A method for studying interface properties of nanocrystal composite glass based on molecular dynamics simulation

Abstract

The application discloses a method for researching interface properties of nanocrystal composite glass based on molecular dynamics simulation, which comprises the following steps: constructing an initial structure model of a glass matrix; performing high-temperature quenching simulation on the initial structure model of the glass based on molecular dynamics; constructing a nanocrystal cluster model; splicing the glass matrix model and the nanocrystal cluster model; simulating relaxation of the composite structure model based on molecular dynamics; outputting atomic motion trajectories of a certain frame number at a specific temperature; and calculating interface properties by means of demarcating a spherical shell layer. The application adopts the molecular dynamics method to construct the interface of the nanocrystal composite glass, calculates the properties of the nanocrystal composite glass by demarcating the spherical shell layer to count the atomic motion trajectories at different positions, solves the problem that the interface properties are difficult to be characterized in experiments, helps to more accurately understand the distribution and diffusion properties of atoms in the interface region of the glass and the crystal, and provides a reference for the interface structure research of the nanocrystal composite glass.

Description

Technical Field

[0001] This invention belongs to the field of glass materials, specifically relating to a method for investigating the properties of the glass-crystal interface in nanocrystalline composite glass systems based on molecular dynamics simulation. Background Technology

[0002] Nanocrystalline composite glass materials are a class of materials in which nanocrystals are encapsulated within a glass matrix. They retain the excellent optical properties of nanocrystals while exhibiting good stability due to the glass's isolation from the external environment, thus attracting considerable research interest. This type of material requires high-temperature composite processing. Intense interfacial diffusion and reactions at high temperatures often damage the crystal structure, leading to a decline in optical performance. Research on how to avoid these phenomena currently focuses on controlling raw materials and processes. Because crystals are nanoscale in size, their structure is difficult to characterize directly experimentally, resulting in insufficient research and explanation of the interfacial microstructure. However, during the molding process of nanocrystalline composite glass materials, interfacial phenomena have a crucial impact on the stability of the crystals and the luminescent properties of the material; therefore, the study of the interfacial microstructure is extremely important.

[0003] With the development of computer science, computer performance has been greatly improved, and high-performance computer clusters are playing an increasingly indispensable role in the scientific community. The development of materials informatics has provided a powerful impetus for the advancement of materials science. In the field of glass science, molecular dynamics (MD) simulates materials at the atomic level, obtaining information about the position and momentum of each atom in the system. Statistical processing of this information allows researchers to easily obtain information that is difficult to obtain through experimental characterization methods, including atomic radial distribution, coordination number, mean square displacement, bond angle and bond length distribution, etc. This information provides important basis for studying glass network structures and glass-crystal interactions. These parameters can be used to further predict the properties of nanocrystalline composite glass materials and guide their formulation design and process optimization, ensuring their performance meets the needs of specific fields.

[0004] Molecular dynamics simulations obtain the changes in atomic positions in the simulated system at each time step by integrating the equations of atomic motion, and control the temperature by altering the kinetic energy of the particles in the system in a specific manner. For nanocrystalline composite glass systems, at different simulation temperatures, atoms in the simulated system diffuse, deviating from their initial positions and forming a diffusion interface at the contact point between the crystal and the glass. Atomic number density refers to the number of a particular atom contained in a unit system. Sampling within concentric spherical shells uniformly distributed at the interface, the atomic number density of each shell can be expressed as:

[0005] Where N is the total number of a certain type of atom in the shell, d0 is the distance from the sampling start position to the center of the sphere, and d is the shell thickness. The atom number density at different positions at the interface can reflect the atomic diffusion situation, and thus obtain the thickness information of the diffusion interface. For a system containing N atoms, taking the simulation system at a certain time as time zero, the position vector of atom i at time t0 is r. i (0), after a certain time Δt, the position vector of atom i is r. i If (Δt) is the mean square displacement (MSD) of the squared displacements of all atoms in the system during this time period, then the mean square displacement (MSD) is defined as the mean square displacement. Angle brackets denote ensemble averages. For d-dimensional diffusion, the diffusion coefficient D of a particle is proportional to the MSD: Finally, according to the formula The average atomic diffusion coefficient within each shell is calculated to obtain the interfacial distribution of the diffusion coefficient, where N is the total number of a certain type of atom within the shell. The diffusion coefficient is influenced by temperature and activation energy; the value of D increases significantly with increasing temperature and is also affected by the local environment and density of the particles. Generally, for the same substance at a certain temperature, the order of D among the crystalline, glassy, ​​and molten structures is: molten > glassy > crystalline. Summary of the Invention

