A method for modeling interstitial atom segregation grain boundaries for molecular dynamics simulations

Abstract

The present invention relates to the field of micro-nanomaterial technology, and specifically to a method for modeling interstitial atom segregation grain boundaries for molecular dynamics simulation, comprising: establishing a unit cell with completely filled interstitials; constructing an initial grain boundary model; determining an interstitial atom distribution density function; segmenting the initial grain boundary model into segments and determining the proportion of interstitial atoms within each segment; deleting excess interstitial atoms to obtain a target grain boundary model that meets segregation distribution requirements; and energy minimizing the target grain boundary model to obtain a final grain boundary model with different degrees of segregation. By introducing an interstitial atom distribution density function, the present invention can flexibly control the distribution of interstitial atoms in the grain boundary model, thereby enabling subsequent molecular dynamics simulations to target interstitial solid solution systems under different segregation conditions, and achieving modeling of arbitrary grain boundary models containing interstitial solutes, thereby enabling subsequent molecular dynamics simulations to target different grain boundary models.

Description

Technical Field

[0001] The present 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 solutions refer to solid solutions formed when solute atoms do not occupy the normal node positions of the solvent lattice, but instead fill the gaps between solvent atoms. The conditions for the formation of interstitial solid solutions mainly depend on the size of the solute atoms. Generally, the smaller the solute atoms, the easier it is to enter the interstitial positions of the solvent lattice, thus forming interstitial solid solutions. Typical interstitial solid solution systems include carbon solid solution in iron, hydrogen solid solution in metals, and oxygen solid solution in metals. These solid solution systems are extremely common in the fields of metallurgy, energy, and mechanical manufacturing, but their interstitial atoms are often difficult to observe experimentally due to their extremely small atomic radius. Therefore, the study of interstitial solid solution systems has enormous scientific and technological significance.

[0003] Molecular dynamics simulations are based on the laws of physics and can accurately determine atomic motion trajectories. They can also handle systems as large as hundreds of millions of atoms. They can simulate realistic micro- and nanoscale systems while providing a deep understanding of molecular dynamics, revealing the dynamic response mechanisms and patterns of change. These advantages make molecular dynamics simulations crucial 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 used for replacing atoms, such as the modeling of multi-principal element alloys. It optimizes the atomic positions by exchanging atomic coordinates to achieve reasonable solid solution system modeling. However, since this method only operates on existing atoms and cannot insert new atoms, it cannot be implemented in the modeling of interstitial solid solution systems. In addition, there is a solid solution modeling method based on chemical potential difference. However, in reality, interstitial elements 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 implementation 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 implemented in interstitial solid solution, and the basic principle of the modeling method based on chemical potential difference is only for equilibrium segregation modeling, which makes it 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:

[0008] Based on 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;

[0009] The unit cell is expanded to obtain a supercell, and the supercell is symmetrically arranged at the required interface to obtain the initial grain boundary model;

[0010] Determine the interstitial atom distribution density function based on the distribution parameters of the required solute atoms;

[0011] 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;

[0012] 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;

[0013] The target grain boundary model is energy minimized to obtain the final grain boundary model.

[0014] Preferably, the steps of establishing a unit cell with completely filled gaps are:

[0015] 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;

[0016] 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;

[0017] 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;

[0018] According to the crystal orientation rotation axis matrix and the offset vector of a single solvent atom corresponding to the solute atom, the rotation axis offset vector of a single solvent atom corresponding to the solute atom after the rotation axis is calculated;

[0019] According to the crystal orientation and lattice constants of solvent atoms required by the grain boundary model, a unit cell of solvent atoms in the desired crystal orientation is established;

[0020] Based on the rotation axis offset vector and the desired unit cell of the solvent atom in the crystal, the positions of all interstitial atoms inserted in the unit cell are determined, and a unit cell with completely filled gaps is established.

[0021] 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.

[0022] Preferably, the steps of calculating the crystal orientation axis matrix are:

[0023] 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;

[0024] 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;

[0025] Obtain the target vectors corresponding to three preset linearly independent vectors in the old and new spatial rectangular coordinate systems respectively;

[0026] 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; The target vectors of three preset linearly independent vectors in the new spatial rectangular coordinate system.

[0027] Preferably, the step of determining the interstitial atom distribution density function is:

[0028]

[0029] 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 on demand.

[0030] Preferably, the expression for the ratio of interstitial atoms in each fragment is:

[0031]

[0032] Where, For the The concentration of interstitial atoms within a fragment, For the The distribution density function value of the interstitial atoms in the fragment, is the concentration of interstitial atoms required for the entire model, is the number of segments divided.

[0033] A modeling system for interstitial atom segregation grain boundaries for molecular dynamics simulations, comprising:

[0034] 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;

[0035] The grain boundary model building module is used to expand the unit cell to obtain a supercell, and symmetric the supercell at the required interface to obtain the initial grain boundary model;

[0036] A ratio calculation module is used to determine the interstitial atom distribution density function based on 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 based on the interstitial atom distribution density function;

[0037] 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.

