Method for calculating diffusion coefficient and atomic mobility parameter of impurities in high-temperature alloy

Abstract

The application relates to a calculation method of a high-temperature alloy impurity diffusion coefficient and an atomic mobility parameter based on a molecular dynamics simulation, which comprises the following steps: parameter setting; model establishment; setting a potential function as a multicomponent EAM alloy potential; energy minimization and setting an initial atomic speed; calculating RDF values of a model system and drawing RDF curves; calculating MSD values of all atoms and respectively outputting MSD values of various atomic groups according to various different metal atom types; defining thermodynamic physical quantity output and commanding each step to output and save; giving a random initial speed to the system, and running under each system in three stages: a temperature rising stage, a temperature keeping stage and continuous temperature keeping and relaxation, and outputting MSD values; calculating the impurity diffusion coefficient of the system based on the MDS values; and taking the measured impurity diffusion coefficient as an input value, and obtaining the atomic mobility parameter through DICTRA software. Compared with the prior art, the application has the advantages of simple method, accurate numerical value and the like.

Description

Technical Field

[0001] This invention relates to the field of computational metallurgy, and in particular to a method for calculating the impurity diffusion coefficient and atomic mobility parameters of high-temperature alloys based on molecular dynamics simulations. Background Technology

[0002] High-temperature alloys, due to their excellent high-temperature strength, good resistance to oxidation and hot corrosion, creep and fatigue resistance, and fracture toughness, meet the requirements of hot-end components of turbojet engines, especially turbine blades, for high-temperature resistance and stress resistance. They are widely used in hot-end components of advanced propulsion systems such as turbojet engines, and also serve as high-temperature corrosion-resistant components in industrial gas turbines, energy, and chemical industries. During the service life of these materials (especially at high temperatures), the stability of their structure and performance often depends on the diffusion process. The diffusion coefficient is a very important physical property of materials, and diffusion kinetics is a crucial theoretical foundation in materials design; however, diffusion experiments are cumbersome and time-consuming. Therefore, by consciously suppressing the diffusion process, it is possible to promote the formation of some non-equilibrium phases and microstructures, thereby producing materials with superior performance.

[0003] However, the diffusion coefficient needs to be obtained through a large number of diffusion experiments. Due to the complicated and time-consuming experimental strategies, it is difficult to obtain the diffusion coefficient quickly and in a timely manner. At the same time, there are also conditions that make simulation experiments difficult or impossible to perform, making it difficult to obtain an accurate result. Summary of the Invention

[0004] The purpose of this invention is to provide a method for calculating the diffusion coefficient and atomic mobility parameters of impurities in high-temperature alloys based on molecular dynamics simulations. The diffusion coefficient is obtained through molecular dynamics, and then the atomic mobility parameters, which are very important in the development of diffusion databases, are obtained. The model parameters are obtained by fitting the CALPHAD method and molecular dynamics simulation data. The DICTRA module is used for further optimization and evaluation, which can effectively avoid the measurement of cumbersome and time-consuming diffusion experiments, and simulate the conditions that are difficult or impossible to perform in experiments, so as to obtain results that are closer to the actual system.

[0005] The objective of this invention can be achieved through the following technical solutions:

[0006] A method for calculating the impurity diffusion coefficient and atomic mobility parameters of high-temperature alloys based on molecular dynamics simulations includes the following steps:

[0007] Step 1) Parameter settings: Model using Lammps software, with metal atoms as the model atoms, three-dimensional spatial dimension, periodic boundary conditions, and settings for simulation time step, iteration step, and nearest neighbor parameters.

