Transition metal disulfide armchair type and sawtooth type nanotube model construction method

Abstract

The invention particularly relates to a construction method of a transition metal disulfide armchair type and sawtooth type nanotube model. Comprising a two-dimensional hexagonal crystal structure based on transition metal disulphide, the two-dimensional hexagonal crystal structure is curled to generate transition metal disulphide nanotubes, and the nanotubes are in an armchair shape and a sawtooth shape; obtaining the radius of the transition metal layer according to the chiral vector and the transverse unit cell length; measuring a vertical distance between the two sulfur atom layers, calculating to obtain a sulfur group atom interlayer spacing, and calculating to obtain an outer layer sulfur radius and an inner layer sulfur radius according to the transition metal layer radius and the sulfur atom interlayer spacing; based on the radius of the outer layer sulfur, defining the side length of a unit cell, and based on the radius of the transition metal layer, the radius of the outer layer sulfur and the radius of the inner layer sulfur, positioning coordinates of transition metal atoms and chalcogenide atoms through a trigonometric function; and generating a nanotube model of the transition metal disulfide according to the direction of the chiral vector. According to the automatic modeling method provided by the invention, the nanotube model is efficiently generated, and structural parameters are accurately controlled.

Description

Technical Field

[0001] The present invention relates to the technical field of nanomaterials, and in particular to a method for constructing armchair-type and zigzag-type transition metal disulfide nanotube models. Background Art

[0002] In recent years, transition metal dichalcogenide nanotubes (TMDs) have garnered increasing attention in scientific research and technological applications due to their unique physicochemical properties. These one-dimensional nanostructures have shown great potential in nanocatalysis, electronic devices, energy storage, and other fields. They also possess high stability and scalability. The diverse chirality of these nanotubes, including armchair and zigzag structures, allows their electronic properties to be further tuned for specific applications.

[0003] However, there is currently no software or code for automating the generation of transition metal disulfide nanotube models. Model generation relies on manual calculation and input of atomic positions, which is time-consuming. Furthermore, due to the complex structure of nanotubes, potential human errors in coordinate calculations can easily lead to deviations in atomic positions and poor reproducibility of nanotube structures. These issues can severely impact the efficiency and reliability of related research. Therefore, there is an urgent need to develop relevant code and software to enable automated, efficient, and high-precision modeling of transition metal disulfide nanotubes.

[0004] The present invention provides an accurate and efficient logic algorithm for generating transition metal dichalcogenide nanotubes, including armchair and zigzag nanotubes, by simplifying the modeling process and automatically calculating atomic positions. This not only reduces the possibility of human error but also ensures higher efficiency and repeatability in nanotube model generation. Furthermore, the present invention enables users to build nanotube models faster and more consistently through precise control of structural parameters such as chirality and diameter. These features make it extremely valuable for large-scale computational simulations and scientific research, where accuracy and efficiency are crucial. Summary of the Invention

[0005] In response to the aforementioned technical problems, a method for constructing armchair and zigzag nanotube models of transition metal disulfide nanotubes is provided. This method primarily utilizes a logical algorithm based on the curling of two-dimensional planar structures, combined with automatic calculation of geometric parameters and trigonometric coordinate positioning techniques, to reduce human error, improve model generation efficiency and accuracy, and ensure the repeatability of nanotube models. By precisely controlling structural parameters such as chirality and diameter, the method enables rapid and consistent generation of armchair and zigzag nanotube models, providing an efficient and reliable tool for large-scale computational simulations and scientific research.

[0006] The technical means adopted in the present invention are as follows:

[0007] The method for constructing armchair and zigzag nanotube models of transition metal disulfide comprises the following steps:

[0008] Based on the two-dimensional hexagonal crystal structure of transition metal disulfide, curling to generate transition metal disulfide nanotubes, and simultaneously determining the nanotube axial lattice parameter and lateral unit cell length of the nanotube, wherein the shape of the nanotube includes armchair type and zigzag type;

[0009] Calculate the chiral vector corresponding to the number of repeating units in the circumferential direction, and obtain the radius of the transition metal layer based on the chiral vector and the lateral unit cell length;

[0010] Measuring the vertical distance between two sulfur atomic layers to calculate the distance between chalcogen atomic layers, and calculating the outer sulfur radius and the inner sulfur radius based on the transition metal layer radius and the distance between the sulfur atomic layers;

[0011] Based on the outer sulfur radius, the unit cell side length is defined, and based on the transition metal layer radius, the outer sulfur radius and the inner sulfur radius, the coordinates of the transition metal atoms and the chalcogen atoms are located by trigonometric functions;

[0012] Based on the coordinates of the transition metal atoms and the chalcogen atoms, a nanotube model of the transition metal disulfide is generated according to the direction of the chiral vector.

[0013] Furthermore, obtaining the radius of the transition metal layer according to the chirality vector and the lateral unit cell length includes:

[0014] Calculate the angle in radians based on the number of chiral vectors:

[0015]

[0016] Where θ is the angle in radians, and n is the number of chiral vectors;

[0017] According to the angle in radians and the lateral unit cell length, the radius of the transition metal layer is calculated as:

[0018]

[0019] Wherein, θ is the angle in radians, L is the lateral unit cell length, and r2 is the radius of the transition metal layer.

[0020] Furthermore, the calculation formula for the chalcogen atomic layer spacing is:

[0021]

[0022] Among them, d o is the distance between chalcogen atoms, d X-X is the vertical distance between two sulfur atomic layers;

[0023] The calculation formula of the outer sulfur radius is:

[0024] r3=r2+d o ,

[0025] Where r2 is the radius of the transition metal layer, d o is the distance between chalcogen atoms, r3 is the outer sulfur radius;

[0026] The calculation formula of the inner sulfur radius is:

[0027] r1=r2-d o ,

[0028] Where r2 is the radius of the transition metal layer, d o is the distance between chalcogen atoms, and r1 is the radius of the inner sulfur layer.

