A method for predicting stacking fault energy in high-entropy alloys based on atomic preferred occupancy

Abstract

This invention relates to a method for predicting stacking fault energy in high-entropy alloys based on atomic preferred occupancy. First, the occupancy fraction (SOFs) of high-entropy alloy atoms in the sublattice is calculated. Based on this structural information, an atomically ordered structural model of the high-entropy alloy is constructed. Then, the constructed unit cell model undergoes structural optimization, faceting, shearing of the (1 1 1) plane after faceting, increasing the number of atomic layers for cell expansion, and adding a vacuum layer for translation, thereby establishing a slip surface structure model without stacking faults. Next, individual stacking fault slip surface structure models are constructed through translation. Finally, the total energy of the high-entropy alloy is calculated using density function theory, thereby predicting the stacking fault energy of the high-entropy alloy. This method can reasonably construct an atomic distribution structure model for predicting the stacking fault energy of high-entropy alloys, thus accurately calculating the stacking fault energy of high-entropy alloys.

Description

Technical Field

[0001] This invention relates to the field of alloy design technology, and specifically to a method for predicting stacking fault energy in high-entropy alloys based on atomic preferred occupancy. Background Technology

[0002] High-entropy alloys (HEAs) represent a novel alloy design concept. They are alloys composed of three or more equimolar or near-equimolar amounts of metallic elements, exhibiting relatively simple phase structures, primarily FCC, BCC, or HCP solid solutions. Some systems also contain small amounts of other alloy phases. While some scholars refer to three-principal-element HEAs as medium-entropy alloys, a growing trend towards using terms like multi-principal-element alloys or complex-composition alloys reflects the ongoing and evolving understanding of this field. To honor originality, this application uses "high-entropy alloy" to refer to this complex multi-principal-element alloy. HEAs encompass numerous systems and offer a wide compositional space. Many HEAs possess one or more unique physical, mechanical, or chemical properties, such as high strength, high corrosion resistance, high-temperature stability, good plasticity, or catalytic activity. HEAs have opened up new avenues for metallic materials research, even driving the development of high-entropy ceramics and high-entropy optoelectronic functional materials. Their research, development, and application potential are limitless, thus attracting widespread attention and research in materials science. However, due to the vast compositional space, the relationships between "composition-heat treatment process-microstructure-properties" in high-entropy alloys are intricate, thus requiring further systematic and in-depth exploration of high-entropy alloys with different compositions. In this era of rapid development of AI for Science, predictions based on reasonable theoretical models are especially needed to accelerate the research and development of these emerging materials.

[0003] Generalized Stacking Fault Energy (GSFE) refers to the total energy difference between a crystal material with fully stacked stacking faults and its original structure without stacking faults per unit area along a certain crystal orientation. It is an important physical quantity used to describe the plastic deformation mechanism of crystal materials and is closely related to the mechanical properties of FCC metal deformation mechanisms. The variation at different stacking fault planes also differs. Although the values ​​of intrinsic stacking fault energy (ISFE), extrinsic stacking fault energy (ESFE), unstable stacking fault energy (USFE), and unstable twinning energy (UTE) within the generalized stacking fault energy can be measured by high-resolution transmission electron microscopy (TEM) or XRD, the complexity of experimental techniques and the difficulty in analysis make it a feasible approach to accurately predict stacking fault energy through theoretical models for comparison of different materials. The GSFE of FCC high-entropy alloys is closely related to the alloy composition and microstructure. Experiments by Tian et al. revealed that high SFE (>45mJ / m) 2 This leads to perfect dislocation slip and shear banding, with an SFE range of 20–40 mJ / m. 2 The TWIP mechanism is evident in FCC steel, with low SFE inducing martensitic transformation and exhibiting a transformation-induced plasticity (TRIP) effect. Studies by Hyun Seok Oh et al. have shown that the presence of negative intrinsic stacking fault energy and atomic and nanoscale barriers in Co-rich FCC_CoCrNi is essential for promoting fault plasticity and suppressing deformation-induced transformation plasticity. Analysis of the generalized stacking fault energy profile can predict dislocation slip, twinning tendency, and martensitic transformation in FCC metals.

