, 800K, 900K, and 1000K.

10. The machine learning method for constructing the irradiation damage potential function in high-entropy transition metal carbide ceramics according to claim 1, characterized in that: Step four describes setting the simulated pressure to 1 standard atmosphere.

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