[0008] Step 2) Model building: Use the lattice command to define the lattice constant and atomic positions using a custom method, and define the model size and atomic replacement ratio, while setting the atomic types and relative atomic masses;

[0009] Step 3) Set the potential function to the multi-element EAM (embedded atom model) alloy potential;

[0010] Step 4) Minimize energy and set initial atomic velocities;

[0011] Step 5) Calculate the RDF (radial distribution function) values ​​of the model system using the compute RDF command and plot the RDF curve;

[0012] Step 6) Calculate the MSD (mean-squared displacement) value of all atoms, and output the MSD value of each group of atoms according to the different types of metal atoms;

[0013] Step 7) Define the thermodynamic physical quantities to be output and use the thermo_style command to output each physical quantity at each step and save the value of each physical quantity. The thermodynamic physical quantities include the number of simulation steps, system temperature, system volume, system pressure, and total system energy.

[0014] Step 8) Give the system a random initial velocity and run it in three stages under each ensemble: heating stage - holding stage - continuous holding and relaxation, and output the MSD value;

[0015] Step 9) Calculate the impurity diffusion coefficient of the system based on the MDS value;

[0016] Step 10) Use the measured impurity diffusion coefficient as the input value to obtain the atomic mobility parameter through DICTRA software.

[0017] In step 1), the periodic boundary condition is the PPP boundary, the simulation time step is set to 0.001 units (Ps), the number of iteration steps is set to every 1 delay 0, and the number of nearest neighbors is set to 2 bins.

[0018] In step 4), energy minimization adopts the cg mode, where the minimum energy value is set to 1e. -15 The minimum energy of the system is obtained after running a preset number of steps.

[0019] In step 4), the specific parameters for setting the initial atomic velocity are: temperature is 100K, and the random number seed is any integer greater than 1,000,000.

[0020] Step 6) specifically involves: calculating the MSD values ​​of all atoms and various types of atoms using the compute MSD command. There are four calculation results, which are stored in the C_msd[1~4] array. The first three vectors are the MSD values ​​in the x, y, and z directions, respectively, and the fourth is the total mean square displacement. The results are output once every preset number of steps, and the dump command is used to output and save the total number of atoms and the mean square displacement MSD values ​​of each group of atoms.

[0021] In step 6), when calculating MSD, the com option is set to yes, which means that the effect of any drift in the center of mass of the atom group will be subtracted before calculating the displacement of each atom.

[0022] In step 8), the temperature rises from 300K to 1600K during the heating stage, the temperature is 1600K during the holding stage, and the temperature is 1600K during the continuous holding and relaxation stage. The first two stages run for 50Ps under the NPT ensemble. Each step is completed by using the unfix command to end the previous step, making each process independent of each other.

[0023] In step 9), in a cubic lattice, atomic diffusion is equivalent in 6 directions, with a determinant of 1 / 6, and the impurity diffusion coefficient D of composition j is... j * Through equation D j * =MSD / 6t, where t is the diffusion time and MSD is the mean square displacement.

[0024] In step 9), the MSD value obtained in step 8) is plotted to obtain the change curve of the simulation step number and the mean square displacement of the particle motion. The value is taken in the stable diffusion range, and a linear interval of the MSD is selected to determine the diffusion coefficient.

[0025] In step 10), the data obtained from molecular dynamics simulation, namely the self-diffusion coefficient of pure metals and the impurity diffusion coefficient of binary alloys, are input into DICTRA software, and atomic mobility parameters are output to optimize the dynamics database.

[0026] Compared with the prior art, the present invention has the following beneficial effects:

[0027] 1. This invention utilizes molecular dynamics to concisely and clearly output the dynamic process of an alloy's temperature rise and hold-up changes, while also easily calculating information such as the alloy's temperature field, MSD value, and RDF curve. The diffusion coefficient is obtained through formulas, leading to the kinetic properties such as atomic mobility parameters, thereby inferring the diffusion process between atoms in the stable binary alloy. The calculated impurity diffusion coefficient is then combined with the CALPHAD method, and the binary alloy system under study is kinetically optimized using DICTRA software. Model parameters are obtained by fitting the CALPHAD method and molecular dynamics simulation data, resulting in a new kinetic database containing atomic mobility parameters. Comparison of these results with experimental values ​​shows a consistent trend.

