Interstitial atom segregation grain boundary modeling method for molecular dynamics simulation

Abstract

The invention relates to the technical field of micro-nano materials, in particular to an interstitial atom segregation grain boundary modeling method for molecular dynamics simulation, which comprises the following steps: establishing unit cells with gaps completely filled; constructing an initial grain boundary model; determining an interstitial atom distribution density function; segmenting the initial grain boundary model into fragments, and determining the proportion of interstitial atoms in each fragment; deleting redundant interstitial atoms to obtain a target grain boundary model meeting segregation distribution requirements; and performing energy minimization on the target grain boundary model to obtain final grain boundary models with different segregation degrees. According to the method, the distribution of interstitial atoms in the grain boundary model can be flexibly controlled by introducing the interstitial atom distribution density function, so that subsequent molecular dynamics simulation can aim at an interstitial solid solution system under different segregation conditions, modeling of any grain boundary model containing interstitial solute is realized, and the modeling efficiency is improved. Therefore, follow-up molecular dynamics simulation can aim at different grain boundary models.

Description

Technical Field

[0001] The invention relates to the technical field of micro-nano materials, and in particular to a method and system for modeling interstitial atom segregation grain boundaries for molecular dynamics simulation. Background Art

[0002] Interstitial solid solution refers to a solid solution formed by solute atoms filling some gaps between solvent atoms instead of occupying the normal node positions of the solvent lattice. The formation conditions of interstitial solid solution mainly depend on the size of the solute atoms. Generally, the smaller the solute atoms are, the easier it is to enter the interstitial positions of the solvent lattice, thus forming interstitial solid solution. Typical interstitial solid solution systems include the solid solution of carbon in iron, the solid solution of hydrogen in metals, and the solid solution of oxygen in metals. These solid solution systems are extremely common in the fields of metallurgy, energy, and mechanical manufacturing industries, but their interstitial atoms are often difficult to be observed experimentally due to their extremely small atomic radius. Therefore, the study of interstitial solid solution systems has great scientific and technological significance.

[0003] The molecular dynamics simulation method is based on the laws of physics and can obtain accurate atomic motion trajectories and process large systems with hundreds of millions of atoms. It can not only simulate real micro-nano systems, but also deeply understand the dynamic behavior of molecules and reveal the dynamic response mechanism and change law of the system. These advantages make molecular dynamics simulation play an important role in scientific research and technological applications.

[0004] Traditional solid solution molecular dynamics modeling methods include Monte Carlo-molecular dynamics simulation modeling and solid solution modeling based on chemical potential difference. Monte Carlo-molecular dynamics simulation modeling is generally only aimed at replacing atoms, such as the modeling of multi-principal alloys. It optimizes the atomic positions by exchanging atomic coordinates to achieve reasonable solid solution system modeling. However, this method cannot be implemented in the modeling of interstitial solid solution systems because it only operates on existing atoms and cannot insert new atoms. In addition, there is a solid solution modeling method based on chemical potential difference. However, interstitial elements in reality are very prone to segregation. The modeling method based on chemical potential difference can only achieve equilibrium segregation modeling due to its low energy and high probability realization principle, but cannot achieve modeling of other segregation degrees. These have brought great difficulties to the study of interstitial atomic segregation at grain boundaries in molecular dynamics simulation.

[0005] Therefore, it is necessary to provide a method and system for modeling interstitial atom segregation grain boundaries for molecular dynamics simulation to solve the above problems. Summary of the invention

[0006] The present invention provides a method and system for modeling interstitial atomic segregation grain boundaries for molecular dynamics simulation, so as to solve the problem that the existing Monte Carlo-molecular dynamics simulation modeling does not consider atomic insertion and cannot be realized in interstitial solid solution, and the basic principle of the modeling method based on chemical potential difference only models segregation in equilibrium state and is difficult to achieve modeling of different segregation degrees.

[0007] The present invention provides a method for modeling interstitial atom segregation grain boundaries for molecular dynamics simulation using the following technical solutions, including: According to the lattice constant of the solvent, the preferred position of the interstitial solute atoms, and the crystal orientation required by the grain boundary model, a unit cell with completely filled interstitials is established; The unit cell is expanded to obtain a supercell, and the supercell is symmetrically placed at the required interface to obtain an initial grain boundary model; Determine the interstitial atom distribution density function based on the distribution parameters of the desired solute atoms; The initial grain boundary model is divided into segments, and the proportion of interstitial atoms in each segment is determined according to the interstitial atom distribution density function; According to the ratio of interstitial atoms in each segment, redundant interstitial atoms are deleted to obtain a target grain boundary model that meets the segregation distribution requirements; The target grain boundary model is energy minimized to obtain the final grain boundary model.