[0004] On the other hand, it is well known that to obtain accurate calculation results, a reasonable calculation model for the stacking fault energy of high-entropy alloys needs to be constructed. Previous researchers have conducted extensive studies on first-principles calculations of the stacking fault energy of high-entropy alloys. Ding Jun et al., through theoretical calculations of the stacking fault energy of FCC_CoCrNi high-entropy alloys, found that short-range chemical ordering affects the stacking fault energy of this system, and that the stacking fault energy can be controlled by atomic positions. However, all current calculation models ignore the actual atomic occupancy ordering behavior present in high-entropy alloys. Previous structural models using random atomic distributions have led to inaccurate calculation results for the stacking fault energy and may have a certain impact on the derivation of dislocation slip and twinning tendency. Wu Jian et al. found that different clusters have different stacking fault energies; for example, CoCr clusters exhibit the highest shear strain and the lowest unstable stacking fault energy. In high-entropy alloys, the differences in the types of constituent atoms and the differences in sublattice structures inevitably lead to preferential occupancy (i.e., occupancy tendency) of alloying elements. This means that the structure is not completely random, and high-entropy alloys exhibit varying degrees of short-range and long-range ordering behavior, depending on the specific high-entropy alloy system and heat treatment conditions. A 2022 academic paper by Wu Bo et al., on a reasonable model and prediction method for atomic distribution in high-entropy alloys, elaborated on the occupancy tendency of atoms in high-entropy alloys. For example, in the FCC_CoCrFeNi high-entropy alloy, Ni atoms occupy only the 1a sublattice (vertex positions), while Co, Cr, and Fe atoms mainly occupy the 3c sublattice (face-centered positions). Previous first-principles calculation models for stacking fault energy in high-entropy alloys, whether using CPA or SQS modeling methods, assumed random solid solution of alloy atoms, which is unreasonable and the prediction results are inaccurate. Therefore, the construction of the structural model required for calculating the stacking fault energy of high-entropy alloys must take into account the actual atomic preferential occupancy behavior (i.e., the tendency of occupancy ordering) in high-entropy alloys. Summary of the Invention

[0005] The purpose of this invention is to provide a method for predicting the stacking fault energy of high-entropy alloys based on atomic preferential occupancy. This method is beneficial for rationally constructing an atomic distribution structure model for predicting the stacking fault energy of high-entropy alloys, thereby accurately calculating the stacking fault energy of high-entropy alloys.

[0006] To achieve the above objectives, the technical solution adopted by this invention is: a method for predicting the stacking fault energy of high-entropy alloys based on atomic preferred occupancy, comprising the following steps:

[0007] Step S1: Based on the crystallographic structure information and alloy thermodynamics principles of the high-entropy alloy, calculate the site fraction (SOFs) of the atoms in the sublattice of the high-entropy alloy.

[0008] Step S2: Based on the prototype structure of the alloy phase, a supercell is constructed using a first-principles calculation toolkit. Based on the occupancy fractions calculated in Step S1, atoms of various types in the high-entropy alloy are randomly distributed on various types of sublattices according to their occupancy fractions. Then, the various sublattices are nested to form an overall high-entropy alloy structure, thus constructing a high-entropy alloy occupancy-ordered structure model and obtaining the model file POSCAR.

[0009] Step S3: Based on the obtained high-entropy alloy occupied ordered structure model file POSCAR, the crystal structure is first optimized by volume using the VASP calculation software package; on this basis, the volume, shape and atomic positions are globally optimized to obtain the high-entropy alloy occupied ordered structure model with the lowest total energy and the most stable structure.

[0010] Step S4: After the high-entropy alloy occupied ordered structure model is optimized, it is cross-sectioned, the coordinate system is transformed in a specified direction, and a vacuum layer of a set thickness is added to obtain the slip surface structure model when no stacking faults are generated in the stacking fault energy calculation; the total energy E0 of the high-entropy alloy slip surface structure model when no stacking faults are generated in the equilibrium state is obtained by calculating with the VASP software package.

[0011] Step S5: According to the set shearing path, translate some atomic layers of the slip surface structure model that has not experienced stacking faults to obtain the stacking fault slip surface structure model.

[0012] Step S6: After constructing the stacking fault slip surface structure model, fix the slip surface (111) of the model and allow its atoms to relax freely in the

[111] direction. Calculate the total energy E of the high-entropy alloy corresponding to the generation of stacking faults in the equilibrium state using the VASP software package. d ;

[0013] Step S7: Total energy E of the slip surface structure model after stacking fault generation d The ratio of the difference between the total energy E0 of the slip surface structure model and that of the model without stacking faults to the stacking fault area A is the desired stacking fault energy γ. d ;

[0014] Step S8: Calculate the stacking fault energy on different shear paths, and then plot the generalized stacking fault energy image with the unit length of the Burgers vector displacement in the [11-2] slip direction as the abscissa and the stacking fault energy as the ordinate.

[0015] Step S9: Predict whether the plastic deformation of the crystal is dominated by twinning or by dislocation slip.

[0016] Furthermore, for high-entropy alloys with different phase structures, including FCC, BCC, and HCP structures, the modeling and calculation prediction steps for the structural models required for stacking fault energy prediction are the same.