[0029] Furthermore, positioning the coordinates of transition metal atoms and chalcogen atoms by trigonometric functions based on the transition metal layer radius, the outer sulfur radius, and the inner sulfur radius includes:

[0030] Define the thickness of the vacuum layer outside the nanotube in the horizontal plane and calculate the unit cell side length of the nanotube in the horizontal plane:

[0031] a=b=Vc+2r3,

[0032] Where a is the side length of the first unit cell, b is the side length of the second unit cell, Vc is the thickness of the vacuum layer on the surface of the nanotube in the horizontal direction, and r3 is the outer sulfur radius;

[0033] Based on the unit cell side length of the nanotube in the horizontal plane and the axial lattice parameter of the nanotube, the coordinates of the first transition metal atom, the coordinates of the second transition metal atom, the coordinates of the first chalcogen atom and the second chalcogen atom in the unit cell are calculated by trigonometric function method;

[0034] By iteratively repeating the above calculation steps, the atomic coordinates along the circular path are generated in sequence to form all the atoms in a unit cell.

[0035] Furthermore, the coordinates of the first transition metal atoms of the armchair nanotubes are as follows:

[0036] M1=(a / 2+r2sin(θ m1 ), b / 2+r2cos(θ m1 ),0),

[0037] Where M1 is the coordinate of the first transition metal atom, a is the side length of the first unit cell, b is the side length of the second unit cell, r2 is the radius of the transition metal layer, θ m1 is the azimuth angle of the first transition metal atom, θm1 =θ*i, θ is the angle in radians, i∈{0,1,2,…,n-1}, n is the number of repeating units on the circumference;

[0038] The coordinates of the second transition metal atoms in the armchair nanotubes are as follows:

[0039] M2=(a / 2+r2sin(θ m2 ), b / 2+r2cos(θ m2 ), c0 / 2),

[0040] Where M2 is the coordinate of the second transition metal atom, a is the side length of the first unit cell, b is the side length of the second unit cell, r2 is the radius of the transition metal layer, θ m2 is the azimuth angle of the second transition metal atom, θ m2 =θ*(i+1 / 2), θ is the angle in radians, i∈{0,1,2,…,n-1}, n is the number of repeating units on the circumference, and c0 is the axial lattice parameter of the nanotube;

[0041] When the first chalcogen atom of the armchair nanotube is in the inner layer, the coordinates of the first chalcogen atom are as follows:

[0042] X1=(a / 2+r1sin(θ x1 ), b / 2+r1cos(θ x1 ),0),

[0043] Where X1 is the coordinate of the first sulfur atom, a is the side length of the first unit cell, b is the side length of the second unit cell, r1 is the radius of the inner sulfur layer, θ x1 is the azimuthal angle of the first chalcogen atom coordinate, θ x1 =θ*(i+2 / 3), where θ is the angle in radians, i∈{0,1,2,…,n-1}, and n is the number of repeating units on the circumference;

[0044] When the first chalcogen atom of the armchair nanotube is in the outer layer, the coordinates of the first chalcogen atom are as follows:

[0045] X1=(a / 2+r3sin(θ x1 ), b / 2+r3cos(θ x1 ),0),

[0046] Where X1 is the coordinate of the first chalcogen atom, a is the side length of the first unit cell, b is the side length of the second unit cell, r3 is the outer sulfur radius, θ x1 is the azimuthal angle of the first chalcogen atom coordinate, θ x1 =θ*(i+2 / 3), where θ is the angle in radians, i∈{0,1,2,…,n-1}, and n is the number of repeating units on the circumference;

[0047] When the second chalcogen atom of the armchair nanotube is in the inner layer, the coordinates of the second chalcogen atom are as follows:

[0048] X2=(a / 2+r1sin(θ x2 ), b / 2+r1cos(θ x2 ), c0 / 2),

[0049] Where X2 is the coordinate of the second sulfur atom, a is the side length of the first unit cell, b is the side length of the second unit cell, r1 is the radius of the inner sulfur layer, θ x2 is the azimuthal angle of the second chalcogen atom coordinate, θ x2 =θ*(i+1 / 6), where θ is the angle in radians, i∈{0,1,2,…,n-1}, and n is the number of repeating units on the circumference;

[0050] When the second chalcogen atom of the armchair nanotube is in the outer layer, the coordinates of the second chalcogen atom are as follows:

[0051] X2=(a / 2+r3sin(θ x2 ), b / 2+r3cos(θ x2 ), c0 / 2),

[0052] Where X2 is the coordinate of the second sulfur atom, a is the side length of the first unit cell, b is the side length of the second unit cell, r3 is the outer sulfur radius, θ x2 is the azimuthal angle of the second chalcogen atom coordinate, θ x2 =θ*(i+1 / 6), θ is the angle in radians, i∈{0,1,2,…,n-1}, and n is the number of repeating units on the circumference.

[0053] Furthermore, the coordinates of the first transition metal atom of the zigzag nanotube are as follows:

[0054] M1=(a / 2+r2sin(θ m1 ), b / 2+r2cos(θ m1 ),0),

[0055] Where M1 is the coordinate of the first transition metal atom, a is the side length of the first unit cell, b is the side length of the second unit cell, r2 is the radius of the transition metal layer, θ m1 is the azimuth angle of the first transition metal atom, θ m1 =θ*i, θ is the angle in radians, i∈{0,1,2,…,n-1}, n is the number of repeating units on the circumference;

[0056] The coordinates of the second transition metal atom of the zigzag nanotube are as follows:

[0057] M2=(a / 2+r2sin(θ m2), b / 2+r2cos(θ m2 ), c0 / 2),

[0058] Where M2 is the coordinate of the second transition metal atom, a is the side length of the first unit cell, b is the side length of the second unit cell, r2 is the radius of the transition metal layer, θ m2 is the azimuth angle of the second transition metal atom, θ m2 =θ*(i+1 / 2), θ is the angle in radians, i∈{0,1,2,…,n-1}, n is the number of repeating units on the circumference, and c0 is the axial lattice parameter of the nanotube;

[0059] When the first chalcogen atom of the zigzag nanotube is in the inner layer, the coordinates of the first chalcogen atom are as follows:

[0060] X1=(a / 2+r1sin(θ x1 ), b / 2+r1cos(θ x1 ), 2c0 / 3),

[0061] Where X1 is the coordinate of the first sulfur atom, a is the side length of the first unit cell, b is the side length of the second unit cell, r1 is the radius of the inner sulfur layer, θ x1 is the azimuthal angle of the first chalcogen atom coordinate, θ x1 =θ*i, θ is the angle in radians, i∈{0,1,2,…,n-1}, n is the number of repeating units on the circumference;

[0062] When the second chalcogen atom of the zigzag nanotube is in the inner layer, the coordinates of the second chalcogen atom are as follows:

[0063] X2=(a / 2+r1sin(θ x2 ), b / 2+r1cos(θ x2 ), c0 / 6),

[0064] Where X2 is the coordinate of the second sulfur atom, a is the side length of the first unit cell, b is the side length of the second unit cell, r1 is the radius of the inner sulfur layer, θ x2 is the azimuthal angle of the second chalcogen atom coordinate, θ x2 =θ(i+1 / 2), where θ is the angle in radians, i∈{0,1,2,…,n-1}, and n is the number of repeating units on the circumference;

[0065] When the first chalcogen atom of the zigzag nanotube is in the outer layer, the coordinates of the first chalcogen atom are as follows:

[0066] X1=(a / 2+r3sin(θ x1 ), b / 2+r3cos(θ x1 ), 2c0 / 3),

[0067] Where X1 is the coordinate of the first chalcogen atom, a is the side length of the first unit cell, b is the side length of the second unit cell, r3 is the outer sulfur radius, θ x1 is the azimuthal angle of the first chalcogen atom coordinate, θ x1 =θ*i, θ is the angle in radians, i∈{0,1,2,…,n-1}, n is the number of repeating units on the circumference;

[0068] When the second chalcogen atom of the zigzag nanotube is in the outer layer, the coordinates of the second chalcogen atom are as follows:

[0069] X2=(a / 2+r3sin(θ x2 ), b / 2+r3cos(θ x2 ), c0 / 6),

[0070] Where X2 is the coordinate of the second sulfur atom, a is the side length of the first unit cell, b is the side length of the second unit cell, r3 is the outer sulfur radius, θ x2 is the azimuthal angle of the second chalcogen atom coordinate, θ x2 =θ(i+1 / 2), θ is the angle in radians, i∈{0,1,2,…,n-1}, and n is the number of repeating units on the circumference.

[0071] Compared with the prior art, the present invention has the following advantages:

[0072] 1. Compared to the traditional method of manually inputting atomic positions, this method achieves automated and efficient generation of unit cells. This method eliminates the need for manual input of atomic positions, significantly reducing the time cost and complexity of manual operations while meeting the user's need for precise control of structural parameters, providing an efficient and reliable modeling tool for large-scale computational simulations and scientific research.

[0073] 2. This invention significantly improves the efficiency and reproducibility of model generation by combining predefined, adjustable lattice parameters and chiral eigenvectors with trigonometric algorithms. This method automatically calculates lattice parameters and chiral eigenvectors through algorithms, ensuring efficient and reproducible model generation while minimizing human error, providing a high-quality foundation for subsequent experiments and simulations.

[0074] 3. This method achieves precise atomic positioning and significantly improves model reliability by combining it with trigonometric calculations of atomic positions along the nanotube's circular trajectory. This method utilizes trigonometric algorithms to precisely locate atomic positions along the circular trajectory, ensuring precise control of the model's geometric parameters and avoiding human error and atomic position deviations. This provides a highly accurate nanotube model for scientific research and technological applications.

[0075] Based on the above reasons, the present invention can be widely promoted in the fields of nanomaterials and the like. BRIEF DESCRIPTION OF THE DRAWINGS

[0076] 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 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 labor.

[0077] Figure 1 Schematic diagram of a hexagonal cell with the parameter settings for generating armchair nanotubes according to the present invention.

[0078] Figure 2 Schematic diagram of a hexagonal cell with parameter settings for generating zigzag nanotubes according to the present invention.

[0079] Figure 3 A schematic cross-sectional view of a transition metal disulfide nanotube showing a typical three-atomic layer distribution of the present invention.

[0080] Figure 4 Schematic diagram of precise atomic positions along the x and y directions.

[0081] Figure 5 Top and side views of (a) armchair and (b) zigzag nanotubes. DETAILED DESCRIPTION

[0082] In order to enable those skilled in the art to better understand the solutions of the present invention, the technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the embodiments described 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 should fall within the scope of protection of the present invention.

[0083] It should be noted that the terms "first", "second", etc. in the description and claims of the present invention and the above-mentioned drawings are used to distinguish similar objects and are not necessarily used to describe a specific order or sequence. It should be understood that the numbers used in this way can be interchanged where appropriate, so that the embodiments of the present invention described herein can be implemented in an order other than those illustrated or described herein. In addition, the terms "including" and "having" and any variations thereof are intended to cover non-exclusive inclusions. For example, a process, method, system, product or device that includes a series of steps or units is not necessarily limited to those steps or units clearly listed, but may include other steps or units that are not clearly listed or inherent to these processes, methods, products or devices.

[0084] The present invention proposes a novel and effective method for constructing models of transition metal disulfide nanotubes, including armchair and zigzag nanotubes. This method can quickly generate accurate nanotube models, avoiding the complex, time-consuming, and labor-intensive process of manually calculating the atomic coordinates of the nanotubes, while providing users with precise control over structural parameters such as chirality and diameter. By employing trigonometric functions, it accurately plots the atomic positions in the zigzag and armchair structures along circular trajectories, ensuring the consistency and clarity of the atomic arrangements. This method can improve the modeling efficiency of transition metal disulfide nanotubes by simplifying the construction of accurate models, saving time and effort, and promoting their application in nanotechnology.

[0085] Example 1

[0086] like Figure 1 、 Figure 3 and Figure 4 As shown, the present invention provides a method for constructing transition metal disulfide armchair and zigzag nanotube models, the steps of which include:

[0087] S1. Based on the two-dimensional hexagonal structure of transition metal dichalcogenides, the two-dimensional structure comprises repeating MX2 units, where M represents a transition metal and X represents a chalcogen element. The two-dimensional hexagonal structure is curled to form transition metal dichalcogenide nanotubes, simultaneously determining the nanotube's axial lattice parameter and lateral unit cell length, resulting in an armchair-shaped nanotube.

