CN111816261B - Molecular dynamics geometric model construction method for amplitude modulation decomposition distribution - Google Patents
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Abstract
The invention belongs to the technical field of material molecular dynamics, and particularly relates to a molecular dynamics geometric model construction method for amplitude modulation decomposition distribution, which comprises the following steps: firstly, constructing a phase field model of system amplitude modulation decomposition based on a Cahn-Hilliard model, iterating the phase field model by utilizing MATLAB, and finally outputting target concentration data of a block in a vtk format; step two, calling a vtk format file of the target concentration data of the block based on the Python environment, and storing the vtk format file in a form of a dictionary which is a built-in type of a sequence in the Python; creating a molecular dynamics geometric model data file, establishing a corresponding relation between an atomic coordinate and coordinates of a block in a dictionary, and setting a concentration threshold of the block; according to the concentration threshold value of the block, sorting the data file of the molecular dynamics geometric model, and outputting a new data file of the molecular dynamics model; and step four, inputting a new molecular dynamics model data file into the LAMMPS to perform molecular dynamics simulation. The invention can be used for molecular dynamics simulation research on porous nano metal materials.
Description
Technical Field
The invention belongs to the technical field of material molecular dynamics, and particularly relates to a molecular dynamics geometric model construction method for amplitude modulation decomposition distribution.
Background
Molecular dynamics simulation is to simulate the structure and behavior of atoms or molecules with the atoms or molecules as basic units by using a computer, thereby obtaining various physical and chemical properties of the atoms or molecular systems. The molecular dynamics simulation can enable the scale of 10000 atoms to be efficiently simulated on a desktop machine to describe the mechanical properties of the atoms, and has higher prediction accuracy.
LAMMPS (Large-scale Atomic/Molecular Massively Parallel Simulator), a Large-scale Atomic molecular parallel simulator, is mainly used for some calculation and simulation works related to molecular dynamics simulation. LAMMPS can support atomic molecular systems including millions of levels in various ensembles in gaseous, liquid or solid phase forms, and can also provide support for a variety of potential functions.
Amplitude modulation decomposition is one type of solid state phase change, and amplitude modulation decomposition is one mechanism by which solid solutions decompose into different phases with different compositions and physical properties. Unlike nucleation driving mechanisms, amplitude-modulated decomposition occurs throughout the material, not just at discrete nucleation sites. Since nucleation is not a thermodynamic barrier, decomposition can only be driven by diffusion processes. Due to this simplicity, the model can be used in other fields besides wide application in material science, such as image restoration, multiphase fluid flow, phase separation, flow visualization, quantum dot formation, taylor flow in microchannels, pore movement in temperature gradients, tumor growth, etc.
The existing molecular dynamics simulation of the porous material only builds one or more spherical or cubic holes in a molecular dynamics model, only the influence of porosity on the material can be simulated, and the effect is far different from the microstructure of the nano porous material actually observed under an electron microscope, and the influence of the real porous structure on the performance of the nano porous material cannot be reflected.
The invention is used for simulating microscopic mechanisms such as damage, fracture and the like of nano porous materials (such as nano silver, nano gold, nano copper and the like) under various working conditions by establishing a molecular dynamics geometric model.
Disclosure of Invention
The invention aims to provide a molecular dynamics geometric model construction method for amplitude modulation decomposition distribution, which is used for simulating the microscopic mechanism of damage and fracture of a nano porous metal material.
