A method for calculating stacking fault energy in close-packed hexagonal metals and alloys via shear deformation

Abstract

The present invention discloses a method for calculating stacking fault energy in close-packed hexagonal metals and alloys by shear deformation. The method comprises: (1) optimizing the structure of a close-packed hexagonal metal unit cell by using a DFT calculation method to obtain its lattice constant, and comparing it with the experimental value; (2) constructing the base plane, the cylindrical surface, the cone surface I and the cone surface II surface to obtain a block model, and determining its three crystal direction indices respectively according to the size of the Burgers vector; (3) changing the coordinate system in the output file containing the geometric position of the atoms to a Cartesian coordinate system, and changing the deformation amount of the lattice vector, obtaining a stacking fault defect at the top of the block model, and achieving the purpose of slip deformation; (4) calculating the generalized stacking fault energy curve of each surface, and obtaining the deformation slip energy barrier. The present invention obtains the stacking fault energy barrier by using the DFT calculation method by changing the size of the lattice vector, thereby improving the calculation efficiency and reducing the calculation cost.

Description

Technical Field

[0001] The invention belongs to the field of structural metals and relates to a method for calculating stacking fault energy in close-packed hexagonal metals and alloys through shear deformation. Background Art

[0002] Since the beginning of the 21st century, as environmental and energy issues have received increasing attention, the development of high-strength, low-density, environmentally friendly metal materials has become the main goal of current research on structural materials. Magnesium alloy is the lightest structural metal material with excellent electrical and thermal conductivity, shock and noise reduction, good biocompatibility, and degradability that is beneficial to environmental protection. It has extremely wide applications in aerospace, automotive, biomedical, and electronic communications industries. However, the strength and plasticity of magnesium alloys at room temperature are relatively low, making it difficult to meet the requirements of large-scale industrial applications. Therefore, research on methods that can more quickly reflect the plasticity characterization indicators of magnesium alloys is important for their future applications.

[0003] Magnesium is a hexagonal close-packed (hcp) structure metal. At room temperature, the lattice constant of magnesium is The axial ratio is c / a = 1.624. Its outermost valence electron structure is 3s 2 , which makes magnesium have no covalent bond properties, and its average valence electron binding energy and interatomic binding force are also very low. The close-packed plane of magnesium is the {0001} plane, and the close-packed direction on the close-packed plane is the <11-20> direction. Its shortest Burgers vector is 1 / 3 <11-20>. From a structural point of view, the common slip systems in close-packed hexagonal metal crystals are: basal plane Slip {0001}<11-20>, cylindrical Slip {10-10}<11-20>, cone type I Slip {10-11} <11-20>, cone II Slip {11-22} <11-20>, cone type I<c+a> Slip {10-11} <11-23> and cone II<c+a> Slip {11-22}<11-23>. For the plasticity of crystalline materials, the number of movable slip systems in the structure is closely related to it. From a crystallographic point of view, the basal slip {0001}<11-20> in close-packed hexagonal crystals at room temperature is the easiest to open, but this slip system can only provide two independent slip systems, which does not meet the requirements of the Mises yield criterion, that is, at least five independent slip system materials are required to have good forming properties during deformation. Therefore, studying the size of the stacking fault energy during the formation of different slip systems in magnesium alloys is of great significance for the further design of magnesium alloy materials with high mechanical properties.

[0004] The literature Acta Materialia.67,168-180 (2014) uses shear deformation to calculate the competitive relationship between stacking fault energy and twinning of partial dislocations in the <10-10> direction of magnesium basal plane. However, as a close-packed plane, the basal plane {0001} plane can only provide two independent slip systems. The method mentioned in the literature is only applicable to basal planes with small Burgers vectors. Dislocations cannot be applied to dislocations with large Burgers vectors, such as conical surfaces.<c+a> Dislocation.<c+a> Dislocations alone can provide five independent slip systems, so studying the stacking fault energy of different slip systems is crucial to the plasticity of magnesium alloys. Summary of the invention

[0005] In view of the problem that the existing methods for calculating stacking fault energy of close-packed hexagonal metals and alloys are not fast enough and there is a vacuum effect, the present invention provides a method for calculating stacking fault energy in close-packed hexagonal metals and alloys by shear deformation. The present invention adopts the first principle method to obtain the stacking fault energy barriers of five slip systems of the basal plane, cylindrical plane, cone surface I and cone surface II of the close-packed cubic metal by shear deformation, thereby improving the calculation efficiency, reducing the calculation cost, and studying the plasticity of close-packed hexagonal metals and alloys more comprehensively and accurately.