[0006] In light of the above research background, this invention provides a method for studying the atomic properties at the interface of nanocrystalline composite glass systems based on molecular dynamics simulation. This method employs molecular dynamics simulation, and by setting appropriate simulation parameters and procedures under a suitable force field, it can accurately obtain the thickness of the interfacial diffusion layer and the properties of different atoms at the interface, thus providing guidance for the research of nanocrystalline composite glasses.

[0007] To achieve the above objectives, the technical solution of the present invention is as follows:

[0008] A method for studying the interfacial properties of nanocrystalline composite glasses based on molecular dynamics simulations includes the following steps:

[0009] Step 1: Construct a box model of amorphous glass and output the structure file;

[0010] Step 2: Perform high-temperature quenching simulation on the box model of amorphous glass based on molecular dynamics to obtain the glass structure file as the matrix;

[0011] Step 3: Construct nanocrystalline clusters to obtain the structure file;

[0012] Step 4: Assemble the initial composite model using the splicing method;

[0013] Step 5: Based on molecular dynamics, heat the composite model to a specific relaxation temperature, quench it to a specific temperature, sample it with a certain step size, and output the trajectory file.

[0014] Step 6: Sort each atom in the trajectory file according to its distance from the center of the box, and determine the position of each atom;

[0015] Step 7: Calculate the properties of atoms in different regions near the interface to obtain the distribution of relevant properties along the interface.

[0016] Furthermore, in step one, the amorphous glass box model was constructed using the program Packmol, with an initial density set to 2.4-2.6 g / cm³. 3 The glass type is potassium aluminum phosphorus glass.

[0017] Furthermore, in step two, the molecular dynamics process uses the Buckingham potential function type and the effective charge, with O... 2- The reference value is -1.2e.

[0018] Furthermore, in step two, the present invention uses the molecular dynamics simulation program LAMMPS (Large-scale Atomic / Molecular Massively Parallel Simulator) to perform quenching by continuous cooling. The glass model is fully relaxed at 5000K and then cooled to 300K and relaxed again, with a cooling rate of 0.01K per step.

[0019] Furthermore, in step two, the glass model was relaxed for 2 ns at both 5000K and 300K to release internal stress and reach equilibrium.

[0020] Furthermore, in step three, the nanocrystal clusters are oxide crystals; the oxide crystals include Y₂O₃, Er₂O₃, and Y₃Al₅O₃. 12 Or CaAl2Si2O8.

[0021] Furthermore, in step three, the nanoclusters are constructed using MaterialsStudio software, and are spherical in shape with a radius of [missing information].

[0022] Furthermore, in step three, the cell files used to construct the nanoclusters are downloaded from the Crystallography OpenDatabase website.

[0023] Furthermore, in step four, the center of the nanocluster cluster is aligned with the center of the matrix box, and the joint is preserved. A vacuum layer is used to avoid excessive stress caused by atomic overlap, and atoms near the interface are randomly removed to maintain the system's charge neutrality.

[0024] Further, in step four, the splicing method includes: 1) deleting atoms in the matrix that coincide with the predetermined placement position of the nanoclusters; 2) modifying the atomic coordinates in the nanocluster structure file to place them in the predetermined placement position; 3) adding the atomic coordinates from the nanocluster structure file to the glass matrix structure file to obtain the structure file of the composite model; 4) calculating the total atomic charge of the structure file of the composite model and randomly deleting atoms near the interface to maintain charge neutrality.

[0025] Furthermore, in step five, the composite model is heated to 1800K, relaxed for 1ns, and then cooled to 300K. The heating and cooling rates are both 5K / ps.

[0026] Furthermore, in step five, the composite model is performed at 1800K and 300K respectively, with sampling steps of 2fs and 200fs, and sampling frames of 20000 frames and 500 frames respectively.

[0027] Furthermore, in step six, taking the crystal surface as the origin, 20 spherical shells are taken from both the crystal portion and the glass portion along the normal direction of the crystal surface. Each shell has its origin at the center of the box and its thickness is... The position of an atom near the interface is represented by the shell in which its coordinates are located.