Based on the above purpose, the invention adopts the following technical scheme: a molecular dynamics geometric model construction method of amplitude modulation decomposition distribution comprises the following steps:
firstly, constructing a phase field model of system amplitude modulation decomposition based on a Cahn-Hilliard model, iterating an initial concentration field of a block by using the phase field model to obtain a target concentration field of the block, and outputting the target concentration field in a vtk format;
step two, calling a block target concentration field based on a Python environment, establishing a connection between block coordinates and corresponding block concentrations, and storing the connection in a dictionary form which is a built-in type of a sequence in the Python, wherein keys in the dictionary are used for storing the coordinates of the blocks, and elements in the dictionary are used for storing the concentrations of the corresponding blocks;
creating a molecular dynamics geometric model data file by taking lattice constants of atoms in a system as units, establishing a corresponding relation between atomic coordinates and coordinates of blocks in a dictionary, and setting a concentration threshold of the blocks; according to the concentration threshold value of the block, sorting the data file of the molecular dynamics geometric model, and outputting a new data file of the molecular dynamics model;
and step four, inputting a new molecular dynamics model data file into the LAMMPS to perform molecular dynamics simulation.
Further, step one, constructing a phase field model of system amplitude modulation decomposition based on a Cahn-Hilliard equation model, iterating an initial concentration field of a block by using the phase field model to obtain a target concentration field of the block, and outputting the target concentration field in a vtk format as follows:
1.1. based on the Cahn-Hilliard model and an explicit Euler time integration scheme, a block concentration field evolution model with time is obtained, and is specifically as follows:
(1) according to the diffusion model Cahn-Hilliard model of the phase change theory, the following equation can be obtained:
wherein c is the concentration of the block; t is time; r is the position of the block; m is mobility; f is the total free energy of the system;
(2) based on the Cahn-hillard model, using an explicit Euler time integration scheme, a time evolution model of the block concentration matrix can be obtained as follows:
wherein,for the n-th step, the block coordinates are the concentrations at (i, j, k); />M is the concentration at the n+1 th step and the block coordinates (i, j, k); i is an x-axis coordinate value, j is a y-axis coordinate value, and k is a z-axis coordinate value; m is mobility; Δt is the time step;
obtained from (2)And->The numerical relation between the two is used for obtaining an evolution model of the block concentration along with time;
1.2. performing iterative operation on the block concentration evolution model along with time based on MATLAB to obtain an initial concentration fieldTarget concentration field with evolution time length of m delta t>And outputs the phase field model result file time_m.vtk in vtk format.
Further, in the time evolution modelThe process of the calculation is as follows:
f(c)＝Ac 2 (1-c) 2 .....(3)；
wherein c is the concentration of the block; f (c) is chemical energy; a is a potential barrier for controlling two-phase balance in a system;
wherein,is the derivative of f (c),>representing the block concentration of the n-th step with the block coordinates of (i, j, k);
wherein the operator is a Las operatorCalculated by a five-point finite difference method, < >>For the n-th step, the block coordinates are the concentrations at (i, j, k), i being the x-axis coordinate values, j being the y-axis coordinate values, k being the z-axis coordinate values; />The concentration of the n-th step at the position where the block coordinates are (i+1, j, k), and the rest are analogized in turn;
the expression (6) is obtained from the expressions (3) to (5).
Further, the block is a square structure formed by a plurality of lattices in the system; the coordinate value of the horizontal axis (x-axis) in the block coordinates is the number of lattices in the block along the horizontal axis direction; the vertical axis (y-axis) coordinate value in the block coordinates is the number of lattices in the block along the vertical axis direction; the vertical (z-axis) coordinate value in the block coordinates is the number of lattices of the block along the vertical direction.
Further, in the fourth step, the method for sorting the molecular dynamics geometric model data file according to the concentration threshold of the block comprises the following steps: retaining atoms higher than the concentration threshold in the molecular dynamics geometric model data file, and deleting atoms lower than the concentration threshold; the block phase above the concentration threshold is a metallic phase and the block phase below the concentration threshold is a hole phase.
The existing simple spherical or cubic pore molecular dynamics model only can reflect the influence of porosity on physical properties of materials such as thermal property, electric property and the like, and is far from the actual cavity of the materials.