[0088] Specifically, when the two-dimensional planar structure is curled to form an armchair nanotube, its axial periodicity corresponds to the MM bond length in the original hexagonal lattice. The lattice parameters c0 and L of the armchair nanotube are defined so that c0 represents the unit cell length along the z-axis, corresponding to the axial direction of the nanotube, and L represents the unit cell length in the xy plane perpendicular to the nanotube axis (see Figure 1 ).

[0089] S2. Calculate the chiral vector corresponding to the number of repeating units in the circumferential direction, and obtain the radius of the transition metal layer based on the chiral vector and the lateral unit cell length.

[0090] This step is specifically:

[0091] Calculate the angle in radians based on the number of chiral vectors:

[0092]

[0093] Where θ is the angle in radians and n is the number of chiral vectors.

[0094] According to the angle in radians and the lateral unit cell length, the radius of the transition metal layer is calculated as:

[0095]

[0096] Wherein, θ is the angle in radians, L is the lateral unit cell length, and r2 is the radius of the transition metal layer.

[0097] S3. Measure the vertical distance between the two sulfur atomic layers and calculate the distance between the chalcogen atomic layers. Based on the radius of the transition metal layer and the distance between the sulfur atomic layers, calculate the outer sulfur radius and the inner sulfur radius.

[0098] Specifically, the calculation formula for the distance between chalcogen atoms is:

[0099]

[0100] Among them, d o is the distance between chalcogen atoms, d X-X is the vertical distance between two sulfur atomic layers.

[0101] like Figure 3 As shown, the calculation formula for the outer sulfur radius is:

[0102] r3=r2+d o ,

[0103] Where r2 is the radius of the transition metal layer, d o is the distance between chalcogen atoms, r3 is the outer sulfur radius;

[0104] The calculation formula of the inner sulfur radius is:

[0105] r1=r2-d o ,

[0106] Where r2 is the radius of the transition metal layer, d o is the distance between chalcogen atoms, and r1 is the radius of the inner sulfur layer.

[0107] S4. Based on the outer sulfur radius, define the unit cell side length, and based on the transition metal layer radius, outer sulfur radius, and inner sulfur radius, locate the coordinates of transition metal atoms and chalcogen atoms using trigonometric functions.

[0108] Specifically, define the thickness of the vacuum layer on the nanotube surface in the horizontal plane and calculate the side length of the unit cell of the nanotube in the horizontal plane:

[0109] a=b=Vc+2r3,

[0110] Wherein, a is the side length of the first unit cell, b is the side length of the second unit cell, Vc is the thickness of the vacuum layer on the surface of the nanotube in the horizontal direction, and r3 is the outer sulfur radius.

[0111] In order to generate the M and X atoms at the correct coordinates on the circumference of the nanotube, a combination of trigonometric mathematical methods must be used to accurately generate the atomic positions to ensure its periodicity and symmetry. The unit cell, in a section perpendicular to the nanotube, has its a-axis along the x-axis and its b-axis along the y-axis, with the center origin O located at a / 2 and b / 2 in the horizontal and vertical directions, respectively. Therefore, the center coordinates are O(a / 2, b / 2). The position of the atom at a point P on the circumference is given by the angular displacement θ measured from the vertical axis. A straight line is drawn from the center O(a / 2, b / 2) to point P, where the length of the line segment (OP) is ro. To determine the coordinates of point P, a horizontal line is drawn from point P to the vertical axis, representing the displacement dx in the x-direction, and a vertical line is drawn from point P to the horizontal axis, representing the displacement dy in the y-direction. Therefore, the coordinates of P are (a / 2+dx, b / 2+dy), where dx and dy can be expressed using trigonometric functions according to the following equations.

[0112] dx=r o sinθ

[0113] dy=r o cosθ

[0114] Among them, r o is the atomic radius and θ is the angle in radians.

[0115] This ensures that the P point can be precisely positioned along the circular trajectory based on a given angular displacement, which is the basic principle for generating the coordinates of the M and X atoms on their respective layers along the circumference of the armchair nanotube (see Figure 4 The difference between the armchair and zigzag nanotube models lies in the arrangement of the M and X atoms along different axes, which is caused by the different orientations of the chiral vectors during the curling of the two-dimensional monolayer to form the nanotube.

[0116] S5. Based on the unit cell side length of the nanotube in the horizontal plane and the axial lattice parameter of the nanotube, calculate the coordinates of the first transition metal atom, the coordinates of the second transition metal atom, the coordinates of the first sulfide atom, and the coordinates of the second sulfide atom in the unit cell by using the trigonometric function method.

[0117] First, the angle values of the M and X atoms are obtained according to their atomic positions along the ab plane in the hexagonal unit cell. The z coordinate is determined according to the relative positions of the atoms along the c axis, which is crucial for describing the three-dimensional arrangement of atoms in the unit cell (see Figure 1 ).

[0118] Therefore, the exact atomic coordinates of the M1, M2, X1, and X2 atoms in the unit cell can be expressed as (a / 2+dx, b / 2+dy, c). Specifically, the first transition metal atomic coordinates of the armchair nanotube are as follows:

[0119] M1=(a / 2+r2sin(θm1 ), b / 2+r2cos(θ m1 ),0),

[0120] Where M1 is the coordinate of the first transition metal atom, a is the side length of the first unit cell, b is the side length of the second unit cell, r2 is the radius of the transition metal layer, θ m1 is the azimuth angle of the first transition metal atom, θ m1 =θ*i, θ is the angle in radians, i∈{0,1,2,…,n-1}, and n is the number of repeating units on the circumference.

[0121] The coordinates of the second transition metal atoms in the armchair nanotubes are as follows:

[0122] M2=(a / 2+r2sin(θ m2 ), b / 2+r2cos(θ m2 ), c0 / 2),

[0123] Where M2 is the coordinate of the second transition metal atom, a is the side length of the first unit cell, b is the side length of the second unit cell, r2 is the radius of the transition metal layer, θ m2 is the azimuth angle of the second transition metal atom, θ m2 =θ*(i+1 / 2), θ is the angle in radians, i∈{0,1,2,…,n-1}, n is the number of repeating units on the circumference, and c0 is the axial lattice parameter of the nanotube.