[0028] 2. This invention is applicable not only to binary alloys but also to the calculation of impurity diffusion coefficients in single-phase multi-component high-temperature alloys. The simulation calculation process of this invention is simple and numerically accurate. By using molecular dynamics calculations, it effectively avoids the cumbersome and time-consuming diffusion experiments and simulates conditions that are difficult or impossible to perform in experiments, obtaining results that more closely resemble the actual system. It is applicable not only to binary alloy systems but also to multi-component alloy systems, various compound materials, semiconductor materials, etc. This method provides a convenient approach to calculating impurity diffusion coefficients and a sound theoretical simulation foundation for studying the diffusion process of alloy materials. It can further investigate the impact of the diffusion process on the material's structure and performance stability during service, contributing to the preparation of materials with superior performance. Attached Figure Description

[0029] Figure 1 This is a flowchart of the method of the present invention;

[0030] Figure 2 This is a crystal model diagram of pure Ni metal atoms established in the embodiments of the present invention;

[0031] Figure 3 This is a crystal model diagram of Ni and Fe atoms established in the embodiments of the present invention;

[0032] Figure 4 This is a crystal model diagram of Ni and Co atoms established in the embodiments of the present invention;

[0033] Figure 5 This is an Arrhenius plot comparing pure Ni with experimental values ​​obtained from an optimized database in an embodiment of the present invention;

[0034] Figure 6 This is an Arrhenius plot comparing pure Co with experimental values ​​obtained from the optimized database in this embodiment of the invention;

[0035] Figure 7This is an Arrhenius plot comparing pure Fe with experimental values ​​obtained from an optimized database in an embodiment of the present invention;

[0036] Figure 8 This is an Arrhenius plot showing the change of the impurity diffusion coefficient of Fe in fcc Ni as a function of temperature in an embodiment of the present invention.

[0037] Figure 9 This is a curve showing the variation of the tracer diffusion coefficient of Ni in a NiCo binary alloy at 1600K with the composition range in an embodiment of the present invention.

[0038] Figure 10 This is a curve showing the variation of the tracer diffusion coefficient of Co in a NiCo binary alloy at 1600K with the composition range in an embodiment of the present invention. Detailed Implementation

[0039] The present invention will now be described in detail with reference to the accompanying drawings and specific embodiments. These embodiments are based on the technical solution of the present invention and provide detailed implementation methods and specific operating procedures. However, the scope of protection of the present invention is not limited to the following embodiments.

[0040] This embodiment provides a method for calculating the impurity diffusion coefficient and atomic mobility parameters of high-temperature alloys based on molecular dynamics simulations, such as... Figure 1 As shown, it includes the following steps:

[0041] Step 1) Parameter settings: Model using Lammps software, with metal atoms as the model atoms, and the spatial dimension set to three dimensions. Use periodic boundary conditions and set the simulation time step, number of iterations, and atomic nearest neighbor parameters.

[0042] In step 1), the periodic boundary condition is PPP boundary, the simulation time step is set to 0.001 units (Ps), the number of iteration steps is set to every 1 delay 0, and the number of nearest neighbors is set to 2 bins.

[0043] Step 2) Model building: Use the lattice command to define the lattice constant and atomic positions using a custom method, and define the model size and atomic replacement ratio, while setting the atomic types and relative atomic masses.

[0044] This embodiment uses the lattice constant as... ( Taking Ni (with length units of angstroms) as the matrix as an example, the atomic positions are randomly distributed Ni and Co atoms, and the simulated size is 20 unit cells in each of the X, Y, and Z directions. like Figure 2As shown, the atom-filled region is a cube that fills the entire model. Using the Atomsk software, a certain number of Ni atoms are randomly replaced with Co atoms via command line to create a NiCo binary alloy model, as shown below. Figure 3 As shown in the diagram, light-colored spheres represent Ni atoms, and dark-colored spheres represent Fe atoms; a NiFe binary alloy model is established by randomly replacing a certain number of Fe atoms, as shown below. Figure 4 As shown in the diagram, light-colored spheres represent Ni atoms, and dark-colored spheres represent Co atoms. The replaced atoms are randomly distributed, and the atomic-filled areas are cubes that fill the entire model. There are three types of atoms: Ni, Co, and Fe. Their relative atomic masses are: Ni 58.693, Co 58.933, and Fe 55.845, respectively. The crystal structure is an FCC structure, and the cube size is 20 unit cells.

