Method for simulating mechanical behavior of an atomically-scaled amorphous carbon material

Abstract

This invention discloses a method for simulating and analyzing the mechanical behavior of atomic-scale amorphous carbon materials, relating to the fields of materials science and computational technology. The method first establishes a diamond supercell with an atomic number equivalent to the target amorphous carbon model and melts it to form liquid carbon. The amorphous carbon model is then obtained by cooling and depressurization. Next, the structural parameters of the amorphous carbon model in its initial state are acquired, strain is applied to the model, and structural relaxation is performed. Then, the Young's modulus of the amorphous carbon model and the structural parameters under different strains are calculated. Using the atomic coordinate information of the initial model and different strains, the von Mises strain of each atom in the model is calculated. Finally, the number of atomic hybridization transitions and their spatial distribution characteristics in the model are statistically analyzed under different strain increments. This invention can accurately characterize the structural evolution and mechanical response of amorphous carbon materials during mechanical loading, providing an effective simulation method for revealing the microscopic mechanisms of the mechanical behavior of amorphous carbon materials.

Description

A Simulation and Analysis Method for the Mechanical Behavior of Amorphous Carbon Materials at the Atomic Scale Technical Field

[0001] This invention relates to the fields of materials science and computational technology, and in particular to a method for simulating and analyzing the mechanical behavior of amorphous carbon materials at the atomic scale. Background Technology

[0002] Amorphous carbon materials contain both sp and sp. 2 with sp 3 Amorphous carbon materials exhibit excellent mechanical properties, wear resistance, and chemical stability through various carbon bonding mechanisms, making them widely used in functional coatings, micro / nano devices, protective films, and extreme service environments. As device scale continues to advance towards the atomic and nanoscale, the mechanical behavior at the microstructural level of amorphous carbon materials has an increasingly significant impact on their macroscopic properties.

[0003] Current research on the mechanical behavior of amorphous carbon materials mainly employs macroscopic mechanical experimental testing, numerical methods based on the continuum assumption, and classical molecular dynamics simulations. While these methods are effective in describing the overall mechanical response of materials, they generally rely on empirical parameters or averaging assumptions, making it difficult to accurately reflect the evolution of atomic bonding states within the highly disordered structure of amorphous carbon. Especially under high strain or complex loading conditions, phenomena such as bonding formation, bond breaking, and hybridization state transitions prevalent in amorphous carbon are difficult to reliably describe using traditional continuum models or empirical potential functions.

[0004] In atomic-scale simulations, classical molecular dynamics methods typically employ empirical potential functions to describe the interactions between carbon atoms. Although these potential functions can reproduce some structural features of amorphous carbon under certain conditions, their parameters are usually fitted to specific structures or equilibrium properties. In simulations of mechanical processes involving drastic structural rearrangements and electronic structure responses, their applicability is limited and their accuracy is insufficient, making it difficult to reveal the microscopic mechanisms of the mechanical behavior of amorphous carbon in essence.

[0005] First-principles methods can directly describe electronic structure and interatomic interactions based on quantum mechanics principles, providing higher theoretical precision for studying the intrinsic mechanical behavior of materials. However, existing research combining first-principles methods with molecular dynamics often focuses on structure formation or thermal stability analysis, lacking a systematic simulation process for mechanical behavior, especially a unified simulation method for atomic-scale stress response, local structure evolution, and failure mechanisms. Furthermore, current research on the mechanical behavior of amorphous carbon often focuses on macroscopic mechanical parameters or statistical averages, and a simulation method that can directly correlate external mechanical loading processes with the evolution of the internal bonding structure of amorphous carbon at the atomic scale has not yet been developed. Summary of the Invention

[0006] The purpose of this invention is to propose a simulation and analysis method for the mechanical behavior of amorphous carbon materials at the atomic scale, so as to accurately describe the structural evolution and mechanical response process of amorphous carbon under external mechanical action, reveal the microscopic mechanism of its mechanical behavior, and overcome the shortcomings of existing methods in terms of accuracy, applicability and physical mechanism revelation.