[0006] The technical solution of the present invention is as follows:

[0007] The method for calculating stacking fault energy in close-packed hexagonal metals and alloys by shear deformation comprises the following steps:

[0008] (1) Using DFT calculation method to optimize the structure of close-packed hexagonal metal unit cell, the lattice constant is obtained and compared with the experimental value;

[0009] (2) The close-packed hexagonal metal primitive cell is sectioned at specific surfaces to construct the base plane (0001), the cylindrical surface (10-10), the cone surface I (10-11) and the cone surface II (10-12) surfaces, and the three appropriate crystal direction indices are determined according to the size of the Burgers vector of the required model to obtain the corresponding block model;

[0010] (3) Output the model as a file containing the geometric positions of atoms and ions, and change the coordinate system therein to a Cartesian coordinate system, keeping the positions of all atoms in the original coordinate system unchanged, while changing their representation in the new coordinate system and the size of the lattice vector matrix, so that a stacking fault defect is obtained at the top or bottom of the block model, thereby achieving the purpose of slip deformation;

[0011] (4) Basal plane (0001) of close-packed hexagonal metals and their alloys Dislocation, prism (10-10) Dislocation, cone I (10-11) A series of structural optimizations were performed on the initial dislocation model and the model after shear deformation to obtain the close-packed hexagonal metal and its alloys. The generalized stacking fault energy (GSFE) curve of the dislocation slip system; secondly, for the cone surface I (10-11)<c+a> Dislocation, cone II (10-12)<c+a> The initial crystal orientation parameters of the dislocation are corrected by a series of tests on the structure diagram to obtain the appropriate crystal orientation index, optimize the structure, and obtain the corresponding close-packed hexagonal metal and its alloy.<c+a> The GSFE curve of the dislocation slip system is used to obtain the stacking fault energy.

[0012] In the present invention, the close-packed hexagonal metal is a close-packed hexagonal metal known in the art, and may be magnesium, zinc, titanium, zirconium and other metals.

[0013] Furthermore, in step (1), the specific method is: using Materials Studio software, importing a close-packed hexagonal metal unit cell structure, optimizing the lattice constants using the DFT method with optB88 van der Waals forces added, and comparing them with experimental parameters to obtain lattice constants that can be used for structural optimization calculations.

[0014] Further, in step (2), the specific method is: in Materials Studio software, a specific face of the close-packed hexagonal metal unit cell is cut to obtain different surfaces of the basal plane (0001), the cylindrical plane (10-10), the conical plane I (10-11) and the conical plane II (10-12), firstly, for the basal plane (0001) and the cylindrical plane (10-10) with smaller Burgers vectors, three simple mutually perpendicular crystal direction indices are selected; secondly, since the Burgers vectors of the conical plane I (10-11) and the conical plane II (10-12) are relatively large, if the mutually perpendicular crystal direction indices are simply selected, the stronger the anisotropic characteristics are, the model will be deformed to a certain extent during the relaxation process, resulting in a large error in the result, so the appropriate three crystal direction indices are selected according to actual needs, and the crystal direction indices of each face are the basal plane, the cylindrical plane (10-10), the conical plane I (10-11), the conical plane II (10-12 ... <-12-10>, <10-10>, <0001> Three crystal directions, cylindrical of <0001> , <11-20>, <-1100> three crystal directions, cone I and<c+a> The three crystal directions of <-2113>, <1-210>, <8-1-73> and cone II<c+a> The three crystal directions of <-1100>, <11-2-3>, and <55-103> are respectively constructed for the initial model using the supercell function, namely, surface (0001), cylinder (10-10), cone I (10-11), and cone II (10-12), to obtain the required block model.

[0015] Furthermore, in step (3), the specific method is: output the obtained block models of the base surface, cylinder, cone surface I and cone surface II as a file containing atomic geometric positions and ion positions, and convert the coordinate system therein into a Cartesian coordinate system, that is, keep the positions and vectors of all atoms inside the original coordinate system unchanged, and change their representation in the new coordinate system, change the size of the lattice vector matrix in the position file, so that only the top layer of the supercell is displaced in the shear direction, while the atoms of all other layers remain in their original positions, so that a stacking fault defect is obtained at the top or bottom of the block model, thereby achieving the purpose of slip deformation.