[0028] Furthermore, in step seven, the properties of the atoms include atomic number density and diffusion coefficient.

[0029] Furthermore, in step seven, the atomic number density is calculated from the atomic motion trajectories obtained by downsampling at 300K using formula (1), and the average value of 500 frames of trajectories is taken:

[0030]

[0031] Where N is the total number of a certain type of atom in the shell, d0 is the distance from the sampling start position to the center of the sphere, d is the shell thickness, and n is the shell number;

[0032] The calculation of the diffusion coefficient involves three steps: the atomic mean square displacement (MSD) is calculated by formula (3) based on the atomic motion trajectory obtained by sampling from 1800K according to formula (2); the diffusion coefficient D of each atom in each shell is calculated from the MSD according to formula (3); and the average value of D in each shell is calculated according to formula (4).

[0033]

[0034]

[0035]

[0036] Where Δt is the time interval between two frames of trajectory, N is the total number of atoms, and r i (t) represents the coordinates of atom i, and d represents the dimension of the simulated system.

[0037] Furthermore, in step seven, the atomic number density is taken as the average value of different conformations under the ensemble, and the diffusion coefficient is calculated as the average value of different time intervals under the ensemble.

[0038] Compared with existing technologies, this invention has the following advantages: This invention provides a method for studying the interface properties of nanocrystalline composite glasses based on molecular dynamics simulation. By simulating the glass forming process and the glass-nanocrystalline interface formation process, the trajectories of atoms at different temperatures are obtained, and properties such as the atomic diffusion distance and diffusion coefficients at the interface are calculated. The entire process is based on molecular dynamics simulation, reducing experimental costs and solving the problem of experimentally characterizing interface properties. This provides guidance for the selection of raw materials, composition determination, and process route optimization for nanocrystalline composite glasses. Attached Figure Description

[0039] Figure 1 Schematic diagrams of the initial structures of the glass matrix model, the nanocrystal cluster model, and the composite model;

[0040] Figure 2 This is a schematic diagram showing the distribution of the glass region, diffusion region, and crystal region across the cross-section of the model.

[0041] Figure 3 Here are the atomic number density distribution and diffusion coefficient distribution diagrams for each ion in Example 1;

[0042] Figure 4 Here are the atomic number density distribution and diffusion coefficient distribution diagrams for each ion in Example 2;

[0043] Figure 5 The atomic number density distribution and diffusion coefficient distribution of each cation in Example 3 are shown. Detailed Implementation

[0044] The present invention will be further described in detail below with reference to the embodiments:

[0045] Example 1

[0046] The interfacial properties of the calcium aluminosilicate glass composite CaAl2Si2O8 crystal system were studied using the above method. (1) First, the composition of the glass matrix was determined to be 0.65SiO2-0.2Al2O3-0.15CaO (wt%), with 15795 Si, 9720 Al, 3645 Ca, and 49815 O atoms. The initial size of the simulation box was... The initial density is 2.74 g / cm³. 3 In step 1 of the method for studying the interface properties of nanocrystalline composite glasses based on molecular dynamics simulation provided by the present invention, an initial structural model is generated using the Packmol program. (2) Using the LAMMPS program, the potential function is set to Pedone form, the time step is 0.2fs, and the initial structural model is relaxed for 1ns under both the canonical ensemble and the microcanonical ensemble at 5000K. Then, it is quenched to 300K under the canonical ensemble at a cooling rate of 0.01K per step, and the matrix glass structure file is output. (3) Using the MaterialsStudio software, the CaAl2Si2O8 structure file downloaded from the Crystallography Open Database is used as the unit cell to construct a structure with a radius of (4) Delete the spherical nanoclusters in the glass matrix that are far from the center of the box. The atomic coordinates in the nanocluster structure file are modified to align the center of the sphere with the center of the box. The structure files of the nanocluster and the matrix glass are then combined to obtain the composite model structure file. Initial structural diagrams of the glass matrix model, nanocluster model, and composite model are shown below. Figure 1 As shown. (5) Using LAMMPS software, the composite model structure file is heated to 1800K at a rate of 0.01K per step under an isothermal and isobaric ensemble and relaxed for 10ns. The sample size is 20ns with a step size of 10 steps to obtain the trajectory file at 1800K. Then, it is cooled to 300K at the same cooling rate. The model is relaxed for 0.5ns under both canonical and microcanonical ensembles. The last 1ps is sampled with a step size of 10 steps under the microcanonical ensemble to obtain the trajectory file at 300K. (6) Using Assuming the thickness of the spherical shell, the calculation interface begins to extend towards the crystalline and glassy regions. The number of spherical shell layers is 30 in total, and the atomic coordinate range corresponding to each shell layer is calculated. (7) For the trajectory files at 1800K and 300K respectively, the distance from each atom to the center of the box is calculated, and the shell layer to which it belongs is numbered according to the distance. The atomic number density and the mean square displacement of the atoms in each shell layer are calculated to obtain the interface distribution of atomic number density. (8) In step 7 of the method for studying the interface properties of nanocrystalline composite glass based on molecular dynamics simulation provided by the present invention, the diffusion coefficient of the atoms in each shell layer is calculated to obtain the interface distribution of atomic diffusion coefficient. The atomic number density distribution diagram and diffusion coefficient distribution diagram of each cation are as follows. Figure 3 As shown (the horizontal axis 0 represents the interface between the glass and crystal during splicing, positive numbers represent the glass region during splicing, and complex numbers represent the crystal region during splicing). Using the transition region of the diffusion coefficients of each element as the diffusion layer, the thickness of the diffusion interface is calculated as follows: A schematic diagram showing the distribution of the glass region, diffusion region, and crystal region in the cross-section of the model is shown below. Figure 2 As shown.

