Method for calculating diffusion activation energy in high-entropy alloy powder metallurgy process

Abstract

The present application belongs to the field of powder metallurgy diffusion activation energy calculation, in particular to a kind of high-entropy alloy powder metallurgy process diffusion activation energy calculation method.The specific steps of the present application are as follows: S1, first, parameters are set in molecular dynamics simulation software, and the atomic model of each atom constituting the alloy is constructed;S2, potential function is selected, and the atomic model of each atom is energy minimized to obtain the alloy model;S3, parameters in the simulation calculation process of the alloy model are set, and temperature rising simulation, temperature holding simulation and temperature dropping simulation are carried out in turn to obtain output data;S4, the parameter values of the fitting formula are obtained by data processing the output data;S5, the parameter values are substituted into the diffusion activation energy calculation formula to obtain the diffusion activation energy calculation formula at each temperature stage.The present application can accurately predict the diffusion coefficient at each moment and avoid the influence of temperature change.

Description

Technical Field

[0001] This invention belongs to the field of diffusion activation energy calculation in powder metallurgy, and particularly relates to a method for calculating diffusion activation energy in high-entropy alloy powder metallurgy. Background Technology

[0002] Hydrogen energy, a clean energy source with zero carbon dioxide emissions, has attracted widespread attention worldwide. Hydrogen energy technology mainly includes four stages: hydrogen production, storage, transportation, and application. Hydrogen storage, as the intermediate link between hydrogen production and application, is also a key bottleneck restricting the rapid development of the hydrogen energy industry. Hydrogen storage methods mainly include high-pressure gaseous storage, cryogenic liquid storage, and solid-state materials. Among these, compared to physical storage methods such as high-pressure gaseous and cryogenic liquid storage, solid-state hydrogen storage (metal hydride hydrogen storage) has advantages such as high volumetric hydrogen storage density, high stability of the hydrogen storage process, good safety, and high flexibility. Furthermore, it does not require harsh conditions such as high pressure and low temperature, and is considered a very promising hydrogen storage technology for the future. However, solid-state hydrogen storage heavily relies on the development and utilization of hydrogen storage materials, and faces problems such as high raw material costs, complex preparation processes, temperature requirements for hydrogen absorption and desorption, and unclear hydrogen storage mechanisms. Therefore, the design and synthesis of new room-temperature hydrogen storage materials with high hydrogen storage capacity remains a challenging task.

[0003] Currently, hydrogen storage alloys with reversible hydrogen absorption / desorption properties at near room temperature mainly include rare earth-based alloys, TiFe-based alloys, TiMn-based alloys, and V-based BCC solid solution alloys. In recent years, high-entropy alloys (HEAs) have gradually become a research hotspot in solid-state hydrogen storage. HEAs are novel multi-component materials composed of five or more elements, with each element's content ranging from 5-35 mol%. Their novel alloying strategy, based on the concept of multi-component (multi-principal element) alloys, is more conducive to alloying design. HEAs possess advantages such as high hydrogen storage capacity, mild hydrogen absorption / desorption conditions, and fast rates, making them a research hotspot for next-generation high-capacity hydrogen storage alloy materials. However, the melting point, density, atomic radius, electronegativity, and mixing enthalpy of the components in HEAs vary significantly. Compositional segregation during preparation leads to poor local atomic structure uniformity. The presence of non-equilibrium structures and inhomogeneous phase structures affects hydrogen storage performance, including hydrogen storage capacity, plateau pressure, and hydrogen absorption / desorption kinetics. Therefore, the preparation technology urgently needs optimization research. Powder metallurgy, as a solid-phase material forming technology, has the characteristics of low time consumption and low energy consumption. It can be used to prepare materials with special structures and properties that are difficult to prepare by traditional smelting methods. It can directly make alloy materials obtain finer grains and more uniform structure, eliminate casting defects, and the synthesis process does not require high temperature (below the melting point). It can effectively solve the phenomenon of volatilization of some low melting point metals caused by the large difference between the melting point and boiling point of metals.