[0017] Furthermore, for the FCC_CoCrNi high-entropy alloy, a double sublattice model of the L12 structure based on AuCu3 is established to characterize the atomic distribution model of the high-entropy alloy, and then the structural model required for stacking fault energy prediction is established to calculate and predict the stacking fault energy.

[0018] Furthermore, for the FCC_CoCrNi high-entropy alloy, step S2 specifically comprises:

[0019] The FCC_CoCrNi high-entropy alloy cell is based on an ordered face-centered cubic FCC_L1. 2— Based on the AuCu3 prototype structure, a 2×2×2 supercell was constructed. Based on the site configuration of high-entropy alloy atoms with site fraction distribution, a high-entropy alloy site-ordered structure model containing 32 atoms was obtained.

[0020] Step S3 specifically involves:

[0021] The VASP first-principles calculation software based on density function theory was used to optimize the occupied ordered structure model of high-entropy alloy in steps. The K-space grid was selected as 5×5×5. Volume relaxation was performed first. On this basis, volume, shape and atomic position were relaxed simultaneously to obtain the optimized high-entropy alloy occupied ordered structure model data, that is, the state with the lowest total energy and the most stable crystal structure.

[0022] Further, step S4 specifically includes:

[0023] Using Materials Studio and VESTA crystal structure visualization software, the optimized FCC_CoCrNi high-entropy alloy occupied ordered structure model was cross-sectioned. The slip plane (111) was selected, and the (111) plane was sheared and the number of atomic layers was increased to establish a slip plane structure model with 8 atoms per layer and a total of 9 atomic layers without stacking faults. Then, additional atomic layers were added to it. A high vacuum layer eliminates the influence of structural mirroring. The supercell size and vacuum layer height of the structural model required for stacking fault energy prediction are determined by the available computational resources, as stacking fault energy calculation involves a large amount of computation, and a balance between computational accuracy and efficiency must be ensured.

[0024] Further, step S5 specifically includes:

[0025] Step S51: Fix the first to sixth atomic layers of the slip surface structure model without stacking faults, and apply shear stress to the seventh to ninth atomic layers in the [11-2] direction, causing them to move by a unit Burgers vector length. This displacement process is divided into 10 segments, and a corresponding stacking fault slip surface structure model POSCAR is obtained for each segment;

[0026] Step S52: Fix the first to seventh atomic layers of the slip surface structure model after moving the Burgers vector, and apply shear stress to the eighth to ninth atomic layers in the [11-2] direction to make them move the Burgers vector. The vector length divides this displacement process into 10 segments, and each segment obtains a corresponding stacked fault slip surface structure model POSCAR;

[0027] Further, step S6 specifically includes:

[0028] When calculating the total energy of each slip surface structure model, the x-axis and y-axis of the atomic coordinates of the slip surface structure model are fixed, and the atoms are relaxed in the z-axis, i.e.

[111] direction, to obtain the total energy of the slip surface structure model after stacking faults are generated in the equilibrium state, and then the total energy of the other slip surface structure models is calculated respectively.

[0029] Further, step S7 specifically includes:

[0030]

[0031] Where E0 is the total energy of a perfect crystal structure, E d Let γ be the total energy of the crystal structure containing defects, A be the total defect area, and γ be the total energy of the crystal structure containing defects. d It is the generalized stacking fault energy.

[0032] Further, step S8 specifically includes:

[0033] After calculating the stacking fault energy on different shear paths, a generalized stacking fault energy image is plotted with the unit length of the Burgers vector displacement in the [11-2] direction as the x-axis and the stacking fault energy as the y-axis.

[0034] Further, step S9 specifically includes:

[0035] Based on the predicted unstable stacking fault energy γ usf Intrinsic stacking fault energy γ isf Unstable twin energy γ utf and extrinsic stacking fault energy γ esf Size can further predict whether the plastic deformation of a crystal is dominated by twinning or by dislocation slip.

[0036] Compared with the prior art, the present invention has the following beneficial effects: The present invention provides a method for predicting the stacking fault energy of high-entropy alloys based on the preferred occupancy of atoms. Unlike the quasi-random model of the SQS and CPA methods which make unreasonable assumptions, the present invention takes into account the actual occupancy ordering behavior of atoms on the sublattice. Based on the thermodynamic principle of alloys, it calculates the accurate occupancy fraction, and then reasonably distributes alloy atoms in the high-entropy alloy to further construct the high-entropy alloy structure required for stacking fault energy prediction, and finally accurately calculates the stacking fault energy of the high-entropy alloy. Attached Figure Description

[0037] Figure 1 This is a schematic diagram of the POSCAR construction of a 2×2×2 supercell for the FCC_CoCrNi high-entropy alloy in an embodiment of the present invention;

[0038] Figure 2 In this embodiment of the invention, the FCC_CoCrNi high-entropy alloy supercell is cut along the (111) plane, and a new spatial rectangular coordinate system is established with the [11-2], [1-10] and

[111] directions as the new x-axis, y-axis and z-axis directions, respectively. Further shearing operations are performed, the number of atomic layers is increased, and then... After the vacuum layer, a slip surface structure model with 9 layers, 8 atoms per layer, and a total of 72 atoms was obtained, which had not yet generated stacking faults.

