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Thesis Draft 12 by Redwan and Ahmad.d
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Ahmad Fatehi Ali Mohammed Hezam

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Summary



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Islamic University of Technology 

 

Department of Mechanical and Production Engineering 

 

LAMMPS MOLECULAR DYNAMICS 

SIMULATION OF TWO DIMENSIONAL 

MATERIALS. 

 

A Thesis by 

 

Ahmad Fatehi Ali Mohammed Hezam 

A.S.M Redwan Haider 

 

 

Submitted in Partial Fulfillment 

of the Requirements 

for the Degree of 

 

Bachelor of Science in Mechanical Engineering 

 

 

 

May 2022 

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LAMMPS MOLECULAR DYNAMICS 

SIMULATION OF TWO DIMENSIONAL 

MATERIALS. 

 

AHMAD FATEHI ALI MOHAMMED HEZAM, 170011070  

A.S.M REDWAN HAIDER, 170011061 

 

Submitted in Partial Fulfillment 

of the Requirements 

for the Degree of 

 

 

Bachelor of Science in Mechanical Engineering 

 

 

DEPARTMENT OF MECHANICAL AND PRODUCTION 

ENGINEERING 

 

May 2022 

 

 

 

 

 

 

 

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CERTIFICATE OF RESEARCH 

 

This thesis titled “THE LAMMPS MOLECULAR DYNAMICS SIMULATION OF TWO 

DIMENSIONAL MATERIALS” submitted by AHMAD FATEHI ALI MOHAMMED HEZAM 

(170011070) and A.S.M Redwan Haider (170011061) has been accepted as satisfactory in 

partial fulfillment of the requirement for the Degree of Bachelor of Science in Mechanical 

Engineering.  

 

Supervisor 

 

 

 

_________________________________ 

 

Md. Rezwanul Karim 

Associate Professor  

Department of Mechanical and Production Engineering (MPE) 

Islamic University of Technology (IUT) 

 

 

 

Head of the Department 

 

 

 

___________________________________ 

 

Dr. Md. Anayet Ullah Patwari 

Professor 

Department of Mechanical and Production Engineering (MPE) 

Islamic University of Technology (IUT) 

  

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DECLARATION 

 

I hereby declare that this thesis entitled “THE LAMMPS MOLECULAR DYNAMICS 

SIMULATION OF TWO DIMENSIONAL MATERIALS.” is an authentic report of our study 

carried out as requirement for the award of degree B.Sc. (Mechanical Engineering) at Islamic 

University of Technology, Gazipur, Dhaka, under the supervision of Md. Rezwanul Karim, 

Associate Professor, MPE, IUT in the year 2022 

 

The matter embodied in this thesis has not been submitted in part or full to any other institute for 

award of any degree. 

 

 

 

_____________________________________ 

 

Ahmad Fatehi Ali Mohammed Hezam 

170011070 

 

 

_____________________________________ 

 

A.S.M Redwan Haider 

170011061 