[0124] The chalcogen atoms (the first chalcogen atom and the second chalcogen atom) are a pair of adjacent atoms located in the inner layer or the outer layer of the tube.

[0125] When the first chalcogen atom of the armchair nanotube is in the inner layer, the coordinates of the first chalcogen atom are as follows:

[0126] X1=(a / 2+r1sin(θ x1 ), b / 2+r1cos(θ x1 ),0),

[0127] Where X1 is the coordinate of the first sulfur atom, a is the side length of the first unit cell, b is the side length of the second unit cell, r1 is the radius of the inner sulfur layer, θ x1 is the azimuthal angle of the first chalcogen atom coordinate, θ x1 =θ*(i+2 / 3), θ is the angle in radians, i∈{0,1,2,…,n-1}, and n is the number of repeating units on the circumference.

[0128] When the first chalcogen atom of the armchair nanotube is in the outer layer, the coordinates of the first chalcogen atom are as follows:

[0129] X1=(a / 2+r3sin(θ x1), b / 2+r3cos(θ x1 ),0),

[0130] Where X1 is the coordinate of the first chalcogen atom, a is the side length of the first unit cell, b is the side length of the second unit cell, r3 is the outer sulfur radius, θ x1 is the azimuthal angle of the first chalcogen atom coordinate, θ x1 =θ*(i+2 / 3), θ is the angle in radians, i∈{0,1,2,…,n-1}, and n is the number of repeating units on the circumference.

[0131] When the second chalcogen atom of the armchair nanotube is in the inner layer, the coordinates of the second chalcogen atom are as follows:

[0132] X2=(a / 2+r1sin(θ x2 ), b / 2+r1cos(θ x2 ), c0 / 2),

[0133] Where X2 is the coordinate of the second sulfur atom, a is the side length of the first unit cell, b is the side length of the second unit cell, r1 is the radius of the inner sulfur layer, θ x2 is the azimuthal angle of the second chalcogen atom coordinate, θ x2 =θ*(i+1 / 6), θ is the angle in radians, i∈{0,1,2,…,n-1}, and n is the number of repeating units on the circumference.

[0134] When the second chalcogen atom of the armchair nanotube is in the outer layer, the coordinates of the second chalcogen atom are as follows:

[0135] X2=(a / 2+r3sin(θ x2 ), b / 2+r3cos(θ x2 ), c0 / 2),

[0136] Where X2 is the coordinate of the second sulfur atom, a is the side length of the first unit cell, b is the side length of the second unit cell, r3 is the outer sulfur radius, θ x2 is the azimuthal angle of the second chalcogen atom coordinate, θ x2 =θ*(i+1 / 6), θ is the angle in radians, i∈{0,1,2,…,n-1}, and n is the number of repeating units on the circumference.

[0137] S6. By iteratively repeating the above calculation steps, the atomic coordinates along the circular path are generated in sequence to form all the atoms in a unit cell.

[0138] Based on the coordinates of transition metal atoms and chalcogen atoms, an armchair nanotube model of transition metal dichalcogenides is generated according to the direction of the chiral vector.

[0139] The above algorithm can be implemented using Python programming language combined with the Atomic Simulation Environment module. Figure 5 As shown in (a), the zigzag nanotube model obtained using this method can maintain a stable structure after the structure is optimized using the DFT method.

[0140] Example 2

[0141] like Figure 2-4 As shown, the present invention provides a method for constructing transition metal disulfide armchair and zigzag nanotube models, the steps of which include:

[0142] S1. Based on the two-dimensional hexagonal structure of transition metal dichalcogenides, the two-dimensional structure comprises repeating MX2 units, where M represents a transition metal and X represents a chalcogen element. The two-dimensional hexagonal structure is curled to form transition metal dichalcogenide nanotubes, while simultaneously determining the nanotube's axial lattice parameter and lateral unit cell length, resulting in a zigzag nanotube shape.

[0143] Specifically, when the two-dimensional planar structure is rolled up to form a zigzag nanotube, its axial periodicity corresponds to the larger periodic repeating unit in the monolayer structure. The lattice parameters c0 and L of the zigzag nanotube are defined so that c0 represents the unit cell length along the z-axis, corresponding to the axial direction of the nanotube, and L represents the unit cell length in the xy plane perpendicular to the nanotube axis (see Figure 2 ).

[0144] S2. Calculate the chiral vector corresponding to the number of repeating units in the circumferential direction, and obtain the radius of the transition metal layer based on the chiral vector and the lateral unit cell length.

[0145] This step is specifically:

[0146] Calculate the angle in radians based on the number of chiral vectors:

[0147]

[0148] Where θ is the angle in radians and n is the number of chiral vectors.

[0149] According to the angle in radians and the lateral unit cell length, the radius of the transition metal layer is calculated as:

[0150]

[0151] Wherein, θ is the angle in radians, L is the lateral unit cell length, and r2 is the radius of the transition metal layer.

[0152] S3. Measure the vertical distance between the two sulfur atomic layers and calculate the distance between the chalcogen atomic layers. Based on the radius of the transition metal layer and the distance between the sulfur atomic layers, calculate the outer sulfur radius and the inner sulfur radius.

[0153] Specifically, the calculation formula for the distance between chalcogen atoms is:

[0154]

[0155] Among them, d o is the distance between chalcogen atoms, d X-X is the vertical distance between two sulfur atomic layers.

[0156] like Figure 3 As shown, the calculation formula for the outer sulfur radius is:

[0157] r3=r2+d o ,

[0158] Where r2 is the radius of the transition metal layer, d o is the distance between chalcogen atoms, r3 is the outer sulfur radius;

[0159] The calculation formula of the inner sulfur radius is:

[0160] r1=r2-d o ,

[0161] Where r2 is the radius of the transition metal layer, d o is the distance between chalcogen atoms, and r1 is the radius of the inner sulfur layer.