[0008] Preferably, the steps of establishing a unit cell with completely filled gaps are: According to the preferred positions of interstitial solute atoms, the corresponding ratios of solvent atoms and solute atoms when the gap is completely filled are obtained; Calculate the offset vector of a single solvent atom relative to the solute atom based on the corresponding ratio of solvent atoms to solute atoms, the lattice constant of the solvent atoms, and the preferred position of the interstitial solute atoms; Perform axis rotation operation according to the current crystal direction to obtain the crystal direction required by the grain boundary model, and calculate the crystal orientation axis matrix according to the crystal direction before axis rotation and the crystal direction required by the grain boundary model; According to the crystal orientation rotation axis matrix and the offset vector of the single solvent atom corresponding to the solute atom, the rotation axis offset vector of the single solvent atom corresponding to the solute atom after the rotation axis is calculated; According to the crystal direction and lattice constants of solvent atoms required by the grain boundary model, a unit cell of solvent atoms in the desired crystal direction is established; According to the rotation axis offset vector and the unit cell of the desired crystal-down solvent atom, the positions of all interstitial atoms inserted in the unit cell are determined, and a unit cell with completely filled gaps is established.

[0009] Preferably, the product of the crystal orientation rotation axis matrix and the offset vector of a single solvent atom corresponding to a solute atom is used as the rotation axis offset vector of a single solvent atom corresponding to a solute atom after the rotation.

[0010] Preferably, the steps of calculating the crystal orientation axis matrix are: The old spatial rectangular coordinate system is established with the a-axis direction in the current crystal orientation as the x-direction, the c-axis direction as the z-direction, and 1 nm as the unit length; According to the orientation required by the grain boundary model, a new spatial rectangular coordinate system is established with 1 nm as the unit length; Obtain target vectors corresponding to three preset linearly independent vectors in the old rectangular coordinate system and the new rectangular coordinate system; The crystal orientation axis matrix is ​​obtained according to the corresponding target vectors in the old and new spatial rectangular coordinate systems, that is, , where The target vectors of three preset linearly independent vectors in the old rectangular coordinate system of space; The target vectors are three preset linearly independent vectors in the new spatial rectangular coordinate system.

[0011] Preferably, the step of determining the interstitial atom distribution density function is:

[0012] in, For any point position, This is the distribution density function here, is the position of the first grain boundary, is the position of the second grain boundary, is the distribution parameter of the solute atoms determined as required.

[0013] Preferably, the expression for the ratio of interstitial atoms in each fragment is:

[0014] In the formula, For the The concentration of interstitial atoms in each fragment, For the The distribution density function value of the interstitial atoms in each fragment, is the concentration of interstitial atoms required for the entire model, is the number of segments divided.

[0015] An interstitial atom segregation grain boundary modeling system for molecular dynamics simulation, comprising: The unit cell building module is used to build a unit cell with completely filled gaps based on the lattice constant of the solvent, the preferred positions of the interstitial solute atoms, and the crystal orientation required by the grain boundary model; The grain boundary model building module is used to expand the unit cell to obtain a supercell, and to symmetric the supercell at the required interface to obtain the initial grain boundary model; A ratio calculation module is used to determine the interstitial atom distribution density function according to the distribution parameters of the required solute atoms; divide the initial grain boundary model into segments, and determine the ratio of interstitial atoms in each segment according to the interstitial atom distribution density function; The final grain boundary model construction module is used to delete redundant interstitial atoms according to the proportion of interstitial atoms in each segment to obtain a target grain boundary model that meets the segregation distribution requirements; the target grain boundary model is energy minimized to obtain the final grain boundary model.

[0016] The beneficial effects of the present invention are: The modeling method of the present invention can perform molecular dynamics simulation on interstitial solid solution, especially solves the problem that traditional methods are difficult to deal with interstitial atomic segregation, which is conducive to the simulation results being closer to the actual physical situation; specifically, the present invention obtains the corresponding coordinates of the solute atoms after the rotation axis through the rotation axis matrix, determines the position of the interstitial solid solution atoms under any crystal orientation, and realizes the modeling of any grain boundary model containing interstitial solute, so that subsequent molecular dynamics simulation can be targeted at different grain boundary models; the present invention can flexibly control the distribution of interstitial atoms in the grain boundary model by introducing the interstitial atom distribution density function, so that subsequent molecular dynamics simulation can be targeted at the interstitial solid solution system under different segregation conditions. BRIEF DESCRIPTION OF THE DRAWINGS

[0017] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative work.

