Based on phase-changeable Fe 50 Mn 30 Cr 10 Co 10 Atomic-level simulation method for phase transition of high entropy alloys

Abstract

The invention discloses a method based on phase-changeable Fe 50 Mn 30 Cr 10 Co 10 Atomic-scale simulation method for phase transition of high entropy alloys, using potential functions that can be used for molecular dynamics simulations, applied to metastable Fe 50 Mn 30 Cr 10 Co 10 Molecular dynamics simulation of phase transition of high entropy alloy. The basic form of the potential function is the EAM function form, which is modeled based on the meso-atom method and optimized by genetic algorithm. This potential function can effectively simulate the phase transition process in single crystal or polycrystalline configuration, which is of great significance for studying the phase transition mechanism of metastable phase-transformable high entropy alloys and accelerating the research and development of new materials.

Description

Technical Field

[0001] The present invention proposes a method suitable for metastable Fe 50 Mn 30 Cr 10 Co 10 Intermetallic atomic potential of high entropy alloys, applied to Fe 50 Mn 30 Cr 10 Co 10 Molecular dynamics simulations of high entropy alloys. Background Art

[0002] In recent years, high entropy alloys have attracted more and more attention from researchers due to their excellent physical and chemical properties such as high strength, high hardness, high temperature resistance and corrosion resistance, as well as their large composition tuning space due to their large number of constituent elements, generally four or more alloying elements, each element accounting for 5% to 35%. 50 Mn 30 Cr 10 Co 10 The high entropy alloy, because of its metastable face-centered cubic structure (FCC) at room temperature, will undergo phase transformation during deformation and become a more stable hexagonal close-packed structure (HCP). The martensitic phase transformation can not only effectively improve the plasticity of the alloy, but also because the newly generated HCP phase has fewer slip systems and higher strength, the metastable high entropy alloy often has both high strength and good plasticity.

[0003] The high strength and hardness of high entropy alloys greatly increase the experimental difficulty of directly observing material properties through traditional experimental methods (such as tensile tests). With the substantial increase in the computing power of computer central processing units (CPUs) and the continuous development of computational materials science, computational simulation methods have become one of the main ways to study the performance and structural changes of alloys. Among them, molecular dynamics (MD) simulations are increasingly used to study the performance of metal materials. Molecular dynamics simulations can simulate the deformation process of materials at the atomic scale, using simple potential functions to represent the interactions between atoms, and then observe in real time the various microstructural evolution processes of atoms during the deformation of materials. MD simulations have become a powerful tool for exploring the deformation mechanism of materials. The accuracy of MD simulation results is mainly determined by the interatomic interaction potential selected during the simulation process, that is, the potential function. For metal materials, the existing potential functions EAM, MEAM, LJ potential, etc. are mainly applicable to pure metals, binary or ternary alloys, which also limits MD simulations to ternary and lower metal materials. The wide variety of elements contained in high entropy alloys makes the development of high entropy alloy potential functions more difficult, which further limits the development of high entropy alloy MD simulation experiments. Among them, there is currently no specific50 Mn 30 Cr 10 Co 10 The potential function developed for high entropy alloys further limits the MD simulation of the high entropy alloys. Summary of the invention

[0004] In order to solve the problems of the prior art, the purpose of the present invention is to overcome the shortcomings of the prior art and provide a phase-changeable Fe 50 Mn 30 Cr 10 Co 10 Based on the EAM potential function framework, this paper develops an atomic-level simulation method for the phase transition process of high entropy alloys. 50 Mn 30 Cr 10 Co 10 Interatomic interaction potential during phase transition of high entropy alloys.

[0005] In order to achieve the above invention purpose, the present invention adopts the following technical solution:

[0006] 1. EAM potential function based on mesoatom method:

[0007] The establishment of the meso-atom molecular dynamics simulation method is based on the following two assumptions:

[0008] (1) Similarity assumption: If two systems have the same material parameters, such as lattice constant, elastic constant, stacking fault energy, etc., then the macroscopic mechanical properties of the two systems determined by these material parameters are consistent.

[0009] (2) Averaging assumption. When using the mesoatom method for molecular dynamics simulation, the specific spatial distribution of different metal elements is not distinguished. Instead, a virtual "mesoatom" is used to represent different alloy elements. The MD simulation is performed using a model composed of mesoatoms.