[0162] S4. Based on the outer sulfur radius, define the unit cell side length, and based on the transition metal layer radius, outer sulfur radius, and inner sulfur radius, locate the coordinates of transition metal atoms and chalcogen atoms using trigonometric functions.

[0163] Specifically, define the thickness of the vacuum layer on the nanotube surface in the horizontal plane and calculate the side length of the unit cell of the nanotube in the horizontal plane:

[0164] a=b=Vc+2r3,

[0165] Wherein, a is the side length of the first unit cell, b is the side length of the second unit cell, Vc is the thickness of the vacuum layer on the surface of the nanotube in the horizontal direction, and r3 is the outer sulfur radius.

[0166] In order to generate the M and X atoms at the correct coordinates on the circumference of the nanotube, a combination of trigonometric mathematical methods must be used to accurately generate the atomic positions to ensure its periodicity and symmetry. The unit cell, in a section perpendicular to the nanotube, has its a-axis along the x-axis and its b-axis along the y-axis, with the center origin O located at a / 2 and b / 2 in the horizontal and vertical directions, respectively. Therefore, the center coordinates are O(a / 2, b / 2). The position of the atom at a point P on the circumference is given by the angular displacement θ measured from the vertical axis. A straight line is drawn from the center O(a / 2, b / 2) to point P, where the length of the line segment (OP) is ro. To determine the coordinates of point P, a horizontal line is drawn from point P to the vertical axis, representing the displacement dx in the x-direction, and a vertical line is drawn from point P to the horizontal axis, representing the displacement dy in the y-direction. Therefore, the coordinates of P are (a / 2+dx, b / 2+dy), where dx and dy can be expressed using trigonometric functions according to the following equations.

[0167] dx=r o sinθ

[0168] dy=r o cosθ

[0169] Among them, r o is the atomic radius and θ is the angle in radians.

[0170] This ensures that the P point can be precisely positioned along the circular trajectory based on a given angular displacement, which is the basic principle for generating the coordinates of the M and X atoms on their respective layers along the circumference of the zigzag nanotube (see Figure 4 The difference between the armchair and zigzag nanotube models lies in the arrangement of the M and X atoms along different axes, which is caused by the different orientations of the chiral vectors during the curling of the two-dimensional monolayer to form the nanotube.

[0171] S4. Based on the unit cell side length of the nanotube in the horizontal plane and the axial lattice parameter of the nanotube, calculate the coordinates of the first transition metal atom, the coordinates of the second transition metal atom, the coordinates of the first sulfide atom, and the coordinates of the second sulfide atom in the unit cell by using the trigonometric function method.

[0172] First, the angle values of the M and X atoms are obtained according to their atomic positions along the ab plane in the hexagonal unit cell. The z coordinate is determined according to the relative positions of the atoms along the c axis, which is crucial for describing the three-dimensional arrangement of atoms in the unit cell (see Figure 1 ).

[0173] Therefore, the precise atomic coordinates of the M1, M2, X1, and X2 atoms in the unit cell can be expressed as (a / 2+dx, b / 2+dy, c). Specifically, the coordinates of the first transition metal atom of the zigzag nanotube are as follows:

[0174] M1=(a / 2+r2sin(θm1 ), b / 2+r2cos(θ m1 ),0),

[0175] Where M1 is the coordinate of the first transition metal atom, a is the side length of the first unit cell, b is the side length of the second unit cell, r2 is the radius of the transition metal layer, θ m1 is the azimuth angle of the first transition metal atom, θ m1 =θ*i, θ is the angle in radians, i∈{0,1,2,…,n-1}, and n is the number of repeating units on the circumference.

[0176] The coordinates of the second transition metal atom of the zigzag nanotube are as follows:

[0177] M2=(a / 2+r2sin(θ m2 ), b / 2+r2cos(θ m2 ), c0 / 2),

[0178] Where M2 is the coordinate of the second transition metal atom, a is the side length of the first unit cell, b is the side length of the second unit cell, r2 is the radius of the transition metal layer, θ m2 is the azimuth angle of the second transition metal atom, θ m2 =θ*(i+1 / 2), θ is the angle in radians, i∈{0,1,2,…,n-1}, n is the number of repeating units on the circumference, and c0 is the axial lattice parameter of the nanotube.

[0179] The chalcogen atoms (the first chalcogen atom and the second chalcogen atom) are a pair of adjacent atoms located in the inner layer or the outer layer of the tube.

[0180] When the first chalcogen atom of the zigzag nanotube is in the inner layer, the coordinates of the first chalcogen atom are as follows:

[0181] X1=(a / 2+r1sin(θ x1 ), b / 2+r1cos(θ x1 ), 2c0 / 3),

[0182] Where X1 is the coordinate of the first sulfur atom, a is the side length of the first unit cell, b is the side length of the second unit cell, r1 is the radius of the inner sulfur layer, θ x1 is the azimuthal angle of the first chalcogen atom coordinate, θ x1 =θ*i, θ is the angle in radians, i∈{0,1,2,…,n-1}, and n is the number of repeating units on the circumference.

[0183] When the second chalcogen atom of the zigzag nanotube is in the inner layer, the coordinates of the second chalcogen atom are as follows:

[0184] X2=(a / 2+r1sin(θ x2), b / 2+r1cos(θ x2 ), c0 / 6),

[0185] Where X2 is the coordinate of the second sulfur atom, a is the side length of the first unit cell, b is the side length of the second unit cell, r1 is the radius of the inner sulfur layer, θ x2 is the azimuthal angle of the second chalcogen atom coordinate, θ x2 =θ(i+1 / 2), θ is the angle in radians, i∈{0,1,2,…,n-1}, and n is the number of repeating units on the circumference.

[0186] When the first chalcogen atom of the zigzag nanotube is in the outer layer, the coordinates of the first chalcogen atom are as follows:

[0187] X1=(a / 2+r3sin(θ x1 ), b / 2+r3cos(θ x1 ), 2c0 / 3),

[0188] Where X1 is the coordinate of the first chalcogen atom, a is the side length of the first unit cell, b is the side length of the second unit cell, r3 is the outer sulfur radius, θ x1 is the azimuthal angle of the first chalcogen atom coordinate, θ x1 =θ*i, θ is the angle in radians, i∈{0,1,2,…,n-1}, and n is the number of repeating units on the circumference.