Compared with the existing spherical or cubic pore molecular dynamics model, the invention simulates the molecular dynamics model structure by constructing the molecular dynamics geometric model of amplitude-modulated decomposition distribution. The molecular dynamics model structure established by the invention is similar to the microstructure of the real nano porous material observed under an electron microscope, and the microstructure of the material such as the size of a ligament, the distribution of the ligament and the like can be better reflected. In addition, the model can be used for carrying out simulation analysis on the physical properties (especially mechanical properties) of the porous metal material, and especially the influence of the porosity of the porous material and the microstructure of the holes on the tensile strength of the porous material can be simulated through molecular dynamics, so that a theoretical basis is provided for the application of the porous metal material.
Drawings
FIG. 1 is a schematic flow chart of the method of the present invention;
FIG. 2 is a block information diagram of the phase field model result vtk file of the present invention;
FIG. 3 is a graph of block concentration information of the phase field model result vtk file of the present invention;
FIG. 4 is a data file of a molecular dynamics geometry model of the present invention;
FIG. 5 is a visual representation of a novel molecular dynamics model of metallic silver with a porosity of 50%;
FIG. 6 is a true microstructure of metallic silver with a porosity of 50% under an electron microscope;
FIG. 7 is a molecular dynamics stretching simulation of metallic silver of different porosities;
FIG. 8 is a graph of surface area analysis of a molecular dynamics geometric model conforming to an amplitude modulated decomposition distribution.
Detailed Description
Example 1
A molecular dynamics geometric model construction method of amplitude modulation decomposition distribution, as shown in figure 1, comprises the following steps:
step one, based on a Cahn-Hilliard model, constructing a phase field model of system amplitude modulation decomposition, namely a block concentration evolution model along with time, and comprising the following steps:
1.1 assuming that a phase field model with length, width and height of 60 lattice numbers is established, build a 60 x 60 matrix Is the initial concentration field; each element in the matrix is the concentration of a block; the concentration range of the block is 0-1, and when the concentration of the block is 0 and 1 respectively, the block is in two different phases.
The concentration of each block of the initialization concentration field is as follows:c 0 ＝0.4，noise＝0.1。
1.2 calculating the Laplacian of the current step and the current block by using a five-point finite difference methodThe calculation formula is as follows:
wherein,for the n-th step, the block coordinates are the concentrations at (i, j, k), i being the x-axis coordinate value, j being the y-axis coordinate value, and k being the z-axis coordinate value.
The chemical energy f (c) of the 1.3 phase field model is calculated as follows:
f(c)＝Ac 2 (1-c) 2 .....(3)；
wherein c is the concentration of the block; f (c) is chemical energy; a is a potential barrier for controlling the balance of two phases in the system.
Obtaining the derivative of chemical energy of the phase field model according to formula (3)The formula is as follows:
1.4 diffusion model Cahn-Hilliard equation of phase transition theory is:
wherein c i Is the concentration of the block; t is time; r is the position of the block; m is mobility; f is the total free energy of the system;
the time evolution of the block concentration matrix can be obtained by using an explicit Euler time integration scheme, and the time evolution formula of the concentration matrix is as follows:
wherein M is mobility, and the value of M is 1; Δt is the time step, and Δt is set to 0.01;
in formula (2)The following formula is used for solving:
in formula (6)The results are obtained by the formulas (4) and (5).
Obtaining the concentration field of the current step according to the formula (6)And the concentration field of the next step->The mathematical relationship between the two is that the concentration field of the next step, namely the block concentration evolution model along with time can be updated through the concentration field of the current step.
Step two, iterating the phase field model by utilizing MATLAB, and finally outputting target concentration data of the block in a vtk format, wherein the specific process is as follows: performing iterative operation on the block concentration evolution model along with time 10000 times based on MATLAB to obtain an initial concentration fieldTarget concentration field with evolution time length of 100 (i.e. 10000 Deltat)>And outputs the phase field model result file time_10000.Vtk in vtk format.
Calling a vtk format file of the target concentration data of the block based on the Python environment, and storing the vtk format file in a form of a dictionary which is a built-in type of a sequence in the Python, namely a molecular dynamics geometric model data file; the specific process is as follows:
3.1 building a Python environment, and using the time_10000.vtk file in the Python importing step two, wherein the time_10000.vtk file is shown in figure 2. And defines the whole reading and integrating function by using the def function, so as to make repeated call of the time_10000.Vtk file.