[0010] Based on the mesoatom method, high entropy alloys are simplified from the original four or more atoms to a virtual mesoatom, which greatly reduces the difficulty of optimizing the potential function.

[0011] Potential functions based on the EAM framework are widely used in MD simulations of metal materials. The EAM theory assumes that each atom in the system is embedded in a local uniform electron gas, which is basically similar to the researchers' description of atoms and their surroundings in metal materials. Therefore, based on the EAM method, the potential function is developed, and the total energy calculation expression of the potential function is:

[0012]

[0013] Where: E represents the total energy of the system; F(ρ i ) is the embedding energy of atom i; φ ij (r ij ) is the potential between atoms i and j; for the basic functions F(ρ) and φ(r) of the potential function, the specific form is:

[0014]

[0015]

[0016] Where: ρ represents the charge density, n, m, p represent the serial number of the optimization parameters, H represents the Heaviside optimization matrix, a 1 、a 2 、a 3 、a 4 、a 5 , b n 、c m，p 、r m are optimization parameters, r represents the radius node in the optimization process, r 0 Represents the cutoff radius of the potential function.

[0017] 2. Optimizing Potential Function

[0018] The potential function is iteratively optimized using a genetic algorithm. The optimization process uses the weighted least squares method to optimize the residual between the optimized value of the material parameter and the target value, and then obtains each parameter of the basis function. Therefore, the optimization process of the potential function can be transformed into a mathematical problem of finding the minimum value:

[0019]

[0020] Where: Z represents the optimized residual; W k represents the weight of the optimization amount k; K represents the total number of optimization amounts; and They represent the fitting result and optimization target of material parameter k respectively. The conjugate gradient method is used to find the minimum value of the residual in the optimization process, and the iterative process is as follows:

[0021] (1) Establish an initial population. Use a given set of basis functions for optimization and mark this set of parameter solutions as A.

[0022] (2) Use the weighted least squares method to optimize the residual between the fitted value and the target value until a possible minimum parameter solution B is found.

[0023] (3) Determine whether B is better than A. If the result is true, replace B with A.

[0024] (4) Add a white noise of appropriate size to each parameter in A and replace the original A with the obtained new solution.

[0025] (5) Repeat the process of (2)-(4) until the residual between the fitted value and the target value is less than the preset threshold, and save the individual information. Stop when the maximum population size is reached.

[0026] (6) Four individuals are selected from the population according to the roulette wheel method, and then the two individuals with the smallest residuals are selected for gene crossover and mutation, so as to obtain the initial parameter sister A of the next population. Then the process (2)-(5) is repeated until the set number of generations is reached.

[0027] The potential function optimization program is a self-written MATLAB program that performs iterative optimization.

[0028] 3. Screening of potential functions

[0029] Not all the potential functions obtained are usable. Therefore, we use the following three steps to screen the available potential functions:

[0030] (1) Read the potential function with a residual less than 0.25, draw the relevant function curve, and import each parameter of the parameter solution of the potential function into the database. Compare the error between the fitting value and the target value of each parameter in the potential function, and select the potential function with the smallest error of each parameter.

[0031] (2) The potential function obtained by screening is subjected to a tensile test using a 2nm×2nm×20nm nanowire configuration. This test can quickly determine whether the potential function has the ability to undergo a complete phase transition.

[0032] (3) For the phase-change potential function selected in step 2, a four-grain configuration of 34.6nm×30nm×2nm is used for tensile testing. This test can verify the stability of the potential function under complex working conditions. Because of the irregular arrangement of atoms in the grain boundary, especially for two atoms whose distance is less than the lattice constant, if the potential function is not stable enough, atomic aggregation or configuration explosion will occur.

[0033] The present invention utilizes a genetic algorithm program to perform iterative optimization and obtain a parameter solution of a potential function; then the obtained parameter solution is introduced into a basic equation of the potential function, and then the basic formula of the potential function is used to calculate the high entropy alloy material parameters, and the gap between the optimized amount and the target amount of the potential function model fitting the main material parameters of the HEA potential function is controlled; then the available potential functions are screened to complete the optimization process of the interatomic interaction potential function.

[0034] Preferably, the present invention is based on the phase-changeable Fe 50 Mn 30Cr 10 Co 10 Atomic-scale simulation method for phase transition of high entropy alloys, used to simulate metastable Fe 50 Mn 30 Cr 10 Co 10 The interatomic interaction potential parameters of the phase transition process in single crystal or polycrystalline configuration of high entropy alloy materials.