[0189] When the second chalcogen atom of the zigzag nanotube is in the outer layer, the coordinates of the second chalcogen atom are as follows:

[0190] X2=(a / 2+r3sin(θ x2 ), b / 2+r3cos(θ x2 ), c0 / 6),

[0191] Where X2 is the coordinate of the second sulfur atom, a is the side length of the first unit cell, b is the side length of the second unit cell, r3 is the outer sulfur radius, θ x2 is the azimuthal angle of the second chalcogen atom coordinate, θ x2 =θ(i+1 / 2), θ is the angle in radians, i∈{0,1,2,…,n-1}, and n is the number of repeating units on the circumference.

[0192] S5. By iteratively repeating the above calculation steps, the atomic coordinates along the circular path are generated in sequence to form all the atoms in a unit cell.

[0193] Based on the coordinates of transition metal atoms and chalcogen atoms, a zigzag nanotube model of transition metal disulfide is generated according to the direction of the chiral vector.

[0194] The above algorithm can be implemented using Python programming language combined with the Atomic Simulation Environment module. Figure 5 As shown in (b), the zigzag nanotube model obtained using this method can maintain a stable structure after the structure is optimized using the DFT method.

[0195] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit it. Although the present invention has been described in detail with reference to the above embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the above embodiments, or replace some or all of the technical features therein with equivalents. However, these modifications or replacements do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for constructing armchair and zigzag nanotube models of transition metal disulfide, characterized in that the steps include: Based on the two-dimensional hexagonal crystal structure of transition metal disulfide, curling to generate transition metal disulfide nanotubes, and simultaneously determining the nanotube axial lattice parameter and lateral unit cell length of the nanotube, wherein the shape of the nanotube includes armchair type and zigzag type; Calculate the chiral vector corresponding to the number of repeating units in the circumferential direction, and obtain the radius of the transition metal layer based on the chiral vector and the lateral unit cell length; Measuring the vertical distance between two sulfur atomic layers to calculate the distance between chalcogen atomic layers, and calculating the outer sulfur radius and the inner sulfur radius based on the transition metal layer radius and the distance between the sulfur atomic layers; Based on the outer sulfur radius, the unit cell side length is defined, and based on the transition metal layer radius, the outer sulfur radius and the inner sulfur radius, the coordinates of the transition metal atoms and the chalcogen atoms are located by trigonometric functions; Based on the coordinates of the transition metal atoms and the chalcogen atoms, a nanotube model of the transition metal disulfide is generated according to the direction of the chiral vector.

2. The method for constructing armchair and zigzag nanotube models of transition metal disulfide according to claim 1, characterized in that: The method of obtaining the radius of the transition metal layer according to the chirality vector and the lateral unit cell length includes: Calculate the angle in radians based on the number of chiral vectors: Where θ is the angle in radians, and n is the number of chiral vectors; According to the angle in radians and the lateral unit cell length, the radius of the transition metal layer is calculated as: Wherein, θ is the angle in radians, L is the lateral unit cell length, and r2 is the radius of the transition metal layer.

3. The method for constructing armchair and zigzag nanotube models of transition metal disulfide according to claim 1, characterized in that: The calculation formula of the chalcogen atomic layer spacing is: Among them, d o is the distance between chalcogen atoms, d X-X is the vertical distance between two sulfur atomic layers; The calculation formula of the outer sulfur radius is: r3＝r2+d o ， Where r2 is the radius of the transition metal layer, d o is the distance between chalcogen atoms, r3 is the outer sulfur radius; The calculation formula of the inner sulfur radius is: r1＝r2-d o ， Where r2 is the radius of the transition metal layer, d o is the distance between chalcogen atoms, and r1 is the radius of the inner sulfur layer.

4. The method for constructing armchair and zigzag nanotube models of transition metal disulfide according to claim 1, characterized in that: The coordinates of transition metal atoms and chalcogen atoms are located by trigonometric functions based on the transition metal layer radius, the outer sulfur radius, and the inner sulfur radius, including: Define the thickness of the vacuum layer outside the nanotube in the horizontal plane and calculate the unit cell side length of the nanotube in the horizontal plane: a=b=Vc+2r3, Where a is the side length of the first unit cell, b is the side length of the second unit cell, Vc is the thickness of the vacuum layer on the surface of the nanotube in the horizontal direction, and r3 is the outer sulfur radius; Based on the unit cell side length of the nanotube in the horizontal plane and the axial lattice parameter of the nanotube, the coordinates of the first transition metal atom, the coordinates of the second transition metal atom, the coordinates of the first chalcogen atom and the second chalcogen atom in the unit cell are calculated by trigonometric function method; By iteratively repeating the above calculation steps, the atomic coordinates along the circular path are generated in sequence to form all the atoms in a unit cell.

