CN110020478A - A kind of Molecular mechanics method measuring single layer molybdenum disulfide elasticity modulus and Poisson's ratio - Google Patents
A kind of Molecular mechanics method measuring single layer molybdenum disulfide elasticity modulus and Poisson's ratio Download PDFInfo
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- CWQXQMHSOZUFJS-UHFFFAOYSA-N molybdenum disulfide Chemical compound S=[Mo]=S CWQXQMHSOZUFJS-UHFFFAOYSA-N 0.000 title claims abstract description 84
- 239000002356 single layer Substances 0.000 title claims abstract description 77
- 229910052982 molybdenum disulfide Inorganic materials 0.000 title claims abstract description 75
- 238000000324 molecular mechanic Methods 0.000 title claims abstract description 24
- 238000000034 method Methods 0.000 title claims abstract description 22
- 230000000694 effects Effects 0.000 claims abstract description 12
- 239000010410 layer Substances 0.000 claims description 32
- 238000005381 potential energy Methods 0.000 claims description 23
- 125000004429 atom Chemical group 0.000 claims description 17
- NINIDFKCEFEMDL-UHFFFAOYSA-N Sulfur Chemical group [S] NINIDFKCEFEMDL-UHFFFAOYSA-N 0.000 claims description 8
- 239000011229 interlayer Substances 0.000 claims description 8
- 239000000126 substance Substances 0.000 claims description 8
- 238000009795 derivation Methods 0.000 claims description 7
- 238000000329 molecular dynamics simulation Methods 0.000 claims description 7
- 125000004434 sulfur atom Chemical group 0.000 claims description 5
- 229910017311 Mo—Mo Inorganic materials 0.000 claims description 3
- 229910052750 molybdenum Inorganic materials 0.000 claims description 3
- ZOKXTWBITQBERF-UHFFFAOYSA-N Molybdenum Chemical compound [Mo] ZOKXTWBITQBERF-UHFFFAOYSA-N 0.000 claims 2
- 239000011733 molybdenum Substances 0.000 claims 2
- 239000005864 Sulphur Substances 0.000 claims 1
- PTISTKLWEJDJID-UHFFFAOYSA-N sulfanylidenemolybdenum Chemical compound [Mo]=S PTISTKLWEJDJID-UHFFFAOYSA-N 0.000 claims 1
- 239000000463 material Substances 0.000 abstract description 17
- 239000002086 nanomaterial Substances 0.000 abstract description 6
- 238000002474 experimental method Methods 0.000 abstract description 3
- 230000007704 transition Effects 0.000 abstract 1
- 238000005516 engineering process Methods 0.000 description 4
- 238000011160 research Methods 0.000 description 4
- 238000010586 diagram Methods 0.000 description 3
- 238000005259 measurement Methods 0.000 description 3
- 238000004364 calculation method Methods 0.000 description 2
- 239000011159 matrix material Substances 0.000 description 2
- UQUKRGMJEGOAKY-UHFFFAOYSA-N molybdenum sulfanylidenemolybdenum Chemical compound [Mo].[Mo]=S UQUKRGMJEGOAKY-UHFFFAOYSA-N 0.000 description 2
- 238000012552 review Methods 0.000 description 2
- 238000013459 approach Methods 0.000 description 1
- 230000009286 beneficial effect Effects 0.000 description 1
- 238000006555 catalytic reaction Methods 0.000 description 1
- 238000013461 design Methods 0.000 description 1
- 238000011161 development Methods 0.000 description 1
- 230000005611 electricity Effects 0.000 description 1
- 238000005461 lubrication Methods 0.000 description 1
- 238000004519 manufacturing process Methods 0.000 description 1
- 238000012827 research and development Methods 0.000 description 1
- 239000004065 semiconductor Substances 0.000 description 1
- 238000004088 simulation Methods 0.000 description 1
- 230000005476 size effect Effects 0.000 description 1
- 238000012360 testing method Methods 0.000 description 1
- 230000009466 transformation Effects 0.000 description 1
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- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F30/00—Computer-aided design [CAD]
- G06F30/20—Design optimisation, verification or simulation
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- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F2119/00—Details relating to the type or aim of the analysis or the optimisation
- G06F2119/06—Power analysis or power optimisation
Abstract
The invention belongs to calculate two-dimension nano materials technical field, a kind of Molecular mechanics method for measuring single layer molybdenum disulfide elasticity modulus and Poisson's ratio is provided.The related mechanical property of single layer molybdenum disulfide is determined by Molecular mechanics method, and gives the dimensional effect of the material.The present invention has initially set up the molecular mechanics theoretical model of single layer molybdenum disulfide, without establishing projection supplementary structure model, has directly obtained the analytical expression that can characterize arbitrary dimension single layer molybdenum disulfide elasticity modulus and Poisson's ratio.The method of the present invention not only can effectively measure the elasticity modulus and Poisson's ratio of single layer molybdenum disulfide, avoid experiment bring sky high cost, and the result shows that single layer molybdenum disulfide with characteristic size increase gradually by anisotropic material transition be isotropic material.This provides important theoretical reference for the application based on single layer molybdenum disulfide material.