[0035] Compared with the prior art, the present invention has the following obvious outstanding substantive features and significant advantages:

[0036] 1. The potential function used in molecular dynamics simulation of the present invention is applied to metastable Fe 50 Mn 30 Cr 10 Co 10 Molecular dynamics simulation of phase transition process of high entropy alloy; the basic form of the potential function is the EAM function form, and the genetic algorithm is used to optimize the parameters; this potential function can effectively simulate the phase transition process in single crystal or polycrystalline configuration, which is of great significance for studying the phase transition mechanism of metastable phase-transformable high entropy alloys and accelerating the research and development of new materials.

[0037] 2. The method of the present invention is for Fe 50 Mn 30 Cr 10 Co 10 The potential function developed for high entropy alloys further promoted the MD simulation of the high entropy alloys. BRIEF DESCRIPTION OF THE DRAWINGS

[0038] Figure 1 This is a flow chart of potential function development of the present invention.

[0039] Figure 2 It is the basic equation curve of the potential function of the present invention. The illustrations (a), (b), and (c) are the energy-strain curves of the configuration along the

[100] ,

[010] , and

[001] directions for stretching and compression, respectively. The illustration (d) is the curve of the F function, (e) is the curve of the potential function, (f) is the Rose curve of the FCC phase, and the illustrations (g) and (h) are the optimization and target values ​​of the configuration energy cloud diagram of the HCP phase, respectively.

[0040] Figure 3 The tensile test results of the nanowire configuration of the present invention are as follows: the strain values ​​corresponding to the illustrations (a), (b), (c), (d), and (e) are 0.0%, 3.3%, 5.4%, 7.9%, and 10.%, respectively.

[0041] Figure 4These are the tensile test results for the four-grain configuration of the present invention: the strain values ​​corresponding to illustrations (a), (b), (c), (d), (e), and (f) are 0.0%, 4.0%, 8.0%, 12.0%, 18.5%, and 22.8%, respectively. DETAILED DESCRIPTION

[0042] The following is a further explanation of the potential function proposed by the present invention in conjunction with specific implementation examples to describe Fe 50 Mn 30 Cr 10 Co 10 The martensitic phase transformation process during the deformation of high entropy alloy. The preferred embodiment of the present invention is described in detail as follows:

[0043] Embodiment 1:

[0044] In this embodiment, based on the phase-changeable Fe 50 Mn 30 Cr 10 Co 10 The atomic-level simulation method of the phase transition process of high entropy alloys and the process of optimizing the potential function include the following steps:

[0045] The development process of the potential function is as follows Figure 1 As shown. First, a set of parameter solutions are substituted into the equations of the F function and the function:

[0046]

[0047]

[0048] Get the new function, and then according to the basic formula of EAM potential function:

[0049]

[0050] Calculate the target value of the material parameter. Then use the formula:

[0051]

[0052] Calculate the residual value and then follow Figure 1 The process is iteratively optimized using a genetic algorithm program. Table 1 shows the parameter solutions of the potential function proposed in this embodiment, and then this set of parameter solutions is used to bring into the basic equation of the potential function, and then the basic formula of the potential function is used to calculate the material parameters in Table 2.

[0053] Table 1. Parameter solutions of potential functions

[0054]

[0055] It can be seen from Table 2 that the gap between the optimized amount and the target amount of fitting the main material parameters of HEA by our potential function model is very small.

[0056] Table 2. Material parameters used for potential function fitting and their optimized and target quantities

[0057]

[0058] Moreover, for the optimal value of FCC and HCP phase energy, 71.0 meV / atom (E c_fcc -E c_hcp ) ensures the occurrence of phase transition. In addition, we also draw the stretching energy curves along the

[100] ,

[010] , and

[001] directions, the F function curve, the function curve, the Rose curve of FCC, and the Rose energy cloud diagram of HCP, such as Figure 2 As shown, the potential function file in HEA.eam.fs format is output for subsequent MD simulation. Figure 2 It can be seen that each curve is smooth and continuous. Especially for the energy optimization of FCC and HCP phases, it can be seen from Figures (f), (g) and (h) that the optimized quantities of the two phases we optimized are highly consistent with the target quantities, thus ensuring the stability of the two phases in the configuration.