3.2 deleting model information of 1 st to 6 th lines and 216006 (60×60×60+6) th to 216009 (60×60×60+9) th lines in the time_10000.Vtk file obtained by the phase field model with length, width and height of 60 lattice numbers established in the first step, artificially deleting part of model information to simulate a cavity structure, establishing connection between a block and a state value, and recording the block and the state value by using a dictionary form which is a built-in type of a sequence in Python. A dictionary is a variable container model in Python, which is a collection of elements, each element having a field called a key, the keys of different elements being different from each other, the elements being keyed with their corresponding key-value pairs. Elements in the dictionary are used for storing block state values of the phase field model, and keys in the dictionary are used for storing block coordinates of the phase field model, the block coordinates corresponding to the block state values.
3.3 after deleting a partial line of the time 10000.Vtk file, the resulting time 10000.Vtk file has a total of 432000 (2 x 60) lines, as shown in figure 3, the last 216000 (60 x 60) lines in the time 10000.Vtk file are recorded, as elements of the dictionary, the element represents the state value of each block of the phase field model. The front 216000 rows and the rear 216000 rows are in one-to-one correspondence and are dictionary keys, and the keys represent the coordinates of each block of the phase field model; each row in the front 216000 is divided into three elements by spaces, namely an x coordinate, a y coordinate and a z coordinate of the block, and the three values of the x coordinate, the y coordinate and the z coordinate are combined into a tuple which is also a container model in Python and recorded by a dictionary.
Step four, setting a concentration threshold of the block; according to the concentration threshold value of the block, sorting the data file of the molecular dynamics geometric model, and outputting a new data file of the molecular dynamics model; the specific process is as follows:
4.1 taking metallic silver with a porosity of 50% as an example, a data file is created which does not contain holes and has a length, width and height of 60 lattice numbers, since one lattice of silver has four silver atoms, 216000 (60X 60) lattice molecular dynamics geometric model has 864000 atoms, and about 432000 atoms in metallic silver with a porosity of 50%. The first 9 rows of the general data file are header file information of the data file, and the 432003 rows of the data file after the 10 th row are coordinate information of atoms, wherein each atom in one row of information rows and two rows of blank rows is one row in 432000 atoms. Each row is divided by a space into an atom ID (1-432000), an atom type ID (1 if only one atom is in the model, and so on), x-coordinate, y-coordinate, and z-coordinate of the atom.
The next 432003 row is atomic speed information, with one row of information, two empty rows, 432000 atoms per atom row. Each row is divided by a space into an atom ID (1-432000), an x-direction speed, a y-direction speed, and a z-direction speed of the atom (the speed is the original data file speed, and is suggested to be zero).
The data file of the molecular dynamics geometric model obtained by using the metallic silver with the porosity of 50% is shown in fig. 4, the data file is a molecular dynamics model file format used by LAMMPS, and the created data file is read in by using the LAMMPS to perform molecular dynamics simulation.
The atomic coordinates in the data file are represented by lattice numbers as in the block coordinates described above, and are also divided into three elements by spaces, which are respectively the x-coordinate, y-coordinate, and z-coordinate of the atoms. And (3) rounding the coordinates of atoms taking the lattice number as a unit to obtain three elements formed by integers between 0 and 60, wherein x coordinates, y coordinates and z coordinates form element progenitors, the element progenitors are of the same type with the block coordinate information obtained in the step (3.3), and the corresponding relation between each atom in the data file and the block is established through indexes.
4.2 setting a block concentration threshold, wherein blocks with the block concentration exceeding the threshold are defined as solids, blocks with the block concentration lower than the threshold are defined as holes, atoms in the holes are deleted, the rest atoms are reserved, and the reserved atoms form an atomic structure conforming to amplitude modulation decomposition distribution, namely a molecular dynamics geometric model. The size of the block concentration threshold is closely related to the porosity, and the higher the porosity is, the higher the set block concentration threshold is; the block concentration threshold is determined by the results of the phase field model and requires iterative attempts to finalize the determination.