[0039] Figure 3 This is a schematic diagram illustrating the process of establishing the structural model required for predicting different stacking fault energies in an embodiment of the present invention;

[0040] Figure 4 This is an image of the generalized stacking fault energy (GSFE) of the FCC_CoCrNi high-entropy alloy in an embodiment of the present invention. Detailed Implementation

[0041] The present invention will be further described below with reference to the accompanying drawings and embodiments.

[0042] It should be noted that the following detailed descriptions are exemplary and intended to provide further explanation of this application. Unless otherwise specified, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this application pertains.

[0043] It should be noted that the terminology used herein is for the purpose of describing particular embodiments only and is not intended to limit the exemplary embodiments according to this application. As used herein, the singular form is intended to include the plural form as well, unless the context clearly indicates otherwise. Furthermore, it should be understood that when the terms "comprising" and / or "including" are used in this specification, they indicate the presence of features, steps, operations, devices, components, and / or combinations thereof.

[0044] This embodiment provides a method for predicting the stacking fault energy of high-entropy alloys based on atomic preferred occupancy, including the following steps:

[0045] Step S1: Based on the crystallographic structure information and alloy thermodynamics principles of the high-entropy alloy, calculate the site fraction (SOFs) of the atoms in the sublattice of the high-entropy alloy.

[0046] Step S2: Based on the prototype structure of the alloy phase, a supercell is constructed using a first-principles calculation toolkit. Based on the occupancy fractions calculated in Step S1, atoms of various types in the high-entropy alloy are randomly distributed on various types of sublattices according to their occupancy fractions. Then, the various sublattices are nested to form an overall high-entropy alloy structure, thus constructing a high-entropy alloy occupancy-ordered structure model and obtaining the model file POSCAR.

[0047] Step S3: Based on the obtained high-entropy alloy occupied ordered structure model file POSCAR, the crystal structure is first optimized by volume using the VASP calculation software package; on this basis, the volume, shape and atomic positions are globally optimized to obtain the high-entropy alloy occupied ordered structure model with the lowest total energy and the most stable structure.

[0048] Step S4: After the high-entropy alloy occupied ordered structure model is optimized, it is cross-sectioned, the coordinate system is transformed in a specified direction, and a vacuum layer of a set thickness is added to obtain the slip surface structure model when no stacking faults are generated in the stacking fault energy calculation; the total energy E0 of the high-entropy alloy slip surface structure model when no stacking faults are generated in the equilibrium state is obtained by calculating with the VASP software package.

[0049] Step S5: According to the set shearing path, translate some atomic layers of the slip surface structure model that has not experienced stacking faults to obtain the stacking fault slip surface structure model.

[0050] Step S6: After constructing the stacking fault slip surface structure model, fix the slip surface (111) of the model and allow its atoms to relax freely in the

[111] direction. Calculate the total energy E of the high-entropy alloy corresponding to the generation of stacking faults in the equilibrium state using the VASP software package. d ;

[0051] Step S7: Total energy E of the slip surface structure model after stacking fault generation d The ratio of the difference between the total energy E0 of the slip surface structure model and that of the model without stacking faults to the stacking fault area A is the desired stacking fault energy γ. d ;

[0052] Step S8: Calculate the stacking fault energy on different shear paths, and then plot the generalized stacking fault energy image with the unit length of the Burgers vector displacement in the [11-2] slip direction as the abscissa and the stacking fault energy as the ordinate.

[0053] Step S9: Predict whether the plastic deformation of the crystal is dominated by twinning or by dislocation slip.

[0054] For high-entropy alloys with different phase structures, such as FCC, BCC, and HCP structures, the modeling and calculation steps for predicting stacking fault energy are similar. This embodiment uses the FCC_CoCrNi high-entropy alloy as an example, establishing a double sublattice model of the L12 structure based on AuCu3 to characterize the atomic distribution model of the high-entropy alloy, and then establishing the structural model required for predicting stacking fault energy to calculate and predict the stacking fault energy.