[0059] Embodiment 2:

[0060] In this embodiment, the potential function obtained in the first embodiment is used, and uniaxial stretching is performed using a nanowire configuration, including the following steps:

[0061] (1) Construct the nanowire configuration file Atoms.lammps with a size of 2nm×2nm×20nm and orientations of X-

[100] , Y-

[010] , and Z-

[001]

[0062] (2) Write the lammps script, i.e., the in file, which mainly contains the following simulation parameters:

[0063] (2-1) Set the boundary conditions along the X-axis and Y-axis to free boundary conditions, and along the Z-axis to periodic boundary conditions.

[0064] (2-2) Set the system temperature to 10K.

[0065] (2-3) The potential function used is the mesoatom EAM potential function proposed in the present invention.

[0066] (2-4) Determine the ensemble to be a canonical ensemble (NVT).

[0067] (2-5) Set the time step to 0.001ps.

[0068] (2-6) Before simulation, the configuration was relaxed and the relaxation time was set to 20000 ps.

[0069] (2-7) Set the stretching direction to the Z axis, the maximum strain to 0.1, and the strain rate to 5×10 8 .

[0070] (3) Import the HEA.eam.fs potential function file and create a test case.

[0071] (4) Molecular dynamics simulation was performed using LAMMPS software.

[0072] (5) The simulation results were visualized using OVITO software, and the CNA algorithm was used to color the atoms in different structures.

[0073] The simulation results are as follows Figure 3 As shown in the figure, as the configuration is stretched, the number of white atoms representing the FCC phase continues to decrease, while the number of orange atoms representing the HCP phase continues to increase. Finally, the FCC phase in the configuration is almost completely transformed into the HCP phase.

[0074] Embodiment three:

[0075] This embodiment is basically the same as the second embodiment, and the difference between the two is that:

[0076] The configuration file used in the simulation was replaced with a four-grain model with a size of 34.6nm×30nm×2nm. For the LAMMPS calculation script: the boundary conditions in the X, Y, and Z axes were modified to periodic boundary conditions; the relaxation time was increased to 80,000ps; and the maximum strain was increased to 0.3.

[0077] Then a new example was created and the simulation results were calculated as follows Figure 4 As shown in the figure, as the deformation increases, FCC continuously transforms into HCP phase. Finally, most of the FCC phase transforms into HCP phase.

[0078] Embodiment 4:

[0079] The optimization method of the potential function of the atomic interaction in this embodiment is characterized by: using the basic equation of the potential function, drawing the curves of the basic functions F(ρ) function and φ(r) function of the potential function, using the energy curves of the configuration along the three crystal directions

[100] ,

[010] , and

[001] calculated by using this potential function, the Rose curve of FCC, and the energy cloud diagram of HCP. 50 Mn 30 Cr 10 Co 10The potential function developed for high entropy alloys further promoted the MD simulation of the high entropy alloys.

[0080] The above describes the embodiments of the present invention in conjunction with the accompanying drawings, but the present invention is not limited to the above embodiments. Various changes can be made according to the purpose of the invention. Any changes, modifications, substitutions, combinations or simplifications made according to the spirit and principle of the technical solution of the present invention should be equivalent replacement methods. As long as they meet the purpose of the invention and do not deviate from the technical principles and inventive concepts of the present invention, they belong to the protection scope of the present invention.

Claims

1. A phase-changeable Fe 50 Mn 30 Cr 10 Co 10 The atomic-level simulation method of the phase transition process of high entropy alloys is characterized by: For simulating Fe 50 Mn 30 Cr 10 Co 10 The molecular dynamics simulation of the phase change process of high entropy alloy materials is as follows: 1) Use the following basic functions F(ρ) and φ(r) of the potential function: Where: ρ represents the charge density, n, m, p represent the order of the optimization parameters, H represents the Heaviside optimization matrix, a1, a2, a3, a4, a5, b n 、c m,p 、r m They are all optimization parameters, r represents the radius node in the optimization process, and r0 represents the cutoff radius of the potential function; Given a set of parameter solutions, substitute them into the equations of the F(ρ) function and the φ(r) function to obtain a new function F(ρ i ),φ ij (r ij ) is, where F(ρ i ) is the embedding energy of atom i; φ ij (r ij ) is the pair potential between atoms i and j; 2) using a genetic algorithm program to perform iterative optimization to obtain a parameter solution of the potential function; then using the obtained parameter solution to bring the basic equation of the potential function in step 1), and then using the basic formula of the potential function to calculate the high entropy alloy material parameters, the gap between the optimization amount and the target amount of the potential function model for the main material parameter fitting of the HEA potential function; then screening the available potential functions to complete the optimization process of the interatomic interaction potential function; In step 2), the following steps are used to screen available potential functions: ① Read the potential function with a residual less than 0.25, draw the relevant function curve, and import each parameter of the parameter solution of the potential function into the database; compare the error between the fitting value and the target value of each parameter in the potential function, and select the potential function with the smaller error of each parameter; ② For the potential function obtained by screening, a 2nm×2nm×20nm nanowire configuration is used for tensile testing to quickly determine whether the potential function has the ability to undergo a complete phase transition; ③ For the phase-changeable potential function screened out in step ②, a tensile test is performed using a four-grain configuration of 34.6nm×30nm×2nm to verify the stability of the potential function under complex working conditions; thereby completing the screening process of the available potential functions.