[0045] Step 3) Set the potential function to the embedded atom model (EAM) alloy potential to accurately predict the interactions between atoms in the material. This potential function provides a reasonable interpretation of the interactions between metal atoms and the elastoplastic deformation behavior.

[0046] Step 4) Minimize energy and set the initial atomic velocity.

[0047] In this embodiment, energy minimization adopts the cg mode, where the minimum energy value is set to 1e. -15 The minimum energy of the system is obtained after running 100,000 steps.

[0048] The specific parameters for setting the initial atomic velocity are: temperature 100K, and random number seed selected as any integer greater than 1,000,000.

[0049] Step 5) Calculate the RDF (radial distribution function) value of the model system using the compute RDF command. Calculate once every 100 steps and save it separately as a txt text file using the fix command. Plot the RDF curve based on the data in the txt file.

[0050] Step 6) Calculate the MSD (mean-squared displacement) value of all atoms using the compute MSD command. There are four calculation results, which are stored in the C_msd[1~4] array. The first three vectors are the MSD in the x, y, and z directions, respectively, and the fourth is the total mean square displacement. Output once every 10,000 steps, and use the dump command to output and save the mean square displacement MSD of the total number of atoms and each group of atoms.

[0051] When calculating MSD, setting the com option to yes means that the effect of any drift in the center of mass of the atom group will be subtracted before calculating the displacement of each atom.

[0052] Step 7) Define the output of thermodynamic physical quantities and use the thermo_style command to output each physical quantity at each step and save the value of each physical quantity. The thermodynamic physical quantities include the simulation step number, system temperature temp, system volume vol, system pressure press, and system total energy etotal.

[0053] Step 8) Give the system a random initial velocity and run it in three stages under each ensemble: heating stage - holding stage - continuous holding and relaxation, and output the MSD value.

[0054] Specifically, the temperature rises from 300K to 1600K during the heating phase, the temperature is 1600K during the holding phase, and the temperature is 1600K during the continuous holding and relaxation phase. The first two phases run for 50Ps under the NPT ensemble. Each step is completed by using the unfix command to end the previous step, making each process independent of the others.

[0055] Step 9) Calculate the impurity diffusion coefficient of the system based on the MDS value.

[0056] Specifically, the MSD value obtained in step 8) is used to plot the change curve between the number of simulation steps and the mean square displacement of particle motion. Values ​​are taken within the stable diffusion range, and a linear interval of the MSD is selected to determine the diffusion coefficient. This step is completed using Origin software for data processing. The horizontal axis t represents diffusion time, and the vertical axis MSD represents the mean square displacement.

[0057] In an FCC cubic lattice, atomic diffusion is equivalent in six directions, with a coefficient of determination of 1 / 6. The impurity diffusion coefficient D of composition j is... j * Through equation D j * =MSD / 6t, where t is the diffusion time and MSD is the mean square displacement.

[0058] Step 10) Use the measured impurity diffusion coefficient as the input value to obtain the atomic mobility parameter through DICTRA software.

[0059] Specifically, using DICTRA software, the data obtained from molecular dynamics simulations are input, namely the self-diffusion coefficient of pure metals and the impurity diffusion coefficient of binary alloys, and the atomic mobility parameters are output.

[0060] In this embodiment, a kinetic database can also be established, storing atomic mobility parameters. The atomic mobility parameters optimized using the above method are then added to the database for further optimization. It can be observed that the diffusion curves of the kinetic database obtained after optimization using molecular dynamics methods, varying with the composition range, show a consistent trend with the experimental values.