[0004] Activation energy is the energy required for crystal atoms to migrate from their equilibrium positions to a new equilibrium or non-equilibrium position. It is also called "activation energy." It is the energy required to initiate a physicochemical process (such as plastic flow, atomic diffusion, chemical reaction, vacancy formation, etc.). This energy can be provided by the energy fluctuations inherent in the system itself or by external factors. The smaller the activation energy, the easier the process is to proceed. Currently, diffusion activation energy is an important physical property for evaluating and predicting atomic diffusion behavior in solid-state diffusion processes in powder metallurgy. However, high-entropy alloys involve many variables in powder metallurgy processes, such as element types, powder particle size, temperature, and time, making it difficult to accurately predict and calculate atomic diffusion behavior during sintering. Currently, the Arrhenius empirical formula can be used to calculate the diffusion activation energy in atomic diffusion processes, but this formula only applies to cases where the temperature is constant or changes only slightly, and cannot fully reflect the diffusion activation energy of the entire powder metallurgy process. Furthermore, when the temperature exceeds 500 K, the activation energy is no longer constant. In the sintering process of high-entropy hydrogen storage alloy powder metallurgy, the temperature usually needs to be heated to above 1500K, followed by a certain holding time. Therefore, the diffusion activation energy in the sintering process of high-entropy hydrogen storage alloy powder metallurgy changes continuously with the temperature.

[0005] The Arrhenius equation, established by the Swedish scientist Arrhenius, is an empirical formula relating the chemical reaction rate constant to temperature. Its differential form is shown in equation (1).

[0006]

[0007] k is the rate constant, R is the molar gas constant, T is the thermodynamic temperature, and Ea is the activation energy. The Arrhenius empirical formula assumes that the activation energy Ea is a constant independent of temperature, which agrees with experimental results within a certain temperature range. In reality, when the temperature fluctuates significantly, the diffusion activation energy is no longer a constant but changes with temperature. Therefore, the Arrhenius formula cannot obtain a relatively accurate diffusion activation energy. Summary of the Invention

[0008] To overcome the shortcomings of the prior art, this invention provides a method for calculating the diffusion activation energy in high-entropy alloy powder metallurgy. This invention can accurately predict and obtain the diffusion coefficient at every moment, avoiding the influence of temperature changes.

[0009] To achieve the above objectives, the present invention adopts the following technical solution:

[0010] A method for calculating the diffusion activation energy in high-entropy alloy powder metallurgy, the specific steps of which are as follows:

[0011] S1. First, set the parameters in the molecular dynamics simulation software and then construct the atomic models of each atom that makes up the alloy.

[0012] S2. Select the potential function to set the interaction relationship between each atom, and perform energy minimization processing on the atomic model of each atom to obtain the alloy model;

[0013] S3. Set the parameters for the alloy model simulation calculation process, and perform heating simulation, heat preservation simulation and cooling simulation in sequence to obtain output data;

[0014] S4. Process the output data to obtain the MSD curve and fitting formula, and obtain the parameter values ​​of the formula through the fitting formula. The fitting formula is as follows:

[0015]

[0016] In the formula, y represents the average square displacement, which is the square of the average displacement of a particle or molecule over a period of time; x represents the simulation time, in ps or s; A, B1, B2, and B3 are all parameters related to powder particle size, temperature, and time, and the values ​​of each parameter can be obtained sequentially through curve fitting.

[0017] S5. Substitute the parameter values ​​obtained in step S4 into the diffusion activation energy calculation formula to obtain the diffusion activation energy for the heating process, the holding process, and the cooling process. The calculation formula is as follows:

[0018] Heating process:

[0019]

[0020] Insulation process:

[0021]

[0022] Cooling process:

[0023]

[0024] In the formula, E a For diffusion activation energy, T max S represents the holding temperature, S represents the actual number of simulation steps, S1 represents the total number of steps set for the heating process, S2 represents the total number of steps set for the holding process, S3 represents the total number of steps set for the cooling process, R represents the molar gas constant, and A, B1, B2, and B3 are parameters related to powder particle size, temperature, and time, which are obtained by fitting the corresponding MSD curve.

[0025] Preferably, in step S1, the parameter settings include setting the boundary conditions to periodic boundary conditions, setting the atom type to atomic (this is a specific definition for metal atoms in LAMMPS, indicating that each atom in the simulation is considered an independent and indivisible unit. This means that each atom is considered to have specific atomic properties, such as position, velocity, mass, etc., and their interactions are described by force field parameters. This is different from other types of atom representations (such as molecules, clusters, etc.), which combine multiple atoms together to form more complex units. In the atomic type, each atom in the system is considered to be independent of each other, and their interactions are described by the force field used in the simulation), and setting the simulation time step to 1fs = 10. -3 ps=10 -15 Set the atomic nearest neighbor parameter to 2bin and set neigh_modify to every 2delay 0.