[0016] Compared with the prior art, the present invention has the following beneficial effects:

[0017] (1) The shear deformation method is used to keep the positions and lattice vectors of all atoms in the original coordinate system unchanged, while changing their representation in the new coordinate system. Only the top layer of the supercell is displaced in the shear direction, while the atoms of all other layers remain in their original positions. The displacement of the top layer initially only affects the next layer, but the relaxation at the fixed displacement of the upper layer causes the displacement to propagate from top to bottom. This method only forms defects at the top or bottom, and can produce the same degree of deformation as the commonly used vacuum plate shear method with half the number of atoms, saving computational costs and improving computational efficiency.

[0018] (2) Since the shear deformation model adopts a periodic structure, the influence of the vacuum layer on the structure and defects in the vacuum plate shear method is not required.

[0019] (3) Because the model results are highly dependent on the initial morphology of the model, the selection of the initial crystal direction is particularly important. Since this situation does not exist in face-centered cubic crystals (the three perpendicular crystal directions of the face-centered cubic metal model conform to the initial crystal directions of the crystal structure), it is relatively easy to find, and the slip deformation results will only have a slight error. However, the impact is greater in the close-packed hexagonal structure, especially in the pyramidal structure of close-packed hexagonal metals. This configuration is more difficult because it contains a large number of atoms in the three perpendicular directions as the three crystal directions and does not conform to the crystallographic initial crystal directions. The most important thing is that the pyramidal slip system of close-packed hexagonal metals is<c+a> The Burgers vector in the dislocation direction is large, which leads to strong structural anisotropy after such slip deformation, and the deviation from the normal result is increased. The present invention improves this problem through a series of tests, so that the results of slip deformation on the close-packed hexagonal metal base, cylindrical surface, cone surface I and II are better.

[0020] In summary, the present invention applies the shear deformation method to<c+a> In dislocation, due to the large non-basal Burgers vector of hexagonal close-packed metal, the shear deformation method applicable to face-centered cubic metal (fcc) cannot be directly applied to hexagonal close-packed metal. Therefore, the present invention searches for crystal direction indexes by comparing the magnesium structure diagram, removes the unreasonable structure, obtains reasonable crystal direction indexes, and thus obtains an accurate generalized stacking fault energy (GSFE) curve. Moreover, the present invention uses shear deformation to change the lattice vector matrix to apply deformation, which is closer to the actual situation than the existing commonly used vacuum plate shear method, requires fewer atoms, improves calculation efficiency, and reduces calculation cost. BRIEF DESCRIPTION OF THE DRAWINGS

[0021] Figure 1 This is the deformation mode of magnesium and its alloys of the present invention.

[0022] Figure 2 It is the primitive cell structure of pure magnesium metal of the present invention.

[0023] Figure 3 The base plane {0001} of the pure magnesium metal of the present invention is Schematic diagram of dislocation structure.

[0024] Figure 4 The cylindrical surface {10-10} of the pure magnesium metal of the present invention is Schematic diagram of dislocation structure.

[0025] Figure 5 The cone surface I{10-11} of the pure magnesium metal of the present invention is Schematic diagram of dislocation structure.

[0026] Figure 6The cone surface I{10-11} of the pure magnesium metal of the present invention is<c+a> Schematic diagram of dislocation structure.

[0027] Figure 7 The cone II {10-12} of the pure magnesium metal of the present invention is<c+a> Schematic diagram of dislocation structure.

[0028] Figure 8 The base surface {0001} of the magnesium alloy of the present invention is Schematic diagram of dislocation structure.

[0029] Fig. 9 The cylindrical surface {10-10} of the magnesium alloy of the present invention is Schematic diagram of dislocation structure.

[0030] Fig.10 The cone surface I{10-11} of the magnesium alloy of the present invention is Schematic diagram of dislocation structure.

[0031] Fig.11 The cone surface I{10-11} of the magnesium alloy of the present invention is<c+a> Schematic diagram of dislocation structure.

[0032] Fig.12 The cone II {10-12} of the magnesium alloy of the present invention is<c+a> Schematic diagram of dislocation structure.

[0033] Fig.13 The pure magnesium metal of the present invention Schematic diagram of the process by which dislocations are generated during shear deformation.

[0034] Fig.14 The pure magnesium metal of the present invention<c+a> Schematic diagram of the process by which dislocations are generated during shear deformation.

[0035] Fig.15 The base surface {0001}, the cylindrical surface {10-10} and the conical surface I {10-11} are calculated by the Cartesian shear deformation method of the pure magnesium metal of the present invention. GSFE curve of dislocation.