[0047] Example 2

[0048] The interfacial properties of the phosphoaluminate glass composite Y2O3 crystal system were studied using the above method. (1) First, the basic formulation for computer simulation was determined, including the glass matrix and the crystal. The glass matrix was selected as 0.5P2O5-0.5Al2O3 (wt%), with the following atomic numbers: 12600 P, 12600 Al, and 50400 O. The crystal was prepared at 2.5 g / cm³. 3 The density calculation simulation box size is In step 1 of the method for studying the interface properties of nanocrystalline composite glasses based on molecular dynamics simulation provided by the present invention, an initial structural model is generated using the Packmol program. (2) Using the LAMMPS program, the potential function is set to Buckingham form, the time step is 0.2fs, and the initial structural model is relaxed for 1ns under both the canonical ensemble and the microcanonical ensemble at 5000K. Then, it is quenched to 300K under the canonical ensemble at a cooling rate of 0.01K per step, and the matrix glass structure file is output. (3) Using the MaterialsStudio software, the Y2O3 structure file downloaded from the Crystallography Open Database is used as the unit cell to construct a structure with a radius of (4) Delete the spherical nanoclusters in the glass matrix that are far from the center of the box. The atomic coordinates in the nanocluster structure file are modified to align the center of the sphere with the center of the box. The structure files of the nanocluster and the matrix glass are then combined to obtain the composite model structure file. Initial structural diagrams of the glass matrix model, nanocluster model, and composite model are shown below. Figure 1 As shown. (5) Using LAMMPS software, the composite model structure file is heated to 1800K at a rate of 0.01K per step under an isothermal and isobaric ensemble and relaxed for 10ns. The sample is taken for 10ns with a step size of 1ps to obtain the trajectory file at 1800K. Then, it is cooled to 300K at the same cooling rate. The model is relaxed for 0.5ns under both canonical and microcanonical ensembles. The last 1ps is sampled with a step size of 10 steps under the microcanonical ensemble to obtain the trajectory file at 300K. (6) Using Assuming the thickness of the spherical shell, the calculation interface begins to extend towards the crystalline and glassy regions. The number of spherical shell layers is 30 in total, and the atomic coordinate range corresponding to each shell layer is calculated. (7) For the trajectory files at 1800K and 300K respectively, the distance from each atom to the center of the box is calculated, and the shell layer to which it belongs is numbered according to the distance. The atomic number density and the mean square displacement of the atoms in the shell layer are calculated to obtain the interface distribution of the atomic number density. The thickness of the diffusion interface is calculated based on the diffusion distance of each atom in the crystalline phase and the glass phase. A schematic diagram showing the distribution of the glass region, diffusion region, and crystal region in the cross-section of the model is shown below. Figure 2 As shown. (8) Calculate the diffusion coefficient for atoms in each shell. To avoid statistical errors caused by a small number of atoms of the same element in some regions, within a sampling length of 10 ns at 1800 K, the shell to which the atoms belong is re-counted every 0.5 ns, and the diffusion coefficient is calculated. Finally, the average value of the diffusion coefficient is calculated. The interface distribution of atomic diffusion coefficients is obtained. The atomic number density distribution diagram and diffusion coefficient distribution diagram of each ion are shown in the figure. Figure 4 As shown (the horizontal axis 0 represents the interface between the glass and the crystal during splicing, positive numbers represent the glass region during splicing, and complex numbers represent the crystal region during splicing).