[0026] `neigh_modify` is a command in LAMMPS used to modify and control the behavior of the neighbor atom list. The neighbor atom list refers to the list of other atoms within the interaction range around each atom. The `neigh_modify` command allows you to adjust how these lists are built, updated, and used to more effectively simulate the interactions of the system.

[0027] `every 2` indicates that the neighbor list is recalculated every two time steps. This parameter allows LAMMPS to control the frequency of neighbor list updates during simulation, rather than recalculating it at every step.

[0028] delay 0: indicates that the recalculation of the neighbor list is not delayed. This means that when recalculating every 2 time steps, the recalculation of the neighbor list begins immediately without waiting for additional time steps.

[0029] Therefore, this command tells LAMMPS to update the list of neighboring atoms every two time steps during the simulation and to start calculating the update immediately without delay.

[0030] Preferably, in step S1, the lattice constant of the atomic model is In the atomic model, the particle size of each atom is 1-50 nm, and the size of the atomic model is more than twice the size of the region where the atom is located.

[0031] Preferably, in step S2, the potential function is a multibody potential function, the formula of which is as follows:

[0032]

[0033] Where E is the multibody potential function, F i The intercalation energy generated by the background electron density, S ij Φ is the masking function. ij This represents the interaction energy between two atoms.

[0034] Preferably, the energy minimization process alternates between CG mode and SD mode, with the minimum energy value set to 1e in both modes. -7 The minimum energy of the system is obtained after running 100,000 steps; the initial temperature of the alloy model is 300K, and the random number seed for the initial temperature is any natural number greater than 10,000.

[0035] Preferably, in step S3, the parameters in the alloy model simulation calculation process include the number of simulation steps, heating temperature, holding temperature, cooling temperature, and ensemble settings.

[0036] Preferably, in step S3, the output data includes the simulation step number step, the system temperature temp of the alloy model, the total potential energy pe of the alloy model, the total kinetic energy ke of the alloy model, the total energy etotal of the alloy model, the pressure, the single-atom temperature, the atomic coordinate information of the heating simulation stage, the atomic coordinate information of the holding simulation stage, and the atomic coordinate information of the cooling simulation stage; single-atom temperature = KE / (1.5 / KB), the kinetic energy of a single atom KE = ke / atom, where ke is the total kinetic energy of the alloy model, and atom is the total number of atoms; the constant KB is defined as 8.625e -5 Use the dump command to output atomic coordinate information.

[0037] Preferably, the ensembles for the heating process, the heat preservation process, and the cooling process are all set as NVT systems.

[0038] Preferably, the initial temperature of the heating process is 273K-300K, the final temperature of the heating process is 1500K-1800K, and the heating simulation step size is 50000-500000; the holding temperature is 1500K-1800K; the initial temperature of the cooling process is 1500K-1800K, the cooling simulation step size is 50000-500000, and the final temperature of the cooling process is 273K-300K.

[0039] Preferably, in step S1, the molecular dynamics simulation software used is LAMMPS software; in step S4, Python code is used to process the output data; and Origin data processing software is used to plot the MSD curve and perform curve fitting to obtain the fitting formula.

[0040] The advantages of this invention are:

[0041] (1) This invention uses atomic-scale molecular dynamics simulation to calculate the diffusion activation energy of the powder metallurgy process and proposes a method for calculating the diffusion activation energy. The new diffusion activation energy calculation formula can accurately predict the diffusion coefficient at each moment, avoid the influence of temperature changes, and accurately predict the diffusion activation energy at any moment under the condition of changes in powder particle size, temperature, etc., so as to better reflect the atomic diffusion behavior of the entire powder metallurgy process. This can be used to better optimize the high-entropy alloy composition design and powder metallurgy process, and promote the better large-scale preparation of high-entropy alloys.

[0042] (2) This method is not only applicable to high-entropy alloys, but also applicable to the calculation of diffusion activation energy in the powder metallurgy process of other alloy systems. This method provides a convenient way to calculate the diffusion activation energy of materials and provides a good theoretical simulation basis for studying the powder metallurgy process and process optimization of materials.

[0043] (3) The potential function in this invention uses the Mixed Element Atomistic Method (MEAM) to describe the interactions between atoms. The MEAM is a simulated potential function that can more accurately predict the interactions between atoms in metals / alloys. The method used combines quantum mechanics and molecular mechanics to evaluate the corresponding interaction potential. Compared with other traditional potential functions, the MEAM potential function can better describe the interactions between atoms, including the stability, formation, and rate of interatomic bonds.