[0055] This embodiment uses FCC_CoCrNi high-entropy alloy as an example to calculate the occupancy fraction under thermodynamic equilibrium at different heat treatment temperatures. Occupancy fraction data corresponding to the heat treatment temperature of interest to the researcher are selected to build an atomic distribution model for the high-entropy alloy. Subsequent calculations simulating structural relaxation, building the structural model required for stacking fault energy prediction, and calculating the predicted stacking fault energy are equivalent to heat-treating this high-entropy alloy to equilibrium at a specified temperature, then quenching the high-temperature structure to a low-temperature temperature, preserving its high-temperature atomic configuration. Therefore, this embodiment uses the occupancy fraction at a specific high temperature to perform atomic occupancy ordering modeling, obtaining the occupancy ordering structural model of the FCC_CoCrNi high-entropy alloy and the corresponding stacking fault energy data.

[0056] This invention takes FCC_CoCrNi high-entropy alloy as an example. In this embodiment, step S2 specifically involves:

[0057] The FCC_CoCrNi high-entropy alloy cell is based on an ordered face-centered cubic FCC_L1. 2— Based on the AuCu3 prototype structure, a 2×2×2 supercell was constructed. Based on the site configuration of high-entropy alloy atoms with site fraction distribution, a site-ordered structure model of high-entropy alloy containing 32 atoms was obtained.

[0058] In this embodiment, step S3 specifically includes:

[0059] The VASP first-principles calculation software based on density function theory was used to optimize (also known as relax) the occupied ordered structure model of the high-entropy alloy stepwise. The K-space grid was selected as 5×5×5. First, volume relaxation was performed (i.e., volume-only optimization, optimization mode ISIF=7, maximum number of ion relaxation steps NSW=10, energy convergence accuracy set to EDIFF=1E-5eV in the INCAR file). On this basis, volume, shape and atomic position relaxation were performed simultaneously (i.e., global optimization, ISIF=3, NSW=20, EDIFF=1E-5eV in the INCAR file). The optimized high-entropy alloy occupied ordered structure model data was obtained, which is the state with the lowest total energy and the most stable crystal structure.

[0060] In this embodiment, step S4 specifically includes:

[0061] Using Materials Studio and VESTA crystal structure visualization software, the optimized FCC_CoCrNi high-entropy alloy occupied ordered structure model was cross-sectioned. The slip plane (111) was selected, and the (111) plane was sheared and the number of atomic layers was increased to establish a slip plane structure model with 8 atoms per layer and a total of 9 atomic layers without stacking faults. Then, additional atomic layers were added to it. A high vacuum layer eliminates the influence of structural mirroring. While theoretically the vacuum layer is infinitely large, this results in an infinite amount of computation, making calculations impossible. The supercell size and vacuum layer height of the structural model required for stacking fault energy prediction are determined by the available computational resources. Because stacking fault energy calculation involves a large amount of computation, a balance between computational accuracy and efficiency must be ensured.

[0062] In this embodiment, step S5 specifically includes:

[0063] Step S51: Fix the first to sixth atomic layers of the slip surface structure model without stacking faults, and apply shear stress to the seventh to ninth atomic layers in the [11-2] direction, causing them to move by a unit Burgers vector length. This displacement process is divided into 10 segments, and a corresponding stacking fault slip surface structure model POSCAR is obtained for each segment;

[0064] Step S52: Fix the first to seventh atomic layers of the slip surface structure model after moving the Burgers vector, and apply shear stress to the eighth to ninth atomic layers in the [1 1 -2] direction to make them move the unit The vector length divides this displacement process into 10 segments, and each segment obtains a corresponding stacked fault slip surface structure model POSCAR;

[0065] Both steps S51 and S52 are obtained by a one-click command from the script program.

[0066] In this embodiment, the self-developed script program, one-click command processing program script-to-Creat-HEAs-SFE-model.py, is as follows.

[0067]

[0068]

[0069] In this embodiment, step S6 specifically includes:

[0070] When calculating the total energy of each slip surface structure model, the x-axis and y-axis of the atomic coordinates of the slip surface structure model are fixed, and the atoms are relaxed in the z-axis, i.e.

[111] direction, to obtain the total energy of the slip surface structure model after stacking faults are generated in the equilibrium state, and then the total energy of the other slip surface structure models is calculated respectively.

[0071] In this embodiment, step S7 specifically includes:

[0072]

[0073] Where E0 is the total energy of a perfect crystal structure, E d Let γ be the total energy of the crystal structure containing defects, A be the total defect area, and γ be the total energy of the crystal structure containing defects. d It is the generalized stacking fault energy.

[0074] In this embodiment, step S8 specifically includes:

[0075] After calculating the stacking fault energy on different shear paths, a generalized stacking fault energy image is plotted with the unit length of the Burgers vector displacement in the [11-2] direction as the x-axis and the stacking fault energy as the y-axis.

[0076] In this embodiment, step S9 specifically includes:

[0077] Based on the predicted unstable stacking fault energy γ usf Intrinsic stacking fault energy γ isf Unstable twin energy γ utf and extrinsic stacking fault energy γ esf Size can further predict whether the plastic deformation of a crystal is dominated by twinning or by dislocation slip.