[0049] Example 3

[0050] The interfacial properties of the phosphoaluminate glass composite Y2O3 crystal system were studied using the above method. (1) First, the basic formulation for computer simulation was determined, including the glass matrix and the crystal. The glass matrix was selected as 0.5P2O5-0.2Al2O3-0.3K2O (wt%), with the following atomic numbers: 14000 P, 5600 Al, 8400 K, and 47600 O. The crystal was prepared at 2.5 g / cm³. 3 The density calculation simulation box size is In step 1 of the method for studying the interface properties of nanocrystalline composite glasses based on molecular dynamics simulation provided by the present invention, an initial structural model is generated using the Packmol program. (2) Using the LAMMPS program, the potential function is set to Buckingham form, the time step is 0.2fs, and the initial structural model is relaxed for 1ns under both the canonical ensemble and the microcanonical ensemble at 5000K. Then, it is quenched to 300K under the canonical ensemble at a cooling rate of 0.01K per step, and the matrix glass structure file is output. (3) Using the MaterialsStudio software, the Y2O3 structure file downloaded from the Crystallography Open Database is used as the unit cell to construct a structure with a radius of (4) Delete the spherical nanoclusters in the glass matrix that are far from the center of the box. The atomic coordinates in the nanocluster structure file are modified to align the center of the sphere with the center of the box. The structure files of the nanocluster and the matrix glass are then combined to obtain the composite model structure file. The initial structures of the glass matrix model, the nanocluster model, and the composite model are as follows: Figure 1 As shown. (5) Using LAMMPS software, the composite model structure file is heated to 1800K at a rate of 0.01K per step under an isothermal and isobaric ensemble and relaxed for 10ns. The sample is taken for 10ns with a step size of 1ps to obtain the trajectory file at 1800K. Then, it is cooled to 300K at the same cooling rate. The model is relaxed for 0.5ns under both canonical and microcanonical ensembles. The last 1ps is sampled with a step size of 10 steps under the microcanonical ensemble to obtain the trajectory file at 300K. (6) Using Assuming the thickness of the spherical shell, the calculation interface begins to extend towards the crystalline and glassy regions. The number of spherical shell layers is 30 in total, and the atomic coordinate range corresponding to each shell layer is calculated. (7) For the trajectory files at 1800K and 300K respectively, the distance from each atom to the center of the box is calculated, and the shell layer to which it belongs is numbered according to the distance. The atomic number density and the mean square displacement of the atoms in the shell layer are calculated to obtain the interface distribution of the atomic number density. The thickness of the diffusion interface is calculated based on the diffusion distance of each atom in the crystalline phase and the glass phase. A schematic diagram showing the distribution of the glass region, diffusion region, and crystal region in the cross-section of the model is shown below. Figure 2 As shown. (8) Calculate the diffusion coefficient for atoms in each shell. To avoid statistical errors caused by a small number of atoms of the same element in some regions, within a sampling length of 10 ns at 1800 K, the shell to which the atoms belong is re-counted every 0.5 ns, and the diffusion coefficient is calculated. Finally, the average value of the diffusion coefficient is calculated. The interface distribution of atomic diffusion coefficients is obtained. The atomic number density distribution diagram and diffusion coefficient distribution diagram of each cation are shown in the figure. Figure 5 As shown (the horizontal axis 0 represents the interface between the glass and the crystal during splicing, positive numbers represent the glass region during splicing, and complex numbers represent the crystal region during splicing).

[0051] Therefore, the present invention employs the above-mentioned method for studying the interface properties of nanocrystalline composite glass based on molecular dynamics simulation, which has the advantages of simple operation, low cost, and intuitive reflection of interface properties. It makes up for the insufficiency of the difficulty in examining the diffusion of elements at the interface in experiments, and greatly improves the testing efficiency and accuracy.