[0036] Fig.16 The cone surface I {10-11} and cone surface II {10-12} are calculated by the Cartesian shear deformation method of the pure magnesium metal of the present invention.<c+a> GSFE curve of dislocation. DETAILED DESCRIPTION

[0037] The present invention is further described in detail below in conjunction with the embodiments and drawings.

[0038] Example 1

[0039] (1) Using Materials Studio software, the magnesium unit cell structure was imported, and the lattice constants were optimized using the DFT method with optB88 van der Waals force added, and compared with the experimental parameters in the literature J. Phys. Condens. Matter. 13, 10767-10776 (2001) By comparison, we can obtain the lattice constants that can be used for structural optimization calculations, such as Figure 2 shown.

[0040] (2) In Materials Studio software, the magnesium unit cell is sectioned at a specific surface to obtain the basal plane (0001) and the cylindrical plane (10-10). Because its Burgers vector is small, three mutually perpendicular crystal direction indices can be directly selected, namely, the basal plane <-12-10>, <10-10>, <0001> Three crystal directions and cylindrical <0001> , <11-20>, <-1100>. The initial model was constructed using the supercell function in the software to construct 1×2×6 basal plane (0001) and 2×2×3 cylindrical (10-10) supercell models. In order to combine the accuracy of the calculation results and the limitations of the calculation software, a 48-atom model was used. Finally, the required block model was obtained, as shown in Figure 3 , Figure 4 shown.

[0041] (3) The obtained block model of the base and cylinder is output as a file containing the geometric positions of atoms and ions, and the coordinate system therein is converted into a Cartesian coordinate system, that is, the positions and vectors of all atoms in the original coordinate system are kept unchanged, while changing their representation in the new coordinate system. The content of the position file is changed to relax in the x, y and z directions, and the size of the lattice vector matrix is ​​changed in this position file to achieve that only the top layer of the supercell is displaced in the shear direction, while the atoms of all other layers remain in their original positions, so that stacking fault defects are obtained at the top or bottom of the block model, achieving the purpose of slip deformation.

[0042] (4) Along the base surface and cylinder The size of the lattice vector matrix of shear deformation in the direction is changed to obtain a series of position files of slip deformation, and the structure of the corresponding model is optimized. During the optimization process, The x and y coordinates of the dislocation are fixed, and only the z coordinate (the direction perpendicular to the slip plane) relaxes. Fig.13 According to the energy difference after relaxation, the basal plane in pure magnesium is obtained. and cylinder The GSFE curve of the slip system is as follows: Fig.15 As shown, the stacking fault energy is 249mJ / m 2 and 214mJ / m 2 .

[0043] Example 2

[0044] This embodiment is a further improvement of the above-mentioned embodiment, and only the improved part is described.

[0045] The present invention is not limited to this. Since the Burgers vectors of cone surface I (0001) and cone surface II (10-12) are relatively large, if the crystal direction indices perpendicular to each other are simply selected, the stronger the anisotropic characteristics will be, resulting in a certain degree of deformation of the model during the relaxation process, thereby causing a large error in the result. Therefore, the crystal direction indices are improved according to actual needs. First, the magnesium primitive cell is sectioned on a specific surface in the Materials Studio software to obtain cone surface I (10-11) and cone surface II (10-12). Three directions are defined according to the Burgers vector, namely, cone surface I (0001) and cone surface II (10-12). and<c+a> The three crystal directions of <-2113>, <1-210>, <8-1-73> and cone II<c+a> The supercell function in the software is used to construct the cone surface I and<c+a> and Cone II<c+a> The initial model has a structure like Figure 4 , Figure 5 , Figure 6 shown.

[0046] Along the cone I and<c+a> and Cone II<c+a> The size of the lattice vector matrix of shear deformation in the direction is changed to obtain a series of position files of slip deformation, and the structure of the corresponding model is optimized. During the optimization process, and<c+a> The slip direction coordinate of the dislocation is fixed, and the other two directions are relaxed. The slip process is as follows Fig.14 According to the energy difference after relaxation, the cone surface I in pure magnesium is obtained. and<c+a> and Cone II<c+a> The GSFE curve of the slip system is as follows: Fig.15 and Fig.16 As shown, the stacking fault energy is 280mJ / m 2 , 362mJ / m 2 and 320mJ / m 2 .