[0007] To achieve the above objectives, this invention proposes a method for simulating and analyzing the mechanical behavior of amorphous carbon materials at the atomic scale, the specific steps of which are as follows:

[0008] Step S1: Establish a diamond supercell with a number of atoms comparable to the target amorphous carbon model;

[0009] Step S2: After applying high temperature and high pressure to the diamond supercell, it is melted into liquid carbon, and then cooled and depressurized to obtain an amorphous carbon model;

[0010] Step S3: Obtain the radial distribution function of the amorphous carbon model in the initial state, determine the atomic bonding cutoff distance based on the position of the first main peak and valley of the radial distribution function, and obtain the relevant structural parameters;

[0011] Step S4: Apply strain to the amorphous carbon model to perform structural relaxation and obtain the stress-strain response and atomic configuration under different strains;

[0012] Step S5: Obtain the Young's modulus of the amorphous carbon model based on the stress-strain response, and obtain the structural parameters after deformation based on the atomic configuration under different strains.

[0013] Step S6: Based on the amorphous carbon model in the initial state and the atomic coordinate information after applying different strains, calculate the von Mises strain of each atom in the model;

[0014] Step S7: Statistically analyze the number of atomic hybridization transitions and the spatial distribution characteristics of atoms in the model under each strain increment.

[0015] Preferably, in step S2, the specific steps are as follows: using first-principles calculation software, selecting a molecular dynamics simulation ensemble, setting the temperature required for supercell melting, applying different pressures, and obtaining different sps after cooling and depressurization. 3 Amorphous carbon model with hybridization content.

[0016] Preferably, in step S3, the radial distribution function g(r) is calculated using the following formula:

[0017] ;

[0018] in, Let dN(r) be the average atomic number density of the system, and dN(r) be the number of atoms in the range from r to r+dr from the central atom.

[0019] Based on the radial distribution function, plot the radial distribution function curve and determine the peak-valley position r1 of the first main peak on the curve. r1 is the longest distance for bonding.

[0020] Preferably, in step S4, the specific method for applying strain to the amorphous carbon model and performing structural relaxation is as follows: the process is carried out in steps with a fixed strain increment, and the entire structure is fully relaxed in each step, reducing the stress components other than those in the direction of applied strain to below a set threshold.

[0021] Preferably, in step S6, the von Mises strain of each atom is calculated using the following method:

[0022] Step S61: By comparing the atomic coordinate information of the initial model and the model after applying different strains, calculate the atomic deformation gradient tensor F, as shown in the following formula:

[0023] ;

[0024] in, Let i be the deformation gradient tensor of atom i. It is the distance vector between atoms j and i, with the superscript 0 indicating the initial configuration. Let T be the total number of nearest neighbor atoms of atom i in the initial configuration, and T be the matrix transpose.

[0025] Step S62: Calculate the Green-Lagrange strain tensor E based on the atomic deformation gradient tensor F, using the following formula:

[0026] ;

[0027] in, Let i be the Green-Lagrange strain tensor of atom i. It is a third-order identity matrix;

[0028] Step S63: Calculate the von Mises strain for each atom, using the following formula:

[0029] ;

[0030] in, For atomic von Mises strain; , , , , , All are tensors The amount.

[0031] Therefore, this invention proposes a method for simulating and analyzing the mechanical behavior of amorphous carbon materials at the atomic scale, with the following beneficial effects:

[0032] (1) Based on first-principles molecular dynamics, this invention does not rely on empirical parameters or averaging assumptions. It can accurately characterize the structural evolution and mechanical response of amorphous carbon materials under mechanical loading at the atomic scale, directly linking external mechanical loading with changes in internal bonding structure, and providing an effective simulation means to reveal the microscopic mechanism of the mechanical behavior of amorphous carbon.