[0078] The generalized stacking fault slip surface structure model constructed in this embodiment surpasses the completely disordered random model structure commonly used in academia, which is unreasonable. This is because the present invention considers the actual ordered occupancy of atoms, and can more reasonably and accurately reflect the influence of long-range and short-range atomic occupancy order on the stacking fault energy of the system.

[0079] The implementation of this embodiment will be further described in detail below with reference to the accompanying drawings.

[0080] This embodiment takes FCC_CoCrNi high-entropy alloy as an example to provide a method for creating and calculating the structural model required for predicting stacking fault energy in occupied-order high-entropy alloys, including the following specific steps:

[0081] Step S1: First, based on the thermodynamic principles and crystallographic structure information of alloys, and using the established end-group thermodynamic database, the site fractions (SOFs) of different types of atoms in the FCC sublattice under different heat treatment conditions are obtained through Thermo-Calc or Pandat.

[0082] Step S2: Based on computing resources, construct a supercell of appropriate size for the L12 prototype structure AuCu3 of ordered FCC. Further, based on the predicted site fractions (SOFs), following the method of atoms being randomly distributed on the sublattice according to their site fractions, and then the sublattices being nested to form an overall high-entropy alloy structure, construct a high-entropy alloy site-ordered structure model; here, the supercell size is 2×2×2, totaling 32 atoms, as shown... Figure 1 As shown.

[0083] Step S3: Using the first-principles calculation software VASP based on density function theory, the crystal structure is optimized step by step (also known as relaxation). First, volume relaxation is performed (optimization mode ISIF=7, maximum number of ion relaxation steps NSW=10, energy convergence precision set to EDIFF=1E-5eV in the INCAR file). Based on this, simultaneous relaxation of volume, shape, and atomic positions is performed (ISIF=3, NSW=20, EDIFF=1E-5eV in the INCAR file). This yields the optimized high-entropy alloy site-ordered structure model, which exhibits a slight lattice distortion that can be ignored. Therefore, the high-entropy alloy is still considered as a face-centered cubic structure with a lattice constant of a.

[0084] Step S4: The optimized FCC_CoCrNi high-entropy alloy site-ordered structure model is used in conjunction with Materials Studio and VESTA crystal structure visualization software. The model is cut along the (111) plane of the original coordinate axis, and the x, y, and z axes are redefined as [11-2], [1-10], and

[111] , respectively, to establish a new spatial rectangular coordinate system atomic distribution model, as shown below. Figure 2 As shown in (a); further shearing operations, increasing the number of atomic layers, and then adding... A vacuum layer was used to obtain a slip plane structure model without stacking faults. The new crystal structure has 9 atomic layers, with 8 atoms per layer, for a total of 72 atoms. The size of the vacuum layer was set to... like Figure 2 As shown in (b).

[0085] Step S5: As is well known, the FCC unit cell has 3 different stacking orders on the (111) crystal plane, which are labeled ABC, as follows: Figure 3 As shown. The arrangement of the 9 atomic layers in the (111) plane of the FCC unit cell is ABCABCABC. First, the atomic layers 1 to 6 are fixed, and the atomic layers 7 to 9 are subjected to shear stress in the [11-2] direction, and moved. An unstable stacking fault (USF) energy glide surface structure model was established, in which the atomic layer arrangement became BCA|ABCABC. Based on the established unstable stacking fault (USF) energy glide surface structure model, the same method was used to continue applying shear stress to the 7th to 9th atomic layers, moving them in the direction of [11-2]. The intrinsic stacking fault (ISF) energy glide surface structure model is obtained, and the atomic layer arrangement becomes CAB|ABCABC. Further, based on the established intrinsic stacking fault (ISF) energy glide surface structure model, atomic layers 1-7 are fixed, and atomic layers 8-9 are subjected to shear stress in the [11-2] direction in the same manner, and moved... A structural model of the unstable twin (UTF) energy glide surface was obtained. Finally, based on the established structural model of the unstable twin (UTF) energy glide surface, atomic layers 1 to 7 were fixed, and atomic layers 8 to 9 were moved in the same manner under shear stress in the direction of [11-2]. The exogenous stacking fault (ESF) energy glide surface structure model is obtained, and the atomic layer arrangement is BC|B|ABCABC.

[0086] Figure 3 This is a schematic diagram of the visualization process of the structural model required for predicting different stacking fault energies in this embodiment, where (a) is the intrinsic stacking fault structure and (b) is the extrinsic stacking fault structure. Figure 3The projection of the stacked fault slip surface structure model along the [1-10] direction is shown, and the movement... This process per unit length is divided into 10 steps, each of which creates a crystal structure file (POSCAR) for calculation.