5. The method for constructing armchair and zigzag nanotube models of transition metal disulfide according to claim 4, characterized in that: The coordinates of the first transition metal atoms in the armchair nanotubes are as follows: M1=(a / 2+r2sin(θ m1 ), b / 2+r2cos(θ m1 ),0), Where M1 is the coordinate of the first transition metal atom, a is the side length of the first unit cell, b is the side length of the second unit cell, r2 is the radius of the transition metal layer, θ m1 is the azimuth angle of the first transition metal atom, θ m1 =θ*i, θ is the angle in radians, i∈{0,1,2,…,n-1}, n is the number of repeating units on the circumference; The coordinates of the second transition metal atoms in the armchair nanotubes are as follows: M2=(a / 2+r2sin(θ m2 ),b / 2+r2cos(θ m2 ),c0 / 2), Where M2 is the coordinate of the second transition metal atom, a is the side length of the first unit cell, b is the side length of the second unit cell, r2 is the radius of the transition metal layer, θ m2 is the azimuth angle of the second transition metal atom, θ m2 =θ*(i+1 / 2), θ is the angle in radians, i∈{0,1,2,…,n-1}, n is the number of repeating units on the circumference, and c0 is the axial lattice parameter of the nanotube; When the first chalcogen atom of the armchair nanotube is in the inner layer, the coordinates of the first chalcogen atom are as follows: X1=(a / 2+r1 sin(θ x1 ), b / 2+r1cos(θ x1 ),0), Where X1 is the coordinate of the first sulfur atom, a is the side length of the first unit cell, b is the side length of the second unit cell, r1 is the radius of the inner sulfur layer, θ x1 is the azimuthal angle of the first chalcogen atom coordinate, θ x1 =θ*(i+2 / 3), where θ is the angle in radians, i∈{0,1,2,…,n-1}, and n is the number of repeating units on the circumference; When the first chalcogen atom of the armchair nanotube is in the outer layer, the coordinates of the first chalcogen atom are as follows: X1=(a / 2+r3 sin(θ x1 ),b / 2+r3 cos(θ x1 ),0), Where X1 is the coordinate of the first chalcogen atom, a is the side length of the first unit cell, b is the side length of the second unit cell, r3 is the outer sulfur radius, θ x1 is the azimuthal angle of the first chalcogen atom coordinate, θ x1 =θ*(i+2 / 3), where θ is the angle in radians, i∈{0,1,2,…,n-1}, and n is the number of repeating units on the circumference; When the second chalcogen atom of the armchair nanotube is in the inner layer, the coordinates of the second chalcogen atom are as follows: X2=(a / 2+r1 sin(θ x2 ),b / 2+r1 cos(θ x2 ),c0 / 2), Where X2 is the coordinate of the second sulfur atom, a is the side length of the first unit cell, b is the side length of the second unit cell, r1 is the radius of the inner sulfur layer, θ x2 is the azimuthal angle of the second chalcogen atom coordinate, θ x2 =θ*(i+1 / 6), where θ is the angle in radians, i∈{0,1,2,…,n-1}, and n is the number of repeating units on the circumference; When the second chalcogen atom of the armchair nanotube is in the outer layer, the coordinates of the second chalcogen atom are as follows: X2=(a / 2+r3 sin(θ x2 ),b / 2+r3 cos(θ x2 ),c0 / 2), Where X2 is the coordinate of the second sulfur atom, a is the side length of the first unit cell, b is the side length of the second unit cell, r3 is the outer sulfur radius, θ x2 is the azimuthal angle of the second chalcogen atom coordinate, θ x2 =θ*(i+1 / 6), θ is the angle in radians, i∈{0,1,2,…,n-1}, and n is the number of repeating units on the circumference.

6. The method for constructing armchair and zigzag nanotube models of transition metal disulfide according to claim 4, characterized in that: The coordinates of the first transition metal atoms in the zigzag nanotubes are as follows: M1=(a / 2+r2sin(θ m1 ),b / 2+r2cos(θ m1 ),0), Where M1 is the coordinate of the first transition metal atom, a is the side length of the first unit cell, b is the side length of the second unit cell, r2 is the radius of the transition metal layer, θ m1 is the azimuth angle of the first transition metal atom, θ m1 =θ*i, θ is the angle in radians, i∈{0,1,2,…,n-1}, n is the number of repeating units on the circumference; The coordinates of the second transition metal atom of the zigzag nanotube are as follows: M2(a / 2+r2 sin(θ m2 ),b / 2+r2 cos(θ m2 ),c0 / 2), Where M2 is the coordinate of the second transition metal atom, a is the side length of the first unit cell, b is the side length of the second unit cell, r2 is the radius of the transition metal layer, θ m2 is the azimuth angle of the second transition metal atom, θ m2 =θ*(i+1 / 2), θ is the angle in radians, i∈{0,1,2,…,n-1}, n is the number of repeating units on the circumference, and c0 is the axial lattice parameter of the nanotube; When the first chalcogen atom of the zigzag nanotube is in the inner layer, the coordinates of the first chalcogen atom are as follows: X1=(a / 2+r1 sin(θ x1 ),b / 2+r1 cos(θ x1 ), 2c0 / 3), Where X1 is the coordinate of the first sulfur atom, a is the side length of the first unit cell, b is the side length of the second unit cell, r1 is the radius of the inner sulfur layer, θ x1 is the azimuthal angle of the first chalcogen atom coordinate, θ x1 =θ*i, θ is the angle in radians, i∈{0,1,2,…,n-1}, n is the number of repeating units on the circumference; When the second chalcogen atom of the zigzag nanotube is in the inner layer, the coordinates of the second chalcogen atom are as follows: X2=(a / 2+r1 sin(θ x2 ),b / 2+r1 cos(θ x2 ),c0 / 6), Where X2 is the coordinate of the second sulfur atom, a is the side length of the first unit cell, b is the side length of the second unit cell, r1 is the radius of the inner sulfur layer, θ x2 is the azimuthal angle of the second chalcogen atom coordinate, θ x2 =θ(i+1 / 2), where θ is the angle in radians, i∈{0,1,2,…,n-1}, and n is the number of repeating units on the circumference; When the first chalcogen atom of the zigzag nanotube is in the outer layer, the coordinates of the first chalcogen atom are as follows: X1=(a / 2+r3 sin(θ x1 ),b / 2+r3 cos(θ x1 ), 2c0 / 3), Where X1 is the coordinate of the first chalcogen atom, a is the side length of the first unit cell, b is the side length of the second unit cell, r3 is the outer sulfur radius, θ x1 is the azimuthal angle of the first chalcogen atom coordinate, θ x1 =θ*i, θ is the angle in radians, i∈{0,1,2,…,n-1}, n is the number of repeating units on the circumference; When the second chalcogen atom of the zigzag nanotube is in the outer layer, the coordinates of the second chalcogen atom are as follows: X2=(a / 2+r3 sin(θ x2 ),b / 2+r3 cos(θ x2 ),c0 / 6), Where X2 is the coordinate of the second sulfur atom, a is the side length of the first unit cell, b is the side length of the second unit cell, r3 is the outer sulfur radius, θ x2 is the azimuthal angle of the second chalcogen atom coordinate, θ x2 =θ(i+1 / 2), θ is the angle in radians, i∈{0,1,2,…,n-1}, and n is the number of repeating units on the circumference.

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