Description
Technical field
The invention belongs to calculate two-dimension nano materials technical field, it is related to a kind of based on Molecular mechanics method measurement single layer two
The method of molybdenum sulfide elasticity modulus and Poisson's ratio.
Background technique
Nanosecond science and technology are a rapidly growing in recent decades high-and-new science and technologies, as the term suggests it is exactly in nanoscale
On to material carry out research and development a science technology.Its birth not only preferably recognizes the material world for people and provides
New technical support, also opens new approach for the development of various fields.As the research object of nanosecond science and technology, nanometer material
Expect to be different from the good characteristic of macroscopic material because of it, in all various aspects such as mechanics, optics, electricity, chemistry and biomedicine
Show the performance of a large amount of Uniques.It is existing such as dimensional effect, table at the nanoscale compared with traditional macroscopic material
The phenomenon that face interfacial effect etc. is different from macroscopic material, so that nano material has unusual researching value.
Molybdenum disulfide is applied as one of popular two-dimension nano materials in recent years in catalysis, lubrication and semiconductor etc.
Field has broad prospects.Therefore essential to its material properties, mechanical property Quality Research.
Research currently for nano material mechanics performance mainly includes experimental method, theoretical method and numerical simulation.To the greatest extent
Pipe related experiment equipment continues to introduce new, but is tested be limited always at the nanoscale, on the one hand the reality under small scale
It is often complex to test operation, or even is difficult to carry out.
For nano material, the mechanical attribute of material can be effectively obtained using the correlation technique of molecular scale.Molecule
Dimension calculation method includes the methods of Molecular mechanics method and molecular dynamics simulation.Wherein, molecular mechanics be built upon through
On the basis of allusion quotation theory of mechanics, by the method that experience and semiempirical parameter calculate molecular structure and energy, material can be effectively obtained
Expect intrinsic performance.
The present invention measures its mechanical property using single layer molybdenum disulfide as research object, based on Molecular mechanics method, and shows
The dimensional effect that single layer molybdenum disulfide changes from anisotropy to isotropic material with the increase of characteristic size is it
Important theoretical reference is provided in actual production and application.