[0052] Finally, the above descriptions are merely some application examples of this invention and are not intended to limit the scope of this invention. This invention has numerous other embodiments, and all technical solutions formed through equivalent transformations fall within the protection scope claimed by this invention.

Claims

1. A method for studying the interfacial properties of nanocrystalline composite glasses based on molecular dynamics simulations, characterized in that: Includes the following steps: Step 1: Construct a box model of amorphous glass and output the structure file; Step 2: Perform high-temperature quenching simulation on the box model of amorphous glass based on molecular dynamics to obtain the glass structure file as the matrix; Step 3: Construct nanocrystalline clusters to obtain the structure file; Step 4: Assemble the initial composite model using the splicing method; The steps of the splicing method include: 1) deleting atoms in the matrix that coincide with the predetermined placement position of the nanoclusters; 2) modifying the atomic coordinates in the nanocluster structure file to place them in the predetermined placement position; 3) adding the atomic coordinates from the nanocluster structure file to the glass matrix structure file to obtain the structure file of the composite model; 4) calculating the total atomic charge of the structure file of the composite model and randomly deleting atoms near the interface to maintain charge neutrality. Step 5: Based on molecular dynamics, heat the composite model to the set relaxation temperature, quench it to the set temperature, sample it at a certain step size, and output the trajectory file. Step 6: Sort each atom in the trajectory file according to its distance from the center of the box, and determine the position of each atom; Step 7: Calculate the properties of atoms in different regions near the interface to obtain the distribution of relevant properties along the interface.

2. The method for studying the interface properties of nanocrystalline composite glasses based on molecular dynamics simulation according to claim 1, characterized in that, In step one, the glass system used is oxide glass; the oxide glass includes silicate glass, phosphate glass or borate glass.

3. The method for studying the interface properties of nanocrystalline composite glasses based on molecular dynamics simulation according to claim 1, characterized in that, In step two, the amorphous glass box model is cooled from 5000 K to 300 K at a cooling rate of 5 K / ps.

4. The method for studying the interface properties of nanocrystalline composite glasses based on molecular dynamics simulation according to claim 1, characterized in that, In step two, the amorphous glass box model underwent 2ns relaxation at 5000 K and 300 K.

5. The method for studying the interface properties of nanocrystalline composite glasses based on molecular dynamics simulation according to claim 1, characterized in that, In step three, the nanocrystal clusters are oxide crystals; the oxide crystals include Y₂O₃, Er₂O₃, and Y₃Al₅O₃. 12 Or CaAl2Si2O8.

6. The method for studying the interface properties of nanocrystalline composite glasses based on molecular dynamics simulation according to claim 1, characterized in that, In step five, the composite model is heated to 1800 K, relaxed for 1 ns, and then cooled to 300 K. The heating and cooling rates are both 5 K / ps.

7. The method for studying the interface properties of nanocrystalline composite glasses based on molecular dynamics simulation according to claim 1, characterized in that, In step six, a spherical shell is defined based on the range of each atom's distance from the center of the box.

8. The method for studying the interface properties of nanocrystalline composite glasses based on molecular dynamics simulation according to claim 1, characterized in that, In step seven, the properties of the atoms include the atomic number density and the atomic diffusion coefficient in different regions; The number density of atoms is calculated using formula (1): (1) Where N is the total number of a certain type of atom in the shell, d0 is the distance from the sampling start position to the center of the sphere, d is the shell thickness, and n is the shell number; The diffusion coefficient of atoms is calculated as follows: the mean square displacement (MSD) of atoms is calculated from the total atomic trajectory using formula (2); the diffusion coefficient (D) is calculated from the mean square displacement of atoms using formula (3); and the average diffusion coefficient of atoms within each shell is calculated using formula (4). ): (2) (3) (4) Where Δt is the time interval between two frames of trajectory, N is the total number of atoms, and r i (t) represents the coordinates of atom i, and d represents the dimension of the simulated system.

9. The method for studying the interface properties of nanocrystalline composite glasses based on molecular dynamics simulation according to claim 1, characterized in that, In step seven, the atomic number density is taken as the average value of different conformations under the ensemble, and the diffusion coefficient is calculated as the average value of different time intervals under the ensemble.

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