[0038] The beneficial effects of the present invention are:

[0039] The modeling method of the present invention can perform molecular dynamics simulation on interstitial solid solutions, and in particular solves the problem that traditional methods are difficult to deal with interstitial atomic segregation, which is conducive to the simulation results being closer to actual physical conditions. Specifically, the present invention obtains the corresponding coordinates of solute atoms after the rotation axis through the rotation axis matrix, determines the position of interstitial solid solution atoms under any crystal orientation, and realizes the modeling of any grain boundary model containing interstitial solutes, so that subsequent molecular dynamics simulations can be performed on different grain boundary models. The present invention can flexibly control the distribution of interstitial atoms in the grain boundary model by introducing an interstitial atom distribution density function, so that subsequent molecular dynamics simulations can be performed on interstitial solid solution systems under different segregation conditions. BRIEF DESCRIPTION OF THE DRAWINGS

[0040] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the embodiments or the description of the prior art. 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 any creative work.

[0041] Figure 1 A flow chart of an embodiment of a method for modeling interstitial atom segregation grain boundaries for molecular dynamics simulation according to the present invention;

[0042] Figure 2 A titanium-oxygen unit cell with a completely filled gap established in an embodiment of the present invention;

[0043] Figure 3 is the initial titanium-oxygen grain boundary model established in the embodiment of the present invention;

[0044] Figure 4 Schematic diagram of the solute oxygen atomic distribution function in an embodiment of the present invention;

[0045] Figure 5 The final grain boundary models with different segregation degrees obtained in the embodiment of the present invention;

[0046] Figure 6 Schematic diagram of the segregation of oxygen atoms in an embodiment of the present invention. DETAILED DESCRIPTION

[0047] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. 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 making creative efforts are within the scope of protection of the present invention.

[0048] An embodiment of a method for modeling interstitial atomic segregation grain boundaries for molecular dynamics simulation of the present invention, in which a size of interstitial oxygen atoms segregate into titanium The grain boundary model of titanium-oxygen grain boundary model is referred to as titanium-oxygen grain boundary model. Figure 1 As shown, the specific steps include:

[0049] S1. Create a unit cell with completely filled gaps;

[0050] Based on 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 gaps is established. The specific steps are: based on 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; based on the corresponding ratio of solvent atoms and solute atoms, the lattice constant of the solvent atoms and the preferred position of the 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 single solvent atom corresponding to the solute atom; based on 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 rotation axis matrix is ​​calculated based on 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 rotation is calculated, that is, ; According to the crystal orientation required by the grain boundary model and the lattice constant of the solvent atoms, a unit cell of the desired crystal-down solvent atoms is established; according to the rotation axis offset vector and the unit cell of the desired crystal-down solvent atoms, the positions of all interstitial atoms inserted in the unit cell are determined, thereby establishing a unit cell with completely filled gaps.

[0051] The steps for calculating the crystal orientation rotation axis matrix are as follows: establish an old rectangular coordinate system with the a-axis as the x-direction, the c-axis as the z-direction, and 1 nm as the unit length. According to the crystal orientation of the target model, establish a new rectangular coordinate system with 1 nm as the unit length. Take three linearly independent vectors and, according to 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 interstitial 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 direction is taken as follows: take three linearly independent vectors. The three independent vectors are (2.9503, 0, 0), (0, 5.1101, 0), (0, 0, 4.6832) in the old coordinate system. The three independent vectors are expressed as (2.7878, -0.9657, 0), (1.6727, 4.8286, 0), (0, 0, 4.6832) in the new coordinate system. 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.

[0052] S2, constructing the initial grain boundary model;

[0053] Specifically, the unit cell is expanded to obtain a supercell, and the supercell is symmetrically arranged at the desired interface to obtain a grain boundary model.

[0054] 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.

[0055] S3. Determine the interstitial atom distribution density function;

[0056] Specifically, the interstitial atom distribution density function is determined according to the distribution parameters of the desired solute atoms.

[0057] like Figure 4 As shown, the expression of the interstitial atom distribution density function is:

[0058]

[0059] Where, 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 on demand.

[0060] 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.

[0061] S4, dividing the initial grain boundary model into segments and determining the proportion of interstitial atoms in each segment;

[0062] 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:

[0063]

[0064] Where, For the The concentration of interstitial atoms within a fragment, For the The distribution density function value of the interstitial atoms in the fragment, is the concentration of interstitial atoms required for the entire model, is the number of segments divided.

[0065] In this embodiment, the initial grain boundary model is divided into 25 segments. For the six distribution conditions of S3, the expected distribution effects are as follows: Figure 4 shown.

[0066] S5. Randomly select interstitial atoms in each segment and delete them according to the ratio of interstitial atoms in each segment 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;

[0067] 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 5shown.