Summary of the invention
Single layer molybdenum disulfide molecule is by the structure of three layers of atomic building class sandwich, and upper layer and lower layer are S atom, middle layer
For Mo atom；Single layer molybdenum disulfide molecule belongs to hexagonal system structure, the honeycomb structure of molecular structure class hexagon；According to
Its boundary is divided into armchair boundary and serrated boundary by the boundary characteristic of single layer molybdenum disulfide molecule；Molecular mechanics and dynamics choosing
Take the periodical representative unit in single layer molybdenum disulfide molecular structure as molecular mechanics theoretical model, the representative unit is as meter
Unit cell is calculated, by 9 atomic buildings, wherein middle layer is 3 Mo atoms, and upper layer and lower layer are respectively 3 S atoms；According to unit cell itself
Geometric relationship, be divided into the chemical bond bond angle of a type of chemical bond and three types, respectively molybdenum sulfide linkage ri, layer
Interior molybdenum sulphur molybdenum angle φi, sulphur molybdenum sulphur angle θ in layeriWith interlayer sulphur molybdenum sulphur angle ψi, wherein i=1,2 respectively represent the angle on different location；
Wherein, layer interior angle refers to two sulphur atoms at the constituted angle S-Mo-S on same atomic scale, and interlayer angle refers to the angle S-Mo-S
Two sulphur atoms are not on same atomic scale；According to the symmetry of structure, meet φi=θi, and in unit cell, upper and lower two
Thickness is equal between sulphur atom layer and Mo atomic layer, therefore interlayer relation can be by variable bond distance and bond angle r1、ψ1And r2、ψ2It indicates
It is as follows:
Then according to the relationship for choosing the distance between adjacent Mo-Mo atom l equal space geometry in unit cell, using cosine
Theorem carries out derivation expression using bond distance's bond angle variable:
Based on formula (1), formula (2) can by abbreviation be it is following in the form of:
Pass through the above-mentioned available ψ of the relational expression provided2With φ1, φ2, ψ1Between relationship.And by formula (1) and formula
It (2) can be by variable r2With variable φ1, φ2, ψ1, r1It is indicated.
The unit cell chosen is calculated in armchair length laWith the length l in sawtooth pattern directionzIt is indicated by bond distance, bond angle:
For the single layer molybdenum disulfide model having a size of (m, n), (wherein, m, n are respectively indicated along armchair direction and edge
The quantity of sawtooth pattern direction unit cell), total length expression formula of the single layer molybdenum disulfide model in both direction are as follows:
Its differential form is as follows:
Potential energy of deformation caused by flexible and bond angle variation of the total potential energy of molecule of the present invention by chemical bond forms, molecule total energy
Amount are as follows:
For the single layer molybdenum disulfide molecular model of finite size, in order to consider the different boundary effect of its boundary nuclear energy
It answers, needs separately to calculate molecular potential, all atoms are treated all in accordance with the energy situation of interior atoms first, are counted
The potential energy of calculation is denoted as Eint；Then it is being revert to boundary atom, is analyzing effective bond distance and bond angle number, this potential energy is denoted as
Ebound.Further, the present invention describes the mechanical property and deformational behavior of single layer molybdenum disulfide, model using CVFF force field parameter
Geometric parameter by DFT calculate obtain, and in particular to parameter as shown in Table 1 and Table 2 (Nanotechnology, 2015,26
(18):185705；Physical Review B, 1975,12 (2): 659-663):
The stiffness parameters of table 1 single layer molybdenum disulfide bond distance and bond angle
The geometric parameter of bond distance and bond angle in 2 single layer molybdenum disulfide theoretical model of table
It is respectively r in the number for completely representing bond distance's bond angle in unit cell1=4, φ1=4, θ1=4, ψ1=2, r2=8,
φ2=8, θ2=8, ψ2=4 (i=1,2).According to molecular mechanics and dynamics formula, the total system of single layer molybdenum disulfide under simple tension
Potential energy may be expressed as:
Π=Eint+Ebound-FdL (8)
Wherein,
Wherein, N=mn indicates the total number of unit cell in model.The load of F expression simple tension；When along armchair side
To carry out simple tension when, dL=dLa, when carrying out simple tension along sawtooth pattern direction, dL=dLz.By the formula of differential form
(1), formula (3) and formula (6), formula (9) substitute into formula (8), are then organized by variable φ1, φ2, ψ1, r1The system being indicated
Total potential energy is obtained further according to Π=0 minimum potential energy principal δ:
The variable φ relatively independent about four is listed as a result,1, φ2, ψ1And r1The system of linear equations of expression, wherein M=
FdL。
It solves equation (11), obtaining using F is function about four relatively independent variable d φ1、dφ2、dψ1And dr1Expression
Formula, and it is based on this, it calculates separately out under simple tension effect along armchair direction strain stressaWith the strain along sawtooth pattern direction
εz:
Sectional area of the single layer molybdenum disulfide on armchair Yu sawtooth pattern boundary uses A respectivelya, Az,Indicate single layer
The thickness of molybdenum disulfide.Based on above-mentioned derivation, elasticity modulus and pool of the single layer molybdenum disulfide along armchair and sawtooth pattern direction
The analytical expression of loose ratio is as follows:
According to the above method, the elasticity modulus and Poisson's ratio of available arbitrary dimension single layer molybdenum disulfide.