[0061] Furthermore, based on the Arrhenius equation D = D0exp(Q / RT), an Arrhenius plot showing the linear correlation between temperature and diffusion coefficient was obtained using the optimized kinetic database. The constants D0 and Q can be determined from the diffusion coefficient at different temperatures, as shown below. Figure 5 , 6 Figures 7 and 8 show the Arrhenius plots for pure Ni, Co, and Fe, respectively. It can be seen that the trend of temperature variation is consistent with the experimental data. Figure 5 In the comparison experiment 1, the experimental results were obtained from "A curvature in the arrhenius plot for the diffusion of iron in single crystals of nickel in the temperature range from 1200 to 1400℃" published by Bakker et al. Comparison method 1 was obtained from the results obtained by optimizing diffusion experimental parameters in "Thermodynamic assessment of the Co-Fe-Ni system and diffusion study of its fcc phase" published by Xia et al. Comparison method 2 was obtained from... The results obtained after parameter optimization in the paper "Ferromagnetic ordering and diffusion of carbon and nitrogen in bcc Cr-Fe-Nialloys" published by et al. Figure 6 In the comparison experiment 2, the experimental results published by Bussmann et al. in "Isotopeeffect and self-diffusion in face-centred cubic cobalt" were used as reference, and the results obtained by the comparison method 3 after parameter optimization were published by Cui et al. in "Computational study of atomic mobility for fcc phase of Co-Fe and Co-Ni binaries". Figure 7In the comparative experiment 3, the experimental results published by Heumman et al. in "Self-diffusion and isotope effect in γ-iron" were used as a reference.

[0062] Simultaneously, the variation of the impurity diffusion coefficient of Fe in FCC Ni with temperature was determined as follows: Figure 8 As shown, the trend is consistent with the experimental comparison; finally, taking the NiCo binary alloy as an example, the curves of the variation of the tracer diffusion coefficients of Ni and Co in the FCC NiCo alloy with the composition range are plotted as follows: Figure 9 , Figure 10 As shown, the results are close to the experimental values, and the trend remains consistent. Figure 8 In the lower left corner, experimental value 4 is compared to the experimental results obtained by Neiman et al. in "Issledovanie diffuzii zheleza v zhelezo-nikelevykh splavakh"; experimental value 5 is compared to the experimental results obtained by Guiraldenq et al. in "Influence des impuretes et de lastucture fritee sur les coefficients de diffusion en volume et aux joints desgrains du fer dans le nickel"; and experimental value 6 is compared to the results obtained by Badia and Vignes et al. in 1967 (M. Badia, A. Vignes, CRAcad Sci, Paris, Serraika). The experimental results obtained in Chron.264(1967)1528e1531.) are as follows: experimental value 7 is the result obtained by Badia and Vignes et al. in 1969 (see https: / / doi.org / 10.1016 / 0001-6160(69)90138-2); experimental value 8 is the result obtained by referring to the content published by Bakker et al. in "Acurvature in the arrhenius plot for the diffusion of iron in singlecrystals of nickel in the temperature range from 1200 to 1400℃"; experimental value 9 is the result obtained by referring to the content published by Kuznetsov in "Uchenye Zapiski Gor'k Gos"; and experimental value 10 is the result obtained by referring to the content published by Million et al. in "Diffusion processes in the Fe-Ni system".

[0063] The preferred embodiments of the present invention have been described in detail above. It should be understood that those skilled in the art can make numerous modifications and variations based on the concept of the present invention without creative effort. Therefore, all technical solutions that can be obtained by those skilled in the art based on the concept of the present invention through logical analysis, reasoning, or limited experimentation on the basis of existing technology should be within the scope of protection defined by the claims.