2. According to claim 1, the phase-changeable Fe 50 Mn 30 Cr 10 Co 10 The atomic-level simulation method of the phase transition process of high entropy alloys is characterized by: In step 2), the potential function is iteratively optimized using a genetic algorithm, and the optimization process uses a weighted least square method to optimize the residual between the optimized value of the material parameter and the target value, and then obtain each parameter of the basis function; the optimization process of the potential function is converted into a mathematical problem of finding the minimum value: The target values ​​of material parameters are calculated according to the basic formula of the EAM potential function as follows: Where E represents the total energy of the system; F(ρ i ) is the embedding energy of atom i; φ ij (r ij ) is the potential between atom i and atom j; then use the following formula: Calculate the residual value; where Z represents the optimized residual; W k represents the weight of the optimization amount k; K represents the total number of optimization amounts; and They respectively represent the fitting results and optimization target quantity of the high entropy alloy material parameter K.

3. According to claim 2, the phase-changeable Fe 50 Mn 30 Cr 10 Co 10 The atomic-level simulation method of the phase transition process of high entropy alloys is characterized by: In step 2), the conjugate gradient method is used to find the minimum value of the residual, and the iterative process is as follows: (1) Establish an initial population and use a given set of basis functions for optimization. This set of parameter solutions is marked as A. (2) Use the weighted least squares method to optimize the residual between the fitted value and the target value until a possible minimum parameter solution B is found; (3) Determine whether B is better than A. If the result is true, replace B with A; (4) Add a white noise of appropriate size to each parameter in A and replace the original A with the obtained new solution; (5) Repeat the process of step (2) to step (4) until the residual between the fitted value and the target value is less than the preset threshold, and save the individual information; stop after reaching the maximum population number; (6) Select four individuals from the population using the roulette method, and then select the two individuals with the smallest residuals for gene crossover and mutation, thereby obtaining the initial parameter sister A of the next population; The process from step (2) to step (5) is then repeated until the set number of generations is reached.

4. The phase-changeable Fe-based 50 Mn 30 Cr 10 Co 10 The atomic-level simulation method of the phase transition process of high entropy alloys is characterized by: The interatomic interaction potential parameters used to simulate the phase transition process in single crystal or polycrystalline configuration of high entropy alloy materials.

5. The phase-changeable Fe-based 50 Mn 30 Cr 10 Co 10 The atomic-level simulation method of the phase transition process of high entropy alloys is characterized by: The specific values ​​of the optimization parameters in the function expression, including: a1, a2, a3, a4, a5, b n , where n = 0 to 2, c m,p Where m = 1 to 7, p = 3 to 5, r m Where m=1~7, the results are as follows: 。 6. The phase-changeable Fe-based 50 Mn 30 Cr 10 Co 10 The atomic-level simulation method of the phase transition process of high entropy alloys is characterized by: Using the basic equation of potential function, the fitting results of the main material parameters of high entropy alloy are as follows: 。 7. The phase-changeable Fe-based 50 Mn 30 Cr 10 Co 10 The atomic-level simulation method of the phase transition process of high entropy alloys is characterized by: Using the basic equation of the potential function, the curves of the basic functions F(ρ) function and φ(r) function of the potential function are plotted. The energy curves of tension and compression of the configuration along the three crystal directions [100], [010], and [001], the Rose curve of FCC, and the energy cloud diagram of HCP are calculated using this potential function.

Images