Beneficial effects of the present invention: proposed by the present invention based on molecular mechanics measurement single layer molybdenum disulfide elasticity modulus and pool
The method of loose ratio can effectively, accurately, fast obtain the elasticity modulus and Poisson's ratio of the single layer molybdenum disulfide of arbitrary dimension, and
It gives under micro/nano-scale, mechanical property gradually tends to isotropic size by anisotropy with the increase of characteristic size
Effect, so as to avoid measuring bring difficulty and cost.
Detailed description of the invention
Fig. 1 is single layer molybdenum disulfide molecular mechanics theoretical model figure, the top view of (a) single layer molybdenum disulfide molecular structure；
(b) side view of the single layer molybdenum disulfide on armchair boundary；(c) side view of the single layer molybdenum disulfide on sawtooth pattern boundary；(d)
Single layer molybdenum disulfide calculates the single cell model perspective view chosen.
Fig. 2 is single layer molybdenum disulfide simple tension schematic diagram, and (a) is to stretch schematic diagram along armchair direction；It (b) is edge
Sawtooth pattern direction stretches schematic diagram.
Fig. 3 is trend chart of the elasticity modulus with single layer molybdenum disulfide characteristic size.
Fig. 4 is trend chart of the Poisson's ratio with single layer molybdenum disulfide characteristic size.
Specific embodiment
With reference to the accompanying drawing with technical solution, a specific embodiment of the invention is further illustrated.
The present invention is compared to the single layer molybdenum disulfide elasticity modulus and Poisson of Molecular mechanics method measurement different characteristic size
For specific embodiment, effectiveness of the invention and correctness are further verified.Specific step is as follows:
Molecular mechanics and dynamics choose the periodical representative unit in single layer molybdenum disulfide structure as theoretical model, the unit
(unit cell) by 9 atomic buildings, wherein middle layer is 3 Mo atoms, and upper layer and lower layer are respectively 3 S atoms.It is specific as shown in Figure 1
Single layer molybdenum disulfide theoretical model.According to the geometric relationship of unit cell itself, wherein contain a type of chemical bond and
The chemical bond bond angle of three types, respectively molybdenum sulfide linkage ri(Mo-S), molybdenum sulphur molybdenum angle φ in layeri(Mo-S-Mo), sulphur molybdenum sulphur in layer
Angle θiWith interlayer sulphur molybdenum sulphur angle ψi(S-Mo-S), wherein (i=1,2) respectively represents the angle on different location.Wherein, refer in layer
For two sulphur atoms at the constituted angle S-Mo-S on same atomic scale, interlayer angle refers to two sulphur atoms at the angle S-Mo-S not same
On one atomic scale.According to the symmetry of structure, meet φi=θi(i=1,2), and in single cell structure between different atomic layers
Thickness is equal, therefore the variable r being related to1、ψ1And r2、ψ2Meet following relationship:
To formula (1) both sides, differential can be obtained simultaneously:
dr2=A1dψ1+A2dψ2+A3dr1 (2)
Wherein coefficient is respectively,
Then equal according to the distance between adjacent Mo-Mo atom l in unit cell is chosen, using space geometry relationship, use
The cosine law carries out derivation expression:
Based on formula (1), formula (2) can by abbreviation be it is following in the form of:
To formula (5) both sides, differential can be obtained simultaneously:
dψ2=B1dφ1+B2dφ2+B3dψ1 (6)
Wherein,
Bring equation (6) into formula (2)
dr2=C1dφ1+C2dφ2+C3dψ1+C4dr1 (8)
Wherein, C1=A2B1,C2=A2B2,C3=A1+A2B3,C4=A3.It, can be by variable r by above-mentioned relation formula2With change
Measure φ1, φ2, ψ1, r1It is indicated.