Claims

1. A method for calculating an impurity diffusion coefficient and an atomic mobility parameter of a high-temperature alloy based on a molecular dynamics simulation, characterized by, The method comprises the following steps: Step 1) parameter setting: modeling is carried out by using the Lammps software, model atoms are metal atoms, the space dimension is set to three dimensions, a periodic boundary condition is used, and simulation time steps, iteration steps, and atomic neighbor parameters are set; Step 2) model establishment: the lattice constant and atomic position are defined by using a self-defined method of a lattice command, and the model size and atomic replacement ratio are demarcated, and the atomic species and relative atomic mass are set; Step 3) setting a potential function as a multicomponent EAM alloy potential; Step 4) energy minimization and setting of an initial atomic velocity; Step 5) calculating the RDF value of the model system by using a compute RDF command, and drawing an RDF curve; Step 6) calculating the MSD value of all atoms, and outputting the MSD value of each atomic group according to different metal atomic species; The step 6) is specifically: the MSD values of all atoms and each atomic group are calculated by using a compute MSD command, and the calculation results are saved in C_msd[1~4] arrays, the first three vectors are the MSDs in x, y and z directions, and the fourth is the total mean square displacement; the total number of atoms and the mean square displacement MSD of each atomic group are output and saved every preset step by using a dump command; wherein, the com option is set to yes when calculating the displacement of each atom, which means that the influence of any drift in the atomic group center of mass will be subtracted before the displacement of each atom is calculated; Step 7) defining the output of thermodynamic physical quantities and outputting and saving the values of each physical quantity by using a thermo_style command every step, wherein the thermodynamic physical quantities include simulation steps, system temperature, system volume, system pressure, and system total energy; Step 8) giving the system a random initial velocity, and running in three stages under each ensemble: a temperature rising stage, a temperature maintaining stage, and a continuous temperature maintaining and relaxation stage, and outputting the MSD value; Step 9) calculating the impurity diffusion coefficient of the system based on the MDS value; Step 10) taking the measured impurity diffusion coefficient as an input value, and obtaining an atomic mobility parameter by using a DICTRA software.

2. The method of claim 1, wherein the method is characterized by, In the step 1), the periodic boundary condition is a PPP boundary, the simulation time step is set to 0.001, the unit is Ps, the iteration step is set to every 1 delay 0, and the number of atomic neighbors is set to 2 bin.

3. The method of claim 1, wherein the method is characterized by: In the step 4), the energy minimization adopts a cg mode, wherein the energy minimum value is set as 1e -15 , and the system minimum energy is obtained after running a preset number of steps.

4. The method of claim 1, wherein the method is characterized by, In the step 4), the setting parameters of the initial atomic velocity are specifically: the temperature is 100 K, and the random number seed is an arbitrary integer greater than 1000000.

5. The method of claim 1, wherein the method is characterized by: In the step 8), the temperature is raised from 300 K to 1600 K in the temperature rising stage, the temperature is 1600 K in the temperature maintaining stage, and the temperature is 1600 K in the continuous temperature maintaining and relaxation stage, and the first two stages are run under an NPT ensemble for 50 Ps, and the running of the previous step is ended by using an unfix command after each step is completed, so that each process is independent of each other.

6. The method of claim 1, wherein the method is characterized by: In the step 9), in the cubic lattice, the atomic diffusion is equivalent in 6 directions, the determination coefficient is 1 / 6, the impurity diffusion coefficient D j * The equation D j * is calculated, wherein t is the diffusion time, and MSD is the mean square displacement.

7. The method of claim 1, wherein the method is characterized by: In step 9), the MSD value obtained in step 8) is plotted to obtain a curve of the simulated step number and the change of the mean square displacement of the particle movement, and a stable diffusion interval is taken, a linear interval of the MSD is taken, and the diffusion coefficient is determined.

8. The method of claim 1, wherein the method is based on molecular dynamics simulation. In step 10), the DICTRA software is used to input the data obtained by the molecular dynamics simulation, that is, the self-diffusion coefficient of the pure metal and the impurity diffusion coefficient of the binary alloy, and the atomic mobility parameter is output, and the kinetic database is optimized.

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