[0087] Step S6: Calculate the total energy of each high-entropy alloy structure model using the VASP first-principles calculation software package. First, calculate the total energy E0 of the slip surface structure model without stacking faults. Then, calculate the total energy E of the stacking fault slip surface structure model (i.e., the high-entropy alloy after undergoing certain shear deformation). d .

[0088] Step S7: Total energy E of each layered fault slip surface structural model d The difference between the total energy E0 of the slip surface structure model without stacking faults and the total energy E0 of the slip surface structure model without stacking faults, and the ratio of this difference to the stacking fault area A, is the desired stacking fault energy γ. d The classical formula for calculating stacking fault energy is given by equation (1) mentioned above;

[0089] Step S8: After calculating the stacking fault energy along different shear paths, plot the generalized stacking fault energy image with the unit length of the Burgers vector displacement in the [11-2] direction as the x-axis and the stacking fault energy as the y-axis, as shown below. Figure 4 As shown. In this FCC_CoCrNi high-entropy alloy example, the generalized stacking fault energy obtained includes the unstable stacking fault energy γ. usf and intrinsic stacking fault energy γ isf The values ​​are: 307.19 mJ / m 2 and -84.51mJ / m 2 Unlike the unreasonable modeling methods of random distribution used by EMTO-CPA and SQS, this invention constructs the structural model required for stacking fault energy prediction based on the actual existence of ordered occupancy behavior in FCC_CoCrNi high-entropy alloy structures.

[0090] Step S9: Based on the predicted unstable stacking fault energy γ usf Intrinsic stacking fault energy γ isf Unstable twin energy γ utf and extrinsic stacking fault energy γ esf Size can further predict whether the plastic deformation of a crystal is dominated by twinning or by dislocation slip.

[0091] The above description is merely a preferred embodiment of the present invention and is not intended to limit the invention in any other way. Any person skilled in the art may make changes or modifications to the above-disclosed technical content to create equivalent embodiments. However, any simple modifications, equivalent changes, and modifications made to the above embodiments based on the technical essence of the present invention without departing from the scope of the present invention shall still fall within the protection scope of the present invention.

Claims

1. A method for predicting stacking fault energy in high-entropy alloys based on atomic preferred occupancy, characterized in that, Includes the following steps: Step S1: Based on the crystallographic structure information and alloy thermodynamics principles of the high-entropy alloy, calculate the site fraction (SOFs) of the high-entropy alloy atoms in the sublattice. Step S2: Based on the prototype structure of the alloy phase, a supercell is constructed using a first-principles calculation toolkit. Based on the occupancy fractions calculated in Step S1, atoms of various types in the high-entropy alloy are randomly distributed on various types of sublattices according to their occupancy fractions. Then, the various sublattices are nested to form an overall high-entropy alloy structure, thus constructing a high-entropy alloy occupancy-ordered structure model and obtaining the model file POSCAR. Step S3: Based on the obtained high-entropy alloy occupied ordered structure model file POSCAR, the crystal structure is first optimized by volume using the VASP calculation software package; on this basis, the volume, shape and atomic positions are globally optimized to obtain the high-entropy alloy occupied ordered structure model with the lowest total energy and the most stable structure. Step S4: After structural optimization, the high-entropy alloy occupied ordered structure model is cross-sectioned, a coordinate system transformation is performed in a specified direction, and a vacuum layer of a set thickness is added to obtain the slip surface structure model without stacking faults in the stacking fault energy calculation; the total energy of the high-entropy alloy slip surface structure model without stacking faults in equilibrium is obtained by calculating using the VASP software package. ; Step S5: According to the set shearing path, translate some atomic layers of the slip surface structure model that has not experienced stacking faults to obtain the stacking fault slip surface structure model. Step S6: After constructing the stacking fault slip surface structure model, fix the slip surface (1 1 1) of the model and allow its atoms to relax freely in the [1 1 1] direction. Calculate the total energy of the high-entropy alloy corresponding to the generation of stacking faults in the equilibrium state using the VASP software package. ; Step S7: Total energy of the slip surface structure model after stacking fault generation The total energy of the slip surface structure model without stacking faults The difference between the two is the ratio of the stacking fault area A to the desired stacking fault energy γ. d ; Step S8: Calculate the stacking fault energy on different shear paths, and then plot the generalized stacking fault energy image with the unit length of the Burgers vector displacement in the [1 1 -2] slip direction as the x-axis and the stacking fault energy as the y-axis. Step S9: Predict whether the plastic deformation of the crystal is dominated by twinning or by dislocation slip.

2. The method for predicting stacking fault energy in high-entropy alloys based on atomic preferred occupancy as described in claim 1, characterized in that, For high-entropy alloys with different phase structures, including FCC, BCC and HCP structures, the modeling and calculation prediction steps for the structural model required for stacking fault energy prediction are the same.