The unit cell chosen is calculated as shown in Figure 1, in its armchair length laWith the length l in sawtooth pattern directionzBy bond distance,
Bond angle is indicated:
For the single layer molybdenum disulfide model having a size of (m, n), (wherein, m, n are respectively indicated along armchair direction and edge
The quantity of sawtooth pattern direction unit cell), total length expression formula of the single layer molybdenum disulfide model in both direction are as follows:
Its differential form is as follows:
It is available that equation (6), (8) are updated to equation (11) arrangement
Wherein coefficient is
Potential energy of deformation caused by flexible and bond angle variation of the total potential energy of molecule of the present invention by bond distance forms, this is because this
Two kinds of potential energy contribution occupies leading part in total molecular potential, therefore the total potential energy of molecule can be written as
For the single layer molybdenum disulfide molecular model of finite size, in order to consider the different boundary effect of its boundary energy,
It needs separately to calculate molecular potential, all atoms is treated all in accordance with the energy situation of interior atoms first, are calculated
Potential energy be denoted as Eint；Then it is being revert to boundary atom, is analyzing effective bond distance and bond angle number, this potential energy is denoted as Ebound。
Further, the present invention describes the mechanical property and deformational behavior of single layer molybdenum disulfide, geometrical relationship using CVFF force field parameter
By DFT calculate obtain, and in particular to the field of force and geometric parameter as shown in 1 table 2 of table (Nanotechnology, 2015,26
(18):185705；Physical Review B, 1975,12 (2): 659-663):
The stiffness parameters of table 1 single layer molybdenum disulfide bond distance and bond angle
The geometric parameter of bond distance and bond angle in 2 single layer molybdenum disulfide theoretical model of table
It is respectively r in the number for completely representing bond distance's bond angle in unit cell1=4, φ1=4, θ1=4, ψ1=2, r2=8,
φ2=8, θ2=8, ψ2=4 (i=1,2).According to molecular mechanics and dynamics formula, the total system of single layer molybdenum disulfide under simple tension
Potential energy may be expressed as:
Π=Eint+Ebound-FdL (15)
Wherein,
N=mn in formula indicates the total number of unit cell in model.The load of F expression simple tension；When along armchair direction
When carrying out simple tension, dL=dLa, when carrying out simple tension along sawtooth pattern direction, dL=dLz.By formula (6), (8), (12),
(16) formula (15) are substituted into, be then organized by variable φ1, φ2, ψ1, r1The total potential energy of the system being indicated, further according to minimal potential
Energy Π=0 principle δ:
The variable φ relatively independent about four is listed as a result,1, φ2, ψ1And r1The system of linear equations of expression, wherein M=
FdL。
Wherein, stiffness matrix expression formula:
When applying simple tension load along armchair direction, have
M1=FD1,M2=FD2,M3=FD3,M4=FD4 (20)
When applying simple tension load along sawtooth pattern direction, have
M1=FD5,M2=FD6,M3=FD7,M4=FD8 (21)
Specific draw direction obtains relatively only about four by function of F as shown in Fig. 2, solution matrix equation (18)
Vertical variable d φ1、dφ2、dψ1And dr1Expression formula, and be based on this, calculate separately out simple tension effect under along armchair side
To strain stressaWith the strain stress along sawtooth pattern directionz:
Sectional area of the single layer molybdenum disulfide on armchair Yu sawtooth pattern boundary uses A respectivelya, Az,Indicate single layer two
The thickness of molybdenum sulfide.Based on above-mentioned derivation, single layer molybdenum disulfide is along the elasticity modulus in armchair direction and the parsing of Poisson's ratio
Expression formula is as follows:
Elasticity modulus and Poisson's ratio along sawtooth pattern direction can be expressed as
By above method step, to obtain the elasticity modulus and Poisson's ratio of single layer molybdenum disulfide.