[0068] 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 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 the results of the experiment. Figure 4 The expected distribution effect is achieved in order to verify the number of interstitial atoms and atomic segregation in the final grain boundary model. By constructing a titanium-oxygen grain boundary model with dense interstitial oxygen atoms and optimizing the number of atoms and segregation degree 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 achieved, which is conducive to the subsequent molecular dynamics simulation research of different segregation degrees.

[0069] A modeling system for interstitial atom segregation grain boundaries for molecular dynamics simulations includes: a unit cell establishment module, a grain boundary model establishment module, a proportion calculation module, and a final grain boundary model construction module. The unit cell establishment module is used to establish a unit cell with completely filled gaps based on the lattice constant of the solvent, the preferred position of interstitial solute atoms, and the crystal orientation required for 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 proportion calculation module is used to determine the interstitial atom distribution density function based on the distribution parameters of the required solute atoms; the initial grain boundary model is divided into segments, and the proportion of interstitial atoms in each segment is determined based on the interstitial atom distribution density function; the final grain boundary model construction module is used to delete redundant interstitial atoms based on 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.

[0070] 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 principles of the present invention should be included in the scope of protection of the present invention.

Claims

1. A method for modeling interstitial atom 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 gaps is established; wherein, the steps of establishing the unit cell with completely filled gaps are: according to the preferred position of the interstitial solute atoms, obtaining the corresponding ratio of solvent atoms and solute atoms when the gap is completely filled; according to the corresponding ratio of solvent atoms and solute atoms, the lattice constant of the solvent atoms and the preferred position of the interstitial solute atoms, calculating the offset vector of a single solvent atom corresponding to the solute atom; performing an axis rotation operation according to the current crystal orientation to obtain the crystal orientation required by the grain boundary model, and calculating the crystal orientation rotation axis matrix according to the crystal orientation before the axis rotation and the crystal orientation required by the grain boundary model; calculating the rotation axis offset vector of a single solvent atom corresponding to the solute atom after the axis rotation according to the crystal orientation rotation axis matrix and the offset vector of a single solvent atom corresponding to the solute atom; according to the crystal orientation required by the grain boundary model and the lattice constant of the solvent atoms, establishing the unit cell of the solvent atoms in the desired crystal direction; according to the rotation axis offset vector and the unit cell of the solvent atoms in the desired crystal direction, determining the positions of all interstitial atoms inserted in the unit cell, and establishing the unit cell with completely filled gaps; The unit cell is expanded to obtain a supercell, and the supercell is symmetrically arranged at the required interface to obtain the initial grain boundary model; Determine the interstitial atom distribution density function based on the distribution parameters of the required 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 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.

3. The interstitial atom segregation grain boundary modeling method for molecular dynamics simulation according to claim 1, 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 1nm 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 the target vectors corresponding to three preset linearly independent vectors in the old and new spatial rectangular coordinate systems respectively; The crystal orientation axis matrix is ​​obtained according to the corresponding target vectors in the old and new spatial rectangular coordinate systems.

4. The interstitial atom segregation grain boundary modeling method for molecular dynamics simulation according to claim 3, characterized in that: The expression of the crystal orientation axis matrix is: Where, The target vectors of three preset linearly independent vectors in the old rectangular coordinate system; The target vectors of three preset linearly independent vectors in the new spatial rectangular coordinate system.

5. 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 atom 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 on demand.

6. 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: Where, For the The concentration of interstitial atoms within a fragment, For the The distribution density function value of the interstitial atoms in the fragment, is the concentration of interstitial atoms required for the entire model, is the number of segments divided.

7. A system for modeling interstitial atom segregation grain boundaries for molecular dynamics simulation, characterized in that: include: A unit cell establishment module is used to establish a unit cell with completely filled gaps based on the lattice constant of the solvent, the preferred position of the interstitial solute atoms, and the crystal orientation required by the grain boundary model; wherein the steps of establishing a unit cell with completely filled gaps are: according to the preferred position of the interstitial solute atoms, obtaining the corresponding ratio of solvent atoms and solute atoms when the gap is completely filled; according to the corresponding ratio of solvent atoms and solute atoms, the lattice constant of the solvent atoms and the preferred position of the interstitial solute atoms, calculating the offset vector of a single solvent atom corresponding to the solute atom; performing an axis rotation operation according to the current crystal orientation to obtain the crystal orientation required by the grain boundary model, and calculating the crystal orientation rotation axis matrix according to the crystal orientation before the axis rotation and the crystal orientation required by the grain boundary model; calculating the axis rotation offset vector of a single solvent atom corresponding to the solute atom after the axis rotation according to the crystal orientation rotation axis matrix and the offset vector of a single solvent atom corresponding to the solute atom; establishing a unit cell of the solvent atom in the desired crystal direction downward according to the crystal orientation required by the grain boundary model and the lattice constant of the solvent atom; determining the positions of all interstitial atoms inserted in the unit cell according to the axis rotation offset vector and the unit cell of the solvent atom in the desired crystal direction downward, and establishing a unit cell with completely filled gaps; The grain boundary model building module is used to expand the unit cell to obtain a supercell, and 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 based on 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 based on 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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