[0018] Figure 1 A flowchart of an embodiment of a method for modeling interstitial atom segregation grain boundaries for molecular dynamics simulation of the present invention; Figure 2 A titanium-oxygen unit cell with a gap completely filled established in an embodiment of the present invention; Figure 3 is the initial titanium-oxygen grain boundary model established in the embodiment of the present invention; Figure 4 Schematic diagram of the solute oxygen atom distribution function in an embodiment of the present invention; Figure 5 The final grain boundary models with different segregation degrees obtained in the embodiments of the present invention; Figure 6 Schematic diagram of the segregation of oxygen atoms in an embodiment of the present invention. DETAILED DESCRIPTION

[0019] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0020] An embodiment of a method for modeling interstitial atomic segregation grain boundaries for molecular dynamics simulation of the present invention is to establish a grain boundary modeling method having a size of Interstitial oxygen atoms segregate in titanium The grain boundary model of titanium-oxygen grain boundary is referred to as titanium-oxygen grain boundary model. Figure 1 As shown, the specific steps include: S1. Establish a unit cell with completely filled gaps; According to the lattice constant of the solvent, the preferred position of the interstitial solute atoms, and the crystal orientation required by the grain boundary model, a unit cell with the gap completely filled is established. The specific steps are: according to the preferred position of the interstitial solute atoms, the corresponding ratio of solvent atoms and solute atoms when the gap is completely filled is obtained; according to the corresponding ratio of solvent atoms and solute atoms, the lattice constant of solvent atoms and the preferred position of interstitial solute atoms, the coordinate difference between the solvent atoms and the corresponding solute atoms is determined, thereby obtaining the offset vector α of the corresponding solute atom of a single solvent atom; according to the current crystal orientation, the axis rotation operation is performed to obtain the crystal orientation required by the grain boundary model, and the crystal orientation axis matrix is ​​calculated according to the crystal orientation before the axis rotation and the crystal orientation required by the grain boundary model. , according to the crystal orientation axis matrix and the offset vector of a single solvent atom corresponding to the solute atom, the axis offset vector of a single solvent atom corresponding to the solute atom after the axis rotation is calculated, that is, ; According to the crystal orientation and lattice constants of the solvent atoms required by the grain boundary model, a unit cell of the solvent atoms in the desired crystal direction is established; according to the rotation axis offset vector and the unit cell of the solvent atoms in the desired crystal direction, the positions of all interstitial atoms inserted in the unit cell are determined, thereby establishing a unit cell with completely filled gaps.

[0021] The steps to calculate the crystal orientation rotation axis matrix are as follows: establish an old spatial rectangular coordinate system with the a-axis direction as the x-direction, the c-axis direction as the z-direction, and 1 nm as the unit length. According to the crystal orientation of the target model, establish a new spatial rectangular coordinate system with 1 nm as the unit length. Take three linearly independent vectors and use the representation of these three vectors in the old coordinate system. And the representation in the new coordinate system , calculate the crystal orientation axis matrix In this embodiment, according to the crystal structure of close-packed hexagonal titanium atoms, the lattice constant in the a direction is: , the lattice constant in the c direction is: , the position of oxygen atoms in the tetrahedral gap distribution is selected as the preferred position, and the corresponding ratio of titanium and oxygen is calculated to be 1:1. According to the preferred position of oxygen atoms, the offset vector of oxygen atoms corresponding to a single titanium atom is determined to be (0.147515, 0.085168, 0.05854). According to the grain boundary model required , , The crystal orientation of , take three linearly independent vectors, the three independent vectors in the old coordinate system are (2.9503, 0, 0), (0, 5.1101, 0), (0, 0, 4.6832), the three independent vectors in the new coordinate system are (2.7878, -0.9657, 0), (1.6727, 4.8286, 0), (0, 0, 4.6832), the crystal orientation axis matrix is The rotation axis offset vector is (0.167266, 0.032191, 0.058540), which is used to calculate the position of the oxygen atom corresponding to each titanium atom and establish a titanium-oxygen unit cell with completely filled gaps.

[0022] S2, constructing an initial grain boundary model; Specifically, the unit cell is expanded to obtain a supercell, and the supercell is symmetric at the required interface to obtain a grain boundary model.