[0033] (2) By adjusting the high temperature and high pressure parameters, this invention can prepare different sps. 3 A model of amorphous carbon with hybridization content, thereby clarifying sp 3 The correlation between hybridization content and material mechanical behavior provides data support for the targeted design of amorphous carbon materials with specific mechanical properties.

[0034] (3) The present invention can intuitively capture the defect region in amorphous carbon and accurately describe the structural evolution process of the defect region through quantitative indicators such as structural parameters and von Mises strain distribution, providing a key basis for understanding the material failure mechanism.

[0035] (4) This invention directly describes electronic structure and interatomic interactions using first principles, overcoming the problem of insufficient accuracy of classical molecular dynamics empirical potential functions in simulating drastic structural rearrangement and electronic structure response. It is especially suitable for simulation analysis under high strain or complex load conditions.

[0036] (5) The simulation method established by this invention is not only applicable to amorphous carbon materials, but can also be extended to the simulation of mechanical behavior of various covalent amorphous materials, opening up an accurate and efficient technical approach for the design and development of new high-performance covalent amorphous materials.

[0037] The technical solution of the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. Attached Figure Description

[0038] Figure 1 is a flowchart of a method for simulating and analyzing the mechanical behavior of atomic-scale amorphous carbon materials according to the present invention.

[0039] Figure 2 is a schematic diagram of the amorphous carbon structure model provided in the embodiment of the present invention; wherein, (a) in Figure 2 represents 27% sp 3 A schematic diagram of the amorphous carbon structure model in Figure 2, where (b) represents 77% sp. 3 A schematic diagram of the amorphous carbon structure model;

[0040] Figure 3 is a schematic diagram of the stress-strain response relationship of the amorphous carbon model provided in the embodiment of the present invention;

[0041] Figure 4 shows the atomic von Mises strain distribution of the amorphous carbon model provided in the embodiment of the present invention; wherein, (a) in Figure 4 represents 77% sp 3The von Mises strain distribution of the amorphous carbon model atoms at 7% strain is shown in Figure 4(b), which represents strain at 77% sp. 3 Figure 4 shows the von Mises strain distribution of amorphous carbon model atoms at a strain of 10.5%, with (c) representing 77% sp. 3 The von Mises strain distribution of the amorphous carbon model atoms at 16% strain is shown in Figure 4, where (d) represents 77% sp. 3 The von Mises strain distribution of the amorphous carbon model atoms at 25% strain is shown in Figure 4, where (e) represents strain at 27% sp. 3 The von Mises strain distribution of the amorphous carbon model atoms at 3% strain is shown in Figure 4(f), where 27% sp is the strain distribution. 3 The von Mises strain distribution of amorphous carbon model atoms at 15% strain is shown in Figure 4, where (g) represents 27% sp. 3 The von Mises strain distribution of amorphous carbon atoms at 20% strain is shown in Figure 4, where (h) represents 27% sp. 3 von Mises strain distribution of atoms in an amorphous carbon model at 25% strain;

[0042] Figure 5 is a schematic diagram of the number of transitions in the amorphous carbon model atomic hybridization provided in the embodiments of the present invention. Detailed Implementation

[0043] To make the technical solutions, advantages, and objectives of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below. The described embodiments are only some, not all, of the embodiments of the present invention. All other embodiments obtained by those skilled in the art based on the described embodiments of the present invention without creative effort are within the protection scope of the present invention.

[0044] Unless otherwise defined, the technical or scientific terms used in this invention shall have the ordinary meaning as understood by one of ordinary skill in the art to which this invention pertains.