[0044] (4) The purpose of energy minimization in this invention is to adjust the positions of atoms in the system so that the total energy of the system reaches a local or global minimum. This process is usually called geometric energy minimization or structural optimization. Energy minimization aims to obtain a stable structure and corresponding potential energy of the system in order to perform calculations and studies on various physical and chemical properties. The objectives of energy minimization include:

[0045] ① Finding stable structures: By minimizing energy, we can find the stable structure of atoms under a given potential field, which is the local minimum of the energy surface. This is very important for studying crystal, molecular structure, and defects;

[0046] ② Calculate the interaction energy: Energy minimization can calculate the total energy of a system in static equilibrium, thereby obtaining the system's potential energy;

[0047] ③ Structural relaxation: In simulations, the initial positions of atoms may not conform to the minimum energy state due to initialization methods or other factors. By minimizing energy, atoms can be gradually adjusted to more reasonable positions along the energy gradient, achieving the most stable structure. Attached Figure Description

[0048] Figure 1 This is a schematic diagram of the initial structural model of the present invention, showing the morphology and distribution of powder particles composed of various metal atoms before the simulation begins after modeling.

[0049] Figure 2 This is a schematic diagram of the structural model of the heating process of the present invention, showing that during the heating process, the metal atoms in each powder particle begin to diffuse due to the gradual increase in temperature, proving the feasibility and accuracy of the simulation process.

[0050] Figure 3 This is a schematic diagram of the thermal insulation process structure model of the present invention, showing that when the temperature rises to the set maximum temperature, the diffusion degree of each metal atom in the powder sintering simulation process is greater than that in the heating process, further verifying the feasibility and accuracy of the simulation process.

[0051] Figure 4 This is a schematic diagram of the cooling process structure model of the present invention. During the cooling simulation, metal atoms will gradually diffuse, but due to the excessive cooling rate, the degree of atomic diffusion is small.

[0052] Figure 5 The MSD curves for the entire powder metallurgy process calculated and simulated in this invention represent the displacement and diffusion of surface atoms during the entire powder sintering simulation process.

[0053] Figure 6 These are the MSD curves of metal powder with a diameter of 2nm and a holding time of 50ps at different temperatures.

[0054] Figure 7 According to Figure 6 The Arrhenius curves for the powder metallurgy process of metals at 1200℃-1400℃ were obtained. Detailed Implementation

[0055] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. All other embodiments obtained by those skilled in the art based on the embodiments of this invention without creative effort are within the scope of protection of this invention.

[0056] A method for calculating the diffusion activation energy in high-entropy alloy powder metallurgy, the specific steps of which are as follows:

[0057] S1. Set parameters in the molecular dynamics simulation software:

[0058] (1) Modeling was performed using LAMMPS software (Large-scale Atomic / Molecular Massively Parallel Simulator), with the unit set to metal.

[0059] (2) The spatial dimension is three-dimensional, and periodic boundary conditions are adopted so that the boundary of the simulation box is periodic in three directions, that is, a particle can pass through a simulation box boundary and re-enter from the opposite boundary.

[0060] (3) The atom type is atomic. In this case, the atom is regarded as a point mass and has no internal structure.

[0061] (4) Set the simulation time step to 1fs = 10 -3 ps=10 -15 `s` sets the length of each time step in the simulation. Smaller time steps result in a more accurate simulation, but may take longer to run.

[0062] (5) Set the nearest neighbor parameter of the atom to 2bin; construct a neighbor list of particles to determine the range of inter-particle interactions to be considered in the simulation.

[0063] (6) Set neigh_modify to every 2delay 0, perform calculations every 2 time steps, and there is no delay.

[0064] S2. Establishment of atomic models for each atom that makes up the alloy:

[0065] (1) Use the lattice command to define the lattice constant.

[0066] (2) Define atomic parameters and proportions, such as Fe mass 155.8 (molar mass), Ti mass 147.9 (molar mass), Zr mass 191.2 (molar mass), Crmass 152 (molar mass), Ni mass 158.7 (molar mass), and Mnmass 154.94 (molar mass), and set the proportion of each element in the high-entropy alloy.

[0067] (3) Define the particle size of each element separately, with a particle size range of 1-50 nm.

[0068] (4) Define the three-dimensional coordinate position of each particle and set the powder particle radius simultaneously to prevent atomic overlap.