[0047] For magnesium alloys, the alloying elements are solid-solution-substituted at the top or bottom of the model, where the slip dislocation defect is located, and the GSFE curve of the magnesium alloy is obtained using a calculation method similar to that of pure magnesium. The slip energy barrier can be obtained through these GSFE curves, thereby obtaining the difficulty of opening different slip systems, such as Figures 8 to 12 shown.

[0048] The present invention is not limited to this, and is also applicable to close-packed hexagonal structure metals other than magnesium alloys. The three crystal directions of slip are determined according to the size of the Burgers vector of the slip dislocation to perform shear slip and determine the corresponding GSFE curve. The above description is only an embodiment of the present invention, and does not limit the protection scope of the present invention. Any equivalent structure or equivalent process transformation made by using the contents of the present invention specification and drawings, or directly or indirectly used in other related technical fields, are also included in the protection scope of the present invention.

Claims

1. A method for calculating stacking fault energy in close-packed hexagonal metals and alloys by shear deformation, characterized in that: The following steps are involved: (1) The DFT calculation method is used to optimize the structure of the close-packed hexagonal metal unit cell to obtain its lattice constant, and then compare it with the experimental value. The specific method is as follows: using Materials Studio software, import the close-packed hexagonal metal unit cell structure, use the DFT method adding optB88 van der Waals force to optimize the lattice constant, and compare it with the experimental parameters to obtain the lattice constant that can be used for structural optimization calculation; (2) The hexagonal metal unit cell is sectioned at specific surfaces to construct the basal plane (0001), cylindrical plane (10-10), cone surface I (10-11) and cone surface II (10-12) surfaces respectively. The three appropriate crystal direction indices are determined according to the size of the Burgers vector of the required model to obtain the corresponding block model. The specific method is as follows: In the Materials Studio software, the hexagonal metal unit cell is sectioned at specific surfaces to obtain the basal plane (0001), cylindrical plane (10-10), cone surface I (10-11) and cone surface II (10-12) surfaces. First, for the basal plane (0001) and cylindrical plane (10-10) with smaller Burgers vectors, three simple mutually perpendicular crystal direction indices are selected, which are the basal plane (0001), cylindrical plane (10-10), cone surface I (10-11) and cone surface II (10-12). <-12-10>, <10-10>, <0001> Three crystal directions, cylindrical of <0001> , <11-20>, <-1100> three crystal directions, cone I and<c+a> The three crystal directions of <-2113>, <1-210>, <8-1-73> and cone II<c+a> The three crystal directions of <-1100>, <11-2-3>, and <55-103> are respectively constructed using the supercell function for the initial model, namely, the surface (0001), the cylinder (10-10), the cone I (10-11), and the cone II (10-12), to obtain the required block model; (3) Output the model as a file containing the geometric positions of atoms and ions, and change the coordinate system therein to a Cartesian coordinate system, keep the positions of all atoms in the original coordinate system unchanged, and change their representation in the new coordinate system, change the size of the lattice vector matrix, so that a stacking fault defect is obtained at the top or bottom of the block model, and achieve the purpose of slip deformation. The specific method is: output the obtained block model of the base plane, cylinder, cone surface I and cone surface II as a file containing the geometric positions of atoms and ions, and convert the coordinate system therein to a Cartesian coordinate system, that is, keep the positions and vectors of all atoms in the original coordinate system unchanged, and change their representation in the new coordinate system, change the size of the lattice vector matrix in the position file, so that only the top layer of the supercell is displaced in the shear direction, while the atoms of all other layers remain in their original positions, so that a stacking fault defect is obtained at the top or bottom of the block model, and achieve the purpose of slip deformation; (4) Basal plane (0001) of close-packed hexagonal metals or their alloys Dislocation, prism (10-10) Dislocation, cone I (10-11) A series of structural optimizations were performed on the initial dislocation model and the model after shear deformation to obtain the close-packed hexagonal metal and its alloys. Generalized stacking fault energy GSFE curve of dislocation slip system; secondly, for cone surface I (10-11)<c+a> Dislocation, cone II (10-12)<c+a> The initial crystal orientation parameters of the dislocation are corrected by a series of tests on the structure diagram to obtain the appropriate crystal orientation index, optimize the structure, and obtain the corresponding close-packed hexagonal metal or its alloy.<c+a> The GSFE curve of the dislocation slip system is used to obtain the stacking fault energy.

2. The method according to claim 1, characterized in that The close-packed hexagonal metal is magnesium, zinc, titanium or zirconium.

Images