[0045] Example

[0046] As shown in Figure 1, this invention provides a method for simulating and analyzing the mechanical behavior of amorphous carbon materials at the atomic scale. The specific steps are as follows:

[0047] Step S1: Establish a diamond supercell with a number of atoms comparable to the target amorphous carbon model;

[0048] Step S2, as shown in Figure 2, involves applying high temperature and pressure to the diamond supercell to melt it into liquid carbon. Cooling and depressurization are then performed to obtain an amorphous carbon model. The specific steps are as follows: First-principles calculation software VASP is used. Based on the density functional theory plane wave pseudopotential method, the interaction between the ionic core and valence electrons is described using the projector-augmented wave method (PAW). The exchange-correlation energy of the electron interaction is handled using the Perdew-Burke-Ernzerhof (PBE) scheme of the generalized gradient approximation (GGA). A plane wave cutoff energy is set. Geometric optimization is performed, with the origin of the Brillouin zone used for integral calculations across the entire Brillouin zone. The grid scheme is centered on the diamond supercell; during structural optimization, an energy convergence criterion that meets the computational accuracy requirements is set; an isothermal and isobaric ensemble is selected, the temperature required for the melting of the diamond supercell is set, different pressures are applied, and different sps are obtained after cooling and depressurization. 3 Amorphous carbon model with hybridization content.

[0049] Step S3: Obtain the radial distribution function of the amorphous carbon model in the initial state. Determine the atomic bonding cutoff distance based on the position of the first main peak and valley of the radial distribution function, and obtain the bond length distribution, bond angle distribution, and distribution of different coordinating atoms. The radial distribution function g(r) is calculated as follows:

[0050] ;

[0051] in, Let dN(r) be the average atomic number density of the system, and dN(r) be the number of atoms in the range from r to r+dr from the central atom.

[0052] Based on the radial distribution function, plot the radial distribution function curve and determine the peak-valley position r1 of the first main peak on the curve. r1 is the longest distance for bonding.

[0053] Step S4, as shown in Figure 3, applies strain to the amorphous carbon model to perform structural relaxation, and obtains the stress-strain response and atomic configuration under different strains.

[0054] In this embodiment, the specific method for applying strain to the amorphous carbon model and performing structural relaxation is as follows: stretching is performed in steps with a strain increment of 0.5%, and the entire structure is fully relaxed using the conjugate gradient method at each step. The convergence criterion for interatomic interaction forces is 0.01 eV / Å, and the stress components other than those in the direction of applied strain are reduced to below 0.02 GPa.

[0055] Step S5: Obtain the Young's modulus of the amorphous carbon model based on the stress-strain response, and obtain the radial distribution function, bond length distribution, bond angle distribution, and distribution of different coordinating atoms of the deformed structure based on the atomic configuration under different strains.

[0056] Step S6: Based on the initial state of the amorphous carbon model and the atomic coordinates after applying different strains, the von Mises strain of each atom in the model is calculated and visualized using a Python script; Figure 4 shows the atomic von Mises strain distribution under several typical strains in the stress-strain response; the von Mises strain calculation method for each atom is as follows:

[0057] Step S61: By comparing the atomic coordinate information of the initial model and the model after applying different strains, calculate the atomic deformation gradient tensor F, as shown in the following formula:

[0058] ;

[0059] in, Let i be the deformation gradient tensor of atom i. It is the distance vector between atoms j and i, with the superscript 0 indicating the initial configuration. Let T be the total number of nearest neighbor atoms of atom i in the initial configuration, and T be the matrix transpose.

[0060] Step S62: Calculate the Green-Lagrange strain tensor E based on the atomic deformation gradient tensor F, using the following formula:

[0061] ;

[0062] in, Let i be the Green-Lagrange strain tensor of atom i. It is a third-order identity matrix;

[0063] Step S63: Calculate the von Mises strain for each atom, using the following formula:

[0064] ;

[0065] in, For atomic von Mises strain; , , , , , All are tensors The amount.

[0066] Step S7: Statistically analyze the number of atomic hybridization transitions and the spatial distribution characteristics of atoms in the model under each strain increment; as shown in Figure 5, the number of atomic hybridization transitions in the amorphous carbon model under one strain increment step when the decrease in stress response is greater than 1 GPa is statistically analyzed.

[0067] It is worth noting that all contents not described in detail in this invention are existing technologies and are well known to those skilled in the art.