[0023] In this embodiment, according to The size needs to be expanded to 20 times in the x direction, 10 times in the y direction, and 20 times in the z direction, and symmetrical along the yz plane, so as to obtain Figure 3 Initial titanium-oxygen grain boundary model with the gap shown completely filled.

[0024] S3, determining the interstitial atomic distribution density function; Specifically, the interstitial atom distribution density function is determined according to the distribution parameters of the required solute atoms.

[0025] like Figure 4 As shown, the expression of the interstitial atomic distribution density function is:

[0026] In the formula, For any point position, This is the distribution density function here, is the position of the first grain boundary, is the position of the second grain boundary, is the distribution parameter of the solute atoms determined as required.

[0027] In this embodiment, the distribution parameters are respectively are 0, 0.2, 0.33, 0.5, 0.67, and 1, which are called distribution situations 1 to 6 respectively.

[0028] S4, dividing the initial grain boundary model into segments, and determining the proportion of interstitial atoms in each segment; The ratio of interstitial atoms in each fragment is determined according to the interstitial atom distribution density function, that is, the expression for the ratio of interstitial atoms in each fragment is:

[0029] In the formula, For the The concentration of interstitial atoms in each fragment, For the The distribution density function value of the interstitial atoms in each fragment, is the concentration of interstitial atoms required for the entire model, is the number of segments divided.

[0030] In this embodiment, the initial grain boundary model is divided into 25 segments. For the six distribution conditions of S3, the distribution effects expected to be achieved are as follows: Figure 4 shown.

[0031] S5. According to the ratio of interstitial atoms in each segment, randomly select interstitial atoms in the segment and delete them until the ratio of interstitial atoms in the segment reaches a certain ratio, thereby obtaining a target grain boundary model that meets the segregation distribution requirements; S6. Minimize the energy of the target grain boundary model to obtain the final grain boundary model with different segregation degrees, where the different segregation degrees of oxygen atoms are as follows: Figure 5 shown.

[0032] like Figure 6 As shown in the figure, it also includes checking the number of interstitial atoms and atomic segregation: the total number of interstitial atoms inserted in the final grain boundary model is counted to calculate the interstitial atom concentration of the final grain boundary model as a whole, and to compare whether it is consistent with the expected concentration; the final grain boundary model established is re-divided into segments along the direction perpendicular to the grain boundary, and the functional relationship between the interstitial atom concentration and position is calculated, and compared with Figure 4 In order to verify whether the expected distribution effect is met, the number of interstitial atoms and atomic segregation of the final grain boundary model are verified. By constructing a titanium-oxygen grain boundary model with dense interstitial oxygen atoms and optimizing the number of atoms and the degree of segregation according to the oxygen atom density function, the segregation grain boundary modeling of the titanium-oxygen system for molecular dynamics simulation is realized. Compared with the traditional modeling method, the problem of interstitial atom insertion is solved, and the control of different segregation degrees of oxygen atoms is realized, which is helpful for the subsequent molecular dynamics simulation research on different segregation degrees.

[0033] A modeling system for interstitial atom segregation grain boundaries for molecular dynamics simulation comprises: a unit cell establishment module, a grain boundary model establishment module, a ratio calculation module and a final grain boundary model construction module, wherein the unit cell establishment module is used to establish a unit cell with completely filled interstitials according to the lattice constant of the solvent, the preferred position of interstitial solute atoms and the crystal orientation required by the grain boundary model; the grain boundary model establishment module is used to expand the unit cell to obtain a supercell, and symmetric the supercell at the required interface to obtain an initial grain boundary model; the ratio calculation module is used to determine the interstitial atom distribution density function according to the distribution parameters of the required solute atoms; the initial grain boundary model is divided into segments, and the ratio of interstitial atoms in each segment is determined according to the interstitial atom distribution density function; the final grain boundary model construction module is used to delete redundant interstitial atoms according to the ratio of interstitial atoms in each segment to obtain a target grain boundary model that meets the segregation distribution requirements; the target grain boundary model is energy minimized to obtain the final grain boundary model.

[0034] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principle of the present invention should be included in the protection scope of the present invention.

Claims

1. A method for modeling interstitial atomic segregation grain boundaries for molecular dynamics simulation, characterized in that: include: According to the lattice constant of the solvent, the preferred position of the interstitial solute atoms, and the crystal orientation required by the grain boundary model, a unit cell with completely filled interstitials is established; The unit cell is expanded to obtain a supercell, and the supercell is symmetrically placed at the required interface to obtain an initial grain boundary model; Determine the interstitial atom distribution density function based on the distribution parameters of the desired solute atoms; The initial grain boundary model is divided into segments, and the proportion of interstitial atoms in each segment is determined according to the interstitial atom distribution density function; According to the ratio of interstitial atoms in each segment, redundant interstitial atoms are deleted to obtain a target grain boundary model that meets the segregation distribution requirements; The target grain boundary model is energy minimized to obtain the final grain boundary model.