[0069] (5) Model size definition: The boundary conditions are set to periodic boundary conditions, and the model size is larger than the region where the atom is located. Generally, it is set to more than twice the region occupied by the atom.

[0070] S3, Potential Function Settings:

[0071] The potential function uses the Mixed Element Atomistic Method (MEAM) to describe the interactions between atoms. The formula for the many-body potential function is as follows:

[0072]

[0073] Where E is the multibody potential function, F i The intercalation energy generated by the background electron density, S ij Φ is the masking function. ij This represents the interaction energy between two atoms.

[0074] S4. Perform energy minimization on the atomic models of each atom to obtain the alloy model:

[0075] Energy minimization is performed alternately using CG mode and SD mode, with the minimum energy value set to 1e-7 for both modes. The minimum energy of the system is obtained after running 100,000 steps. The initial atomic velocity settings are as follows: temperature is 300K, and the random number seed is any natural number greater than 10,000.

[0076] S5. Set the parameters for the alloy model simulation calculation process, and perform heating simulation, holding simulation, and cooling simulation in sequence to obtain output data:

[0077] (1) Output of thermodynamic physical quantities: Use the thermo_style command to output and save the values ​​of each physical quantity every 100 steps. The physical quantities that need to be output are the simulation step number step, system temperature temp, system potential energy pe, system kinetic energy ke, system total energy etotal, and pressure.

[0078] (2) Temperature calculation: The kinetic energy of a single atom is KE = ke / atom, and the constant is defined as KB = 8.625e-5. The kinetic energy of a single atom is KE / (1.5 / KB).

[0079] (3) Output of each stage: Use the dump command to output the XYZ file, which contains the atomic coordinate information of each stage.

[0080] S5.1 Heating process

[0081] (1) The ensemble is set as an NVT system;

[0082] (2) The initial temperature for heating is set to 273K-300K;

[0083] (3) The final temperature of the heating is determined according to the powder metallurgy process, and is generally set to 1500K-1800K. The heating simulation step size is set to 50000-500000.

[0084] (4) When the heating process ends, use the undump command to cancel the saving of the heating process data, so as to ensure that the data of each process is saved independently and reduce data interference.

[0085] S5.2, Insulation Process

[0086] (1) The ensemble is set as an NVT system with the temperature remaining constant and the temperature fluctuation within ±2K.

[0087] (2) The heat preservation temperature is set to 1500K-1800K according to the heating process;

[0088] (3) When the heat preservation process ends, use the undump command to cancel the data saving of the heat preservation process, so as to ensure that the data of each process is saved independently and reduce data interference.

[0089] S5.3 Cooling process

[0090] (1) The ensemble is set as an NVT system;

[0091] (3) The initial cooling temperature is set to 1500K-1800K, and the cooling simulation step size is set to 50000-500000;

[0092] (2) The final temperature for cooling is set to 273K-300K;

[0093] (4) When the cooling process ends, use the undump command to cancel the data saving of the heating process, so as to ensure that the data of each process is saved independently and reduce data interference.

[0094] S6. Process the output data to obtain the MSD curve and fitting formula, and obtain the parameter values ​​of the formula through the fitting formula:

[0095] The output data was processed using Python code to obtain MSD curve data, and the atomic structure was visualized using the OVITO software.

[0096] MSD is an abbreviation for "Mean Squared Displacement." In physics and materials science, MSD is a metric used to describe the movement of particles or molecules over a time series. The shape and slope of the MSD curve reflect the motion state of the system. In steady-state conditions, the MSD curve may show a linear or square root time dependence, indicating that the particles have reached equilibrium. In unsteady-state conditions, the MSD curve may show more complex behavior, potentially involving multiple time periods or stages. The MSD curve provides important information about the motion properties and diffusion behavior of particles or molecules. By analyzing and interpreting the MSD curve, data on system dynamics, diffusion coefficients, particle exchange, etc., can be obtained, contributing to the understanding and study of the motion behavior of various physical systems.

[0097] The MSD curve was plotted and fitted using Origin data processing software, resulting in the following formula:

[0098]

[0099] Where y represents the average square displacement, which is the square of the average displacement of a particle or molecule over a period of time; x represents the simulation time, in ps or s; A, B1, B2, and B3 are all parameters related to powder particle size, temperature, and time, and the values ​​of each parameter can be obtained sequentially through curve fitting.