[0068] Therefore, this invention provides a method for simulating and analyzing the mechanical behavior of amorphous carbon materials at the atomic scale, which can accurately characterize the structural evolution and mechanical response of amorphous carbon materials during mechanical loading at the atomic scale, and regulate sp 3 The method can be used to determine the hybridization content and its relationship with mechanical behavior, and to quantitatively describe the evolution of defect regions. At the same time, it can be extended to the simulation of various covalent amorphous materials, providing an accurate and efficient simulation method for revealing the microscopic mechanism of the mechanical behavior of amorphous carbon and for the design and development of new high-performance materials.

[0069] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and not to limit them. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can still be made to the technical solutions of the present invention, and these modifications or equivalent substitutions cannot cause the modified technical solutions to deviate from the spirit and scope of the technical solutions of the present invention.

Claims

1. A method for simulating and analyzing the mechanical behavior of atomic-scale amorphous carbon materials, characterized in that, The specific steps are as follows: Step S1, establish a diamond supercell with a number of atoms comparable to the target amorphous carbon model; Step S2, melt the diamond supercell into liquid carbon after applying high temperature and pressure, and then cool and depressurize to obtain the amorphous carbon model; Step S3, obtain the radial distribution function of the amorphous carbon model in the initial state, determine the atomic bonding cutoff distance based on the position of the first main peak and valley of the radial distribution function, and obtain the relevant structural parameters; Step S4, apply strain to the amorphous carbon model, perform structural relaxation, and obtain the stress-strain response and atomic configuration under different strains. Step S5: Obtain the Young's modulus of the amorphous carbon model based on the stress-strain response, and obtain the structural parameters after deformation based on the atomic configuration under different strains; Step S6: Calculate the von Mises strain of each atom in the model based on the atomic coordinate information of the amorphous carbon model in the initial state and after applying different strains; Step S7: Statistically analyze the number of atomic hybridization transitions and the spatial distribution characteristics of atoms in the model under each strain increment; In Step S6, the von Mises strain of each atom is calculated as follows: Step S61: Calculate the atomic deformation gradient tensor F by comparing the atomic coordinate information of the initial model and the model after applying different strains, using the following formula: ;in, Let i be the deformation gradient tensor of atom i. It is the distance vector between atoms j and i, with the superscript 0 indicating the initial configuration. Let T be the total number of nearest neighbor atoms of atom i in the initial configuration, and T be the matrix transpose; Step S62: Calculate the Green-Lagrange strain tensor E based on the atomic deformation gradient tensor F, as shown in the following formula: ;in, Let i be the Green-Lagrange strain tensor of atom i. The matrix is ​​a third-order identity matrix; Step S63: Calculate the von Mises strain of each atom, using the following formula: ;in, For atomic von Mises strain; 、 、 、 、 、 All are tensors The amount.

2. The method for simulating and analyzing the mechanical behavior of atomic-scale amorphous carbon materials according to claim 1, characterized in that, In step S2, the specific steps are as follows: using first-principles calculation software, selecting the molecular dynamics simulation ensemble, setting the temperature required for supercell melting, applying different pressures, and obtaining different sps after cooling and depressurization. 3 Amorphous carbon model with hybridization content.

3. The method for simulating and analyzing the mechanical behavior of atomic-scale amorphous carbon materials according to claim 2, characterized in that, In step S3, the radial distribution function g(r) is calculated using the following formula: ;in, Let dN(r) be the average atomic number density of the system, and dN(r) be the number of atoms in the range from r to r+dr from the central atom. Based on the radial distribution function, a radial distribution function curve is plotted, and the position of the first main peak and valley r1 is determined on the curve. r1 is the longest distance for bonding.

4. The method for simulating and analyzing the mechanical behavior of atomic-scale amorphous carbon materials according to claim 3, characterized in that, In step S4, the specific method for applying strain to the amorphous carbon model and performing structural relaxation is as follows: the process is carried out in steps with a fixed strain increment, and the entire structure is fully relaxed in each step, reducing the stress components other than those in the direction of applied strain to below a set threshold.

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