The single layer molybdenum disulfide molecule for measuring different sizes (3nm-50mn) the present invention is based on Molecular mechanics method is counted respectively
Calculate its elasticity modulus and Poisson's ratio, obtain elasticity modulus with the variation tendency of size as shown in figure 3, along different boundary stretch when,
The variation tendency of its elasticity modulus is different, as size increase gradually reaches unanimity.Poisson's ratio with size variation tendency such as Fig. 4
Institute, when stretching single layer molybdenum disulfide along different boundary, with the increase of characteristic size, Poisson's ratio equally gradually tends to be same steady
Definite value.Calculated result shows: the elasticity modulus and pool of single layer molybdenum disulfide not only can be effectively obtained based on Molecular mechanics method
Loose ratio, and illustrate the dimensional effect of single layer molybdenum disulfide mechanical property.When the characteristic size of single layer molybdenum disulfide is smaller
(50nm or less), elasticity modulus and Poisson's ratio show apparent anisotropy；With the increase of characteristic size, along handrail
Chair form and sawtooth pattern direction single layer molybdenum disulfide elasticity modulus, Poisson's ratio tend to same stationary value respectively, i.e. 179.25GPa and
0.22.The variation tendency of mechanical property shows increase of the single layer molybdenum disulfide with characteristic size gradually by anisotropic material mistake
It crosses as isotropic material.Consistent (the Journal of Materials of calculated result of the present invention and Bao et al. result of study
Science,2016,51(14):6850-6859).For it, design effectively and building electronic component are provided at the nanoscale
Valuable theoretical basis.
In conclusion only a specific embodiment of the invention, but the protection scope invented is not limited thereto, and it is any ripe
The engineers and technicians for knowing the art within the technical scope of the present invention, can do some transformation, such as single layer molybdenum disulfide ruler
Very little size, the selection for calculating unit cell etc., all should be as infringement protection scope of the present invention.Therefore protection scope of the present invention
It should be subject to the scope of protection of the claims.
Claims (1)
1. a kind of Molecular mechanics method for measuring single layer molybdenum disulfide elasticity modulus and Poisson's ratio, first building single layer molybdenum disulfide
Molecular mechanics theoretical model, regard molecule as one group of atom set maintained by elastic force together, according to itself geometry
Relationship, and without establishing projection supplementary structure, direct derivation goes out single layer molybdenum disulfide system energy under the effect of simple tension load
The function expression of amount；Then by minimum potential energy principal, arbitrary dimension single layer molybdenum disulfide elasticity modulus and Poisson's ratio are obtained
Analytical expression, finally solve system of linear equations obtain its elasticity modulus and Poisson's ratio；It is characterized in that, specific steps are such as
Under:
Single layer molybdenum disulfide molecule is by the structure of three layers of atomic building class sandwich, and upper layer and lower layer are S atom, middle layer Mo
Atom；Single layer molybdenum disulfide molecule belongs to hexagonal system structure, the honeycomb structure of molecular structure class hexagon；According to single layer
Its boundary is divided into armchair boundary and serrated boundary by the boundary characteristic of molybdenum disulfide molecule；Molecular mechanics and dynamics are chosen single
For periodical representative unit in layer molybdenum disulfide molecular structure as molecular mechanics theoretical model, the representative unit is single as calculating
Born of the same parents, by 9 atomic buildings, wherein middle layer is 3 Mo atoms, and upper layer and lower layer are respectively 3 S atoms；According to the several of unit cell itself
What structural relation, is divided into the chemical bond bond angle of a type of chemical bond and three types, respectively molybdenum sulfide linkage ri, molybdenum in layer
Sulphur molybdenum angle φi, sulphur molybdenum sulphur angle θ in layeriWith interlayer sulphur molybdenum sulphur angle ψi, wherein i=1,2 respectively represent the angle on different location；Its
In, layer interior angle refers to two sulphur atoms at the constituted angle S-Mo-S on same atomic scale, and interlayer angle refers to the two of the angle S-Mo-S
A sulphur atom is not on same atomic scale；According to the symmetry of structure, meet φi=θi, and in unit cell, upper and lower two sulphur
Thickness is equal between atomic layer and Mo atomic layer, therefore interlayer relation is by variable bond distance and bond angle r1、ψ1And r2、ψ2It is expressed as follows:
Then according to the relationship for choosing the distance between adjacent Mo-Mo atom l equal space geometry in unit cell, using the cosine law
Derivation expression is carried out using bond distance's bond angle variable:
It is following form based on formula (1) and formula (2) abbreviation:
ψ is obtained by the above-mentioned relational expression provided2With φ1, φ2, ψ1Between relationship；And by formula (1) and formula (2) by variable r2
With variable φ1, φ2, ψ1, r1It is indicated；
The unit cell chosen is calculated in armchair length laWith the length l in sawtooth pattern directionzIt is indicated by bond distance, bond angle:
For the single layer molybdenum disulfide model having a size of (m, n), wherein m, n are respectively indicated along armchair direction and along sawtooth
The quantity of type direction unit cell, total length expression formula of the single layer molybdenum disulfide model in both direction are as follows:
Its differential form is as follows:
Potential energy of deformation caused by flexible and bond angle variation of the total potential energy of molecule of the present invention by chemical bond forms, total energy
Are as follows:
For the single layer molybdenum disulfide molecular model of finite size, in order to consider the different boundary effect of its boundary nuclear energy,
Molecular potential need to separately be calculated, first treat all atoms all in accordance with the energy situation of interior atoms, it is calculated
Potential energy is denoted as Eint；Then it is being revert to boundary atom, is analyzing effective bond distance and bond angle number, this potential energy is denoted as Ebound；Into
One step, describes the mechanical property and deformational behavior of single layer molybdenum disulfide using CVFF force field parameter, the geometric parameter of model by
DFT calculate obtain, and in particular to parameter it is as shown in Table 1 and Table 2:
The stiffness parameters of table 1 single layer molybdenum disulfide bond distance and bond angle
The geometric parameter of bond distance and bond angle in 2 single layer molybdenum disulfide theoretical model of table
It is respectively r in the number for completely representing bond distance's bond angle in unit cell1=4, φ1=4, θ1=4, ψ1=2, r2=8, φ2=
8,θ2=8, ψ2=4, wherein i=1,2；According to molecular mechanics and dynamics formula, the total system gesture of single layer molybdenum disulfide under simple tension
It can be represented as:
Π=Eint+Ebound-FdL (8)
Wherein,
Wherein, N=mn indicates the total number of unit cell in model；The load of F expression simple tension；When along armchair direction into
When row simple tension, dL=dLa, when carrying out simple tension along sawtooth pattern direction, dL=dLz；By formula (1), the formula of differential form
(3), formula (6) and formula (9) substitute into formula (8), are then organized by variable φ1, φ2, ψ1, r1The total potential energy of the system being indicated,
It is obtained further according to Π=0 minimum potential energy principal δ:
The variable φ relatively independent about four is listed as a result,1, φ2, ψ1And r1The system of linear equations of expression, wherein M=FdL；
It solves equation (11), obtaining using F is function about four relatively independent variable d φ1、dφ2、dψ1And dr1Expression formula, and
Based on this, calculate separately out under simple tension effect along armchair direction strain stressaWith the strain stress along sawtooth pattern directionz:
Sectional area of the single layer molybdenum disulfide on armchair Yu sawtooth pattern boundary uses A respectivelya, Az,Indicate single layer curing
The thickness of molybdenum；Based on above-mentioned derivation, elasticity modulus and Poisson's ratio of the single layer molybdenum disulfide along armchair Yu sawtooth pattern direction
Analytical expression is as follows:
According to the above method, the elasticity modulus and Poisson's ratio of arbitrary dimension single layer molybdenum disulfide are obtained.
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| Title |
|---|
| JIN-WU JIANG等: "Molecular dynamics simulations of single-layer molybdenum disulphide: Stillinger-Weber parametrization,mechanical properties,and thermal conductivity", 《JOURNAL OF APPLIED PHYSICS》 * |
| 赵俊飞: "基于分子尺度计算方法的单层二硫化钼力学性质研究", 《中国优秀硕士学位论文全文数据库工程科技Ⅰ辑》 * |
Cited By (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN114186456A (en) * | 2021-12-02 | 2022-03-15 | 大连理工大学 | Time-interval fracture state-based near-field dynamics method for structural impact elastoplasticity fracture analysis |
| CN114186456B (en) * | 2021-12-02 | 2022-06-14 | 大连理工大学 | Time interval fracture state based near field dynamics method for structural impact elastoplastic fracture analysis |
Also Published As
| Publication number | Publication date |
|---|---|
| CN110020478B (en) | 2021-10-15 |
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