The specific process of constructing an atomic structure that meets the amplitude modulation decomposition profile is as follows:
(1) traversing each atom in the molecular dynamics geometric model data file obtained by using the metallic silver with the porosity of 50%, indexing coordinates of each atom after 4.1 processing in the dictionary created in the step 3.3, returning to the state value of the atom, and comparing with a threshold value. Atoms smaller than the threshold value are deleted, and the deleted atoms are not written into a new data file; atoms above the threshold are reserved and written into the new data file. The number of atoms remaining is recorded during the traversal.
(2) Creating a new data file for writing atomic information. First, header information required for LAMMPS in the data file, i.e., description of the data file, the number of atoms (i.e., the number of atoms recorded in 4.3), the kind of atoms, minimum and maximum values of x-coordinate, y-coordinate, z-coordinate in the phase field model. Wherein, other information is consistent with the data file before modification except that the number of atoms needs to be changed.
Inputting a new molecular dynamics model data file into the LAMMPS to perform molecular dynamics simulation.
A new molecular dynamics model visual diagram of the metal silver with the porosity of 50% is shown in fig. 5, a microstructure of the metal silver with the porosity of 50% under an electron microscope is shown in fig. 6, and the molecular dynamics model structure established by the invention is similar to a microstructure of a real nano porous material observed under the electron microscope, so that the microstructure of the metal material can be more intuitively represented by the molecular dynamics model established by the invention.
The molecular dynamics model data file of the metallic silver with the porosity of 50% is input into LAMMPS for molecular dynamics stretching simulation, a strain stress diagram of the silver conforming to amplitude modulation decomposition distribution is obtained, as shown in fig. 7, wherein ρ represents the porosity, as can be seen from fig. 7, when the stress reaches the maximum value of 0.4GPa at the strain of 0.05, and the stress-strain curve shows obvious toughness fracture characteristics.
Example 2
Referring to the molecular dynamics geometric model construction method of amplitude modulation decomposition distribution in example 1, a molecular dynamics geometric model data file conforming to the amplitude modulation decomposition distribution is constructed for metallic silver with porosities of 10%, 20% and 40% respectively, and is input into LAMMPS for molecular dynamics stretching simulation, and as a result, as shown in fig. 7, ρ in fig. 7 represents the porosity, and as the porosity increases, the tensile ultimate strength of the material decreases greatly. And it can be observed that a low porosity model exhibits brittle fracture characteristics, while a high porosity model is ductile fracture. Further dislocation analysis of the model showed that the low porosity model broke directly after the presence of the motionless dislocations (Hirth dislocation and ladder bar dislocation), while the high porosity model entered the hardening stage after the presence of the motionless dislocations, and the stress gradually decreased after a large number of dislocations had accumulated.
The surface area analysis is carried out on a molecular dynamics geometric model conforming to amplitude modulation decomposition distribution, and the result is shown in figure 8, and the surface area-volume ratio of the model of brittle fracture is found to be greatly lower than that of the model of ductile fracture, so that the high porosity is deduced to bring more surfaces so that dislocation has sufficient surface to slip, and the influence of motionless dislocation on dislocation accumulation is reduced; while the low porosity model causes rapid accumulation of dislocations after the generation of motionless dislocations, resulting in material breakage.
For the metallic silver conforming to the molecular dynamics geometric model of amplitude modulation decomposition distribution, the influence of porosity and the microstructure of holes on the tensile strength of the porous silver material is simulated through molecular dynamics, so that the mechanism of dislocation evolution to cause brittle-tough conversion of the porous silver material is clarified, and a theoretical basis is laid for application of the nano porous silver material.