[0100] Therefore, in order to more accurately predict the diffusion activation energy in the powder metallurgy process, the diffusion activation energy can be calculated separately for the heating process, the holding process, and the cooling process using the following formulas:

[0101] Heating process:

[0102]

[0103] Insulation process:

[0104]

[0105] Cooling process:

[0106]

[0107] In the formula, Ea is the activation energy, Tmax is the holding temperature, S is the actual number of simulation steps, S1 is the total number of steps set for the heating process, S2 is the total number of steps set for the holding process, S3 is the total number of steps set for the heating process, R is the molar gas constant, and A, B1, B2, and B3 are parameters related to powder particle size, temperature, and time, which are obtained by fitting the corresponding MSD curve.

[0108] Example 1 (e.g.) Figure 1-5 As shown,

[0109] S1. Parameter settings (maximum temperature, time step, nearest neighbor parameters, atom type, periodic boundary conditions, etc. in powder metallurgy process);

[0110] S2. Use the region, create_box, and create_atoms commands to establish the size and coordinates of the metal powder for each element;

[0111] S3. Use the mass command to define the types of metal elements, as shown below:

[0112] mass 155.8#Fe

[0113] mass 247.9#Ti

[0114] mass 391.2#Zr

[0115] mass 452#Cr

[0116] mass 558.7#Ni

[0117] mass 654.94#Mn

[0118] S4. Use the pair_style and pair_coeff commands to set the potential function;

[0119] S5. Energy minimization is achieved by alternating between CG mode and SD mode.

[0120] S6. Use the `write_data` command to output the model, and the output model is as follows: Figure 1 As shown;

[0121] S7. Use the thermo_style command to define the physical quantities output during the simulation process;

[0122] S8. Calculate the kinetic energy of a single atom in the system using the compute command;

[0123] S9. Use the variable command to calculate the temperature of a single atom in the system;

[0124] S10. Use the compute command to calculate the displacement of a single atom in the system;

[0125] S11. Use the dump command to output a data file containing the coordinate information, kinetic energy information, and temperature information of each atom in the system;

[0126] S12. Use the velocity command to initialize the temperature of the entire system (300K);

[0127] S13. Use the fix command to heat the system from 300K to 1573K in the NPT system;

[0128] S14. Use the run command to set the number of steps to run from 50,000 to 500,000.

[0129] S15. Use the unfix and undump commands to cancel the commands in the heating stage to prevent interference with the execution of commands in subsequent stages;

[0130] S16. Use the fix command to heat the system at 1573K in the NPT system;

[0131] S17. Use the run command to set the number of steps to run from 50,000 to 500,000.

[0132] S18. Use the unfix and undump commands to cancel the commands in the heat preservation stage to prevent interference with the execution of commands in subsequent stages;

[0133] S19. Use the fix command to cool the system from 1573K to 300K in the NPT system;

[0134] S20. Use the run command to set the number of steps to run (50,000-500,000).

[0135] S21. Use the unfix and undump commands to cancel all stage commands, and the simulation ends;

[0136] S22. Process the simulation data to obtain the MSD curve data of the entire powder metallurgy sintering process, and plot the MSD curve.

[0137] S23. By performing curve fitting on the MSD curve, the following formula is obtained:

[0138]

[0139] Among them, the curve fitting results are: y = 214.981, A = -15, B1 = 7385, B2 = 34172, B3 = 44138.

[0140] S24. Substituting the above parameters into the following heat preservation process formula, the diffusion activation energy E of the heat preservation process can be obtained. a =74.05 kJ / mol

[0141]

[0142] Comparative Example 1

[0143] Comparative Example 1 was also simulated using LAMMPS, employing the aforementioned Arrhenius empirical formula. Since the calculation of the diffusion coefficient and diffusion activation energy using this empirical formula can only be performed during a constant-temperature holding process, the holding process at three temperatures of 1473K, 1573K, and 1673K was simulated according to the Arrhenius empirical formula. To ensure better comparison, parameters other than temperature, including composition, were kept largely consistent. Figure 6-7 As shown, the specific steps are as follows:

[0144] S1. Parameter settings (maximum temperature, time step, nearest neighbor parameters, atom type, periodic boundary conditions, etc. in powder metallurgy process);

[0145] S2. Use the region, create_box, and create_atoms commands to establish the size and coordinates of the metal powder for each element;

[0146] S3. Use the mass command to define the types of metal elements, as shown below:

[0147] mass 155.8#Fe

[0148] mass 247.9#Ti

[0149] mass 391.2#Zr

[0150] mass 452#Cr

[0151] mass 558.7#Ni

[0152] mass 654.94#Mn

[0153] S4. Use the pair_style and pair_coeff commands to set the potential function;

[0154] S5. Energy minimization is achieved by alternating between CG mode and SD mode.