3. The method for predicting stacking fault energy in high-entropy alloys based on atomic preferred occupancy as described in claim 1, characterized in that, For the FCC_CoCrNi high-entropy alloy, a double sublattice model of the L12 structure based on AuCu3 is established to characterize the atomic distribution model of the high-entropy alloy, and then the structural model required for the prediction of stacking fault energy is established to calculate the predicted stacking fault energy.

4. The method for predicting stacking fault energy in high-entropy alloys based on atomic preferred occupancy as described in claim 1, characterized in that, For the FCC_CoCrNi high-entropy alloy, step S2 specifically involves: The FCC_CoCrNi high-entropy alloy cell is based on the ordered face-centered cubic FCC_L1. 2— Based on the AuCu3 prototype structure, a 2×2×2 supercell was constructed. Based on the site configuration of high-entropy alloy atoms with site fraction distribution, a high-entropy alloy site-ordered structure model containing 32 atoms was obtained. Step S3 specifically involves: The VASP first-principles calculation software based on density function theory was used to optimize the occupied ordered structure model of high-entropy alloy in steps. The K-space grid was selected as 5×5×5. Volume relaxation was performed first. On this basis, volume, shape and atomic position were relaxed simultaneously to obtain the optimized high-entropy alloy occupied ordered structure model data, that is, the state with the lowest total energy and the most stable crystal structure.

5. The method for predicting stacking fault energy in high-entropy alloys based on atomic preferred occupancy as described in claim 1, characterized in that, Step S4 specifically involves: Using Materials Studio and VESTA crystal structure visualization software, the optimized FCC_CoCrNi high-entropy alloy occupied ordered structure model was cross-sectioned. The (1 1 1) plane was selected, and the (1 1 1) plane was sheared and the number of atomic layers was increased to establish a slip plane structure model with 8 atoms per layer and a total of 9 atomic layers without stacking faults. A vacuum layer with a height of 15 Å was then added to eliminate the influence of structural mirroring. The supercell size and vacuum layer height of the structure model required for stacking fault energy prediction were determined by the available computing resources, because stacking fault energy calculation involves a large amount of computation, and it is necessary to ensure a balance between computational accuracy and efficiency.

6. The method for predicting stacking fault energy in high-entropy alloys based on atomic preferred occupancy as described in claim 1, characterized in that, Step S5 specifically involves: Step S51: Fix the first to sixth atomic layers of the slip surface structure model without stacking faults, and apply shear stress to the seventh to ninth atomic layers in the [11-2] direction, causing them to move by a unit Burgers vector length. This displacement process is divided into 10 segments, and a corresponding stacking fault slip surface structure model POSCAR is obtained for each segment. Step S52: Fix the first to seventh atomic layers of the slip surface structure model after moving the unit Burgers vector, and apply shear stress to the eighth to ninth atomic layers in the [1 1 -2] direction to make its unit Burgers vector length... This displacement process is divided into 10 segments, and a corresponding stacking fault slip surface structure model POSCAR is obtained for each segment.

7. The method for predicting stacking fault energy in high-entropy alloys based on atomic preferred occupancy as described in claim 1, characterized in that, Step S6 specifically involves: When calculating the total energy of each slip surface structure model, the x-axis and y-axis of the atomic coordinates of the slip surface structure model are fixed, and the atoms are relaxed in the z-axis direction [1 1 1] to obtain the total energy of the slip surface structure model after stacking faults are generated in the equilibrium state. Then, the total energy of the other slip surface structure models is calculated respectively.

8. The method for predicting stacking fault energy in high-entropy alloys based on atomic preferred occupancy according to claim 1, characterized in that, Step S7 specifically involves: （1） Where E0 is the total energy of a perfect crystal structure, E d Let γ be the total energy of the crystal structure containing defects, A be the total defect area, and γ be the total energy of the crystal structure containing defects. d It is the generalized stacking fault energy.

9. The method for predicting stacking fault energy in high-entropy alloys based on atomic preferred occupancy as described in claim 1, characterized in that, Step S8 specifically involves: After calculating the stacking fault energy on different shear paths, a generalized stacking fault energy image is plotted with the unit length of the Burgers vector displacement in the [1 1 -2] direction as the x-axis and the stacking fault energy as the y-axis.

10. The method for predicting stacking fault energy in high-entropy alloys based on atomic preferred occupancy according to claim 1, characterized in that, Step S9 specifically involves: Based on the predicted unstable stacking fault energy Intrinsic fault energy Unstable twin energy and extrinsic fault energy Size can further predict whether the plastic deformation of a crystal is dominated by twinning or by dislocation slip.

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