2. The interstitial atom segregation grain boundary modeling method for molecular dynamics simulation according to claim 1, characterized in that: The steps to create a unit cell with completely filled gaps are: According to the preferred positions of interstitial solute atoms, the corresponding ratios of solvent atoms and solute atoms when the gap is completely filled are obtained; Calculate the offset vector of a single solvent atom relative to the solute atom based on the corresponding ratio of solvent atoms to solute atoms, the lattice constant of the solvent atoms, and the preferred position of the interstitial solute atoms; Perform axis rotation operation according to the current crystal direction to obtain the crystal direction required by the grain boundary model, and calculate the crystal orientation axis matrix according to the crystal direction before axis rotation and the crystal direction required by the grain boundary model; According to the crystal orientation rotation axis matrix and the offset vector of the single solvent atom corresponding to the solute atom, the rotation axis offset vector of the single solvent atom corresponding to the solute atom after the rotation axis is calculated; According to the crystal direction and lattice constants of solvent atoms required by the grain boundary model, a unit cell of solvent atoms in the desired crystal direction is established; According to the rotation axis offset vector and the unit cell of the desired crystal-down solvent atom, the positions of all interstitial atoms inserted in the unit cell are determined, and a unit cell with completely filled gaps is established.

3. The interstitial atom segregation grain boundary modeling method for molecular dynamics simulation according to claim 2, characterized in that: The product of the crystal orientation rotation axis matrix and the offset vector of a single solvent atom corresponding to the solute atom is taken as the rotation axis offset vector of a single solvent atom corresponding to the solute atom after the rotation.

4. The interstitial atom segregation grain boundary modeling method for molecular dynamics simulation according to claim 2, characterized in that: The steps to calculate the crystal orientation axis matrix are: The old spatial rectangular coordinate system is established with the a-axis direction in the current crystal orientation as the x-direction, the c-axis direction as the z-direction, and 1 nm as the unit length; According to the orientation required by the grain boundary model, a new spatial rectangular coordinate system is established with 1 nm as the unit length; Obtain target vectors corresponding to three preset linearly independent vectors in the old rectangular coordinate system and the new rectangular coordinate system; The crystal orientation rotation axis matrix is ​​obtained according to the corresponding target vectors in the old and new spatial rectangular coordinate systems.

5. The interstitial atom segregation grain boundary modeling method for molecular dynamics simulation according to claim 4, characterized in that: The expression of the crystal orientation axis matrix is: In the formula, The target vectors of three preset linearly independent vectors in the old rectangular coordinate system of space; The target vectors are three preset linearly independent vectors in the new spatial rectangular coordinate system.

6. The interstitial atom segregation grain boundary modeling method for molecular dynamics simulation according to claim 1, characterized in that: The steps to determine the interstitial atomic distribution density function are: in, For any point position, This is the distribution density function here, is the position of the first grain boundary, is the position of the second grain boundary, is the distribution parameter of the solute atoms determined as required.

7. The interstitial atom segregation grain boundary modeling method for molecular dynamics simulation according to claim 1, characterized in that: The expression for the ratio of interstitial atoms in each fragment is: In the formula, For the The concentration of interstitial atoms in each fragment, For the The distribution density function value of the interstitial atoms in each fragment, is the concentration of interstitial atoms required for the entire model, is the number of segments divided.

8. A system for modeling interstitial atomic segregation grain boundaries for molecular dynamics simulation, characterized in that: include: The unit cell building module is used to build a unit cell with completely filled gaps based on the lattice constant of the solvent, the preferred positions of the interstitial solute atoms, and the crystal orientation required by the grain boundary model; The grain boundary model building module is used to expand the unit cell to obtain a supercell, and to symmetric the supercell at the required interface to obtain the initial grain boundary model; A ratio calculation module is used to determine the interstitial atom distribution density function according to the distribution parameters of the required solute atoms; divide the initial grain boundary model into segments, and determine the ratio of interstitial atoms in each segment according to the interstitial atom distribution density function; The final grain boundary model construction module is used to delete redundant interstitial atoms according to the proportion of interstitial atoms in each segment to obtain a target grain boundary model that meets the segregation distribution requirements; the target grain boundary model is energy minimized to obtain the final grain boundary model.

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