Claims (4)
1. A molecular dynamics geometric model construction method of amplitude modulation decomposition distribution is characterized by comprising the following steps:
firstly, constructing a phase field model of system amplitude modulation decomposition based on a Cahn-Hilliard model, and then iterating an initial concentration field of a block by using the phase field model to obtain a target concentration field of the block, and outputting the target concentration field in a vtk format, wherein the specific process is as follows:
1.1. based on the Cahn-Hilliard model and an explicit Euler time integration scheme, a block concentration field evolution model with time is obtained, and is specifically as follows:
(1) according to the diffusion model Cahn-Hilliard model of the phase change theory, the following equation can be obtained:
wherein c is the concentration of the block; t is time; r is the position of the block; m is mobility; f is the total free energy of the system;
(2) based on the Cahn-hillard model, using an explicit Euler time integration scheme, a time evolution model of the block concentration matrix can be obtained as follows:
wherein,for the n-th step, the block coordinates are the concentrations at (i, j, k); />For the n+1 th step, the block coordinates are the concentrations at (i, j, k); i is an x-axis coordinate value, j is a y-axis coordinate value, and k is a z-axis coordinate value; m is mobility; Δt is the time step;
obtained from (2)And->The numerical relation between the two is used for obtaining an evolution model of the block concentration along with time;
1.2. performing iterative operation on the block concentration evolution model along with time based on MATLAB to obtain an initial concentration fieldTarget concentration field with evolution time length of m delta t>Outputting a phase field model result file time_m.vtk in a vtk format;
step two, calling a block target concentration field based on a Python environment, establishing a connection between block coordinates and corresponding block concentrations, and storing the connection in a dictionary form which is a built-in type of a sequence in the Python, wherein keys in the dictionary are used for storing the coordinates of the blocks, and elements in the dictionary are used for storing the concentrations of the corresponding blocks;
creating a molecular dynamics geometric model data file by taking lattice constants of atoms in a system as units, establishing a corresponding relation between atomic coordinates and coordinates of blocks in a dictionary, and setting a concentration threshold of the blocks; according to the concentration threshold value of the block, sorting the data file of the molecular dynamics geometric model, and outputting a new data file of the molecular dynamics model;
and step four, inputting a new molecular dynamics model data file into the LAMMPS to perform molecular dynamics simulation.
2. The method for constructing a molecular dynamics geometric model of amplitude modulation decomposition distribution according to claim 1, wherein in the time evolution modelThe process of the calculation is as follows:
f(c)＝Ac 2 (1-c) 2 .....(3)；
wherein c is the concentration of the block; f (c) is chemical energy; a is a potential barrier for controlling two-phase balance in a system;
wherein,is the derivative of f (c),>representing the block concentration of the n-th step with the block coordinates of (i, j, k);
wherein the operator is a Las operatorCalculated by a five-point finite difference method, < >>For the n-th step, the block coordinates are the concentrations at (i, j, k), i being the x-axis coordinate values, j being the y-axis coordinate values, k being the z-axis coordinate values; />The concentration of the n-th step at the position where the block coordinates are (i+1, j, k), and the rest are analogized in turn;
the expression (6) is obtained from the expressions (3) to (5).
3. The method for constructing a molecular dynamics geometric model of amplitude modulation decomposition distribution according to claim 2, wherein the block is a square structure composed of a plurality of lattices in the system; the coordinate value of the horizontal axis in the block coordinates is the number of lattices in the block along the horizontal axis direction; the vertical axis coordinate value in the block coordinates is the number of lattices along the vertical axis direction in the block; the vertical axis coordinate value in the block coordinates is the number of lattices of the block along the vertical axis direction.
4. The method for constructing a molecular dynamics geometric model of amplitude modulation decomposition distribution according to claim 3, wherein the method for sorting the molecular dynamics geometric model data file according to the concentration threshold of the block in the third step is as follows: retaining atoms higher than the concentration threshold in the molecular dynamics geometric model data file, and deleting atoms lower than the concentration threshold; the block phase above the concentration threshold is a metallic phase and the block phase below the concentration threshold is a hole phase.
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