[0155] S6. Use the `write_data` command to output the model, and the output model is as follows: Figure 1 As shown;

[0156] S7. Use the thermo_style command to define the physical quantities output during the simulation process;

[0157] S8. Calculate the kinetic energy of a single atom in the system using the compute command;

[0158] S9. Use the variable command to calculate the temperature of a single atom in the system;

[0159] S10. Use the compute command to calculate the displacement of a single atom in the system;

[0160] S11. Use the dump command to output a data file containing the coordinate information, kinetic energy information, and temperature information of each atom in the system;

[0161] S12. Use the velocity command to initialize the temperature of the entire system (300K);

[0162] S13. Use the fix command to heat the system from 300K to 1573K in the NPT system;

[0163] S14. Use the run command to set the number of steps to run from 50,000 to 500,000.

[0164] S15. Use the unfix and undump commands to cancel the commands in the heating stage to prevent interference with the execution of commands in subsequent stages;

[0165] S16. Use the fix command to hold the system at 1473K in the NPT system;

[0166] S17. Use the run command to set the number of steps to run from 50,000 to 500,000.

[0167] S18. Use the unfix and undump commands to cancel the commands in the heat preservation stage to prevent interference with the execution of commands in subsequent stages;

[0168] S19. Then repeat steps 1-18, with the temperature in step 16 changed to 1573K, and complete the simulation calculation.

[0169] S20. Continue to repeat steps 1-18, with the temperature in step 16 changed to 1573K, and complete the simulation calculation;

[0170] S21. Process the simulation data to obtain the MSD curve data during the heat preservation process at three different temperatures, and plot the MSD curves, such as... Figure 6 As shown;

[0171] S22. Obtain the slope of the MSD curve, substitute it into the Arrhenius empirical formula, plot the Arrhenius curve, and fit the curve to obtain the slope K and diffusion activation energy E. a =R×K, where R is the molar gas constant, and E is obtained. a = 73.69 kJ / mol.

[0172] Comparison shows that Example 1 simulated the diffusion activation energy throughout the powder sintering process. While the Arrhenius empirical formula agrees with experimental results within a certain temperature range, in reality, with larger temperature fluctuations, the diffusion activation energy is no longer a constant and changes with temperature. This invention uses atomic-scale molecular dynamics simulations to calculate the diffusion activation energy in the powder metallurgy process, proposing a new method. This novel formula can accurately predict the diffusion coefficient at every moment, avoiding the influence of temperature changes. Furthermore, it can accurately predict the diffusion activation energy at any given moment, even with variations in powder particle size and temperature, better reflecting the atomic diffusion behavior of the entire powder metallurgy process. This allows for better optimization of high-entropy alloy powder metallurgy processes and promotes the large-scale preparation of high-entropy alloys.

[0173] Comparative Example 1 presents three simulations at different temperatures based on the Arrhenius empirical formula. Furthermore, to minimize interference between simulations, a separate simulation calculation must be performed for each temperature, significantly increasing computational costs. Figure 6 It can be seen that even during the simulation at isothermal temperature, the MSD curve fluctuates continuously, which interferes with the calculation of the curve's slope and consequently affects the subsequent calculation of the diffusion activation energy. Furthermore, from... Figure 6 It can also be seen that if the temperature changes during the heat preservation process, the curve is no longer a relatively complete straight line, and the slope will also change drastically. It is impossible to obtain a single slope for the entire curve, and therefore it is impossible to substitute it into the Arrhenius empirical formula to solve for the subsequent diffusion activation energy.

[0174] To ensure the Arrhenius empirical formula is more applicable in the comparative example, the holding temperature was deliberately kept constant, resulting in a diffusion activation energy of 73.69 kJ / mol. In Example 1, Ea was calculated to be 74.05 kJ / mol, further demonstrating the accuracy of the formula of this invention. As mentioned earlier, the formula of this invention has a wider range of applications and can eliminate the influence of changes in the diffusion coefficient caused by drastic temperature changes, thus better reflecting the atomic diffusion behavior of the entire powder metallurgy process.

[0175] The above are merely preferred embodiments of the present invention and are not intended to limit the scope of the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for calculating the diffusion activation energy in high-entropy alloy powder metallurgy, characterized in that, The specific steps are as follows: S1. First, set the parameters in the molecular dynamics simulation software and then construct the atomic models of each atom that makes up the alloy. S2. Select the potential function and perform energy minimization processing on the atomic model of each atom to obtain the alloy model; S3. Set the parameters for the alloy model simulation calculation process, and perform heating simulation, heat preservation simulation and cooling simulation in sequence to obtain output data; S4. Process the output data to obtain the MSD curve and fitting formula, and obtain the parameter values ​​of the formula through the fitting formula. The fitting formula is as follows: In the formula, y represents the average square displacement, which is the square of the average displacement of a particle or molecule over a period of time; x represents the simulation time, in ps or s; A, B1, B2, and B3 are all parameters related to powder particle size, temperature, and time. S5. Substitute the parameter values ​​obtained in step S4 into the diffusion activation energy calculation formula to obtain the diffusion activation energy for the heating process, the holding process, and the cooling process. The calculation formula is as follows: Heating process: Insulation process: Cooling process: In the formula, E a For diffusion activation energy, T max S represents the holding temperature, S represents the actual number of simulation steps, S1 represents the total number of steps set for the heating process, S2 represents the total number of steps set for the holding process, S3 represents the total number of steps set for the cooling process, R represents the molar gas constant, and A, B1, B2, and B3 are parameters related to powder particle size, temperature, and time, which are obtained by fitting the corresponding MSD curve.

2. The method for calculating the diffusion activation energy in high-entropy alloy powder metallurgy according to claim 1, characterized in that: In step S1, the parameter settings include setting the boundary conditions to periodic boundary conditions, the atom type to atomic, the simulation time step to 1fs, the atom nearest neighbor parameter to 2bin, and setting neigh_modify to every2delay 0.

3. The method for calculating the diffusion activation energy in high-entropy alloy powder metallurgy according to claim 1, characterized in that: In step S1, the lattice constant of the atomic model is In the atomic model, the particle size of each atom is 1-50 nm, and the size of the atomic model is more than twice the size of the region where the atom is located.

4. The method for calculating the diffusion activation energy in high-entropy alloy powder metallurgy according to claim 1, characterized in that: In step S2, the potential function is a multibody potential function, and the formula for the multibody potential function is as follows: Where E is the multibody potential function, F i The intercalation energy generated by the background electron density, S ij Φ is the masking function. ij This represents the interaction energy between two atoms.

5. The method for calculating the diffusion activation energy in high-entropy alloy powder metallurgy according to claim 1, characterized in that: The energy minimization process is performed alternately using CG mode and SD mode, with the minimum energy value set to 1e in both modes. -7 The minimum energy of the system is obtained after running 100,000 steps; the initial temperature of the alloy model is 300K, and the random number seed for the initial temperature is any natural number greater than 10,000.

6. The method for calculating the diffusion activation energy in high-entropy alloy powder metallurgy according to claim 1, characterized in that: In step S3, the parameters in the alloy model simulation calculation process include the number of simulation steps, heating temperature, holding temperature, cooling temperature, and ensemble settings.

7. The method for calculating the diffusion activation energy in high-entropy alloy powder metallurgy according to claim 1, characterized in that: In step S3, the output data includes the number of simulation steps, the system temperature of the alloy model, the total potential energy of the alloy model, the total kinetic energy of the alloy model, the total energy of the alloy model, the pressure, the temperature of a single atom, the atomic coordinate information of the heating simulation stage, the atomic coordinate information of the holding simulation stage, and the atomic coordinate information of the cooling simulation stage.

8. The method for calculating the diffusion activation energy in high-entropy alloy powder metallurgy according to claim 6, characterized in that: The ensembles for the heating process, the heat preservation process, and the cooling process are all configured as NVT systems.

9. The method for calculating the diffusion activation energy in a high-entropy alloy powder metallurgy process according to claim 7, characterized in that, The initial temperature of the heating process is 273K-300K, the final temperature of the heating process is 1500K-1800K, and the heating simulation step size is 50000-500000; the temperature of the holding process is 1500K-1800K; the initial temperature of the cooling process is 1500K-1800K, the cooling simulation step size is 50000-500000, and the final temperature of the cooling process is 273K-300K.

10. The method for calculating the diffusion activation energy in a high-entropy alloy powder metallurgy process according to claim 1, characterized in that: In step S1, the molecular dynamics simulation software used is LAMMPS software; in step S4, Python code is used to process the output data; Origin data processing software is used to plot the MSD curve and perform curve fitting to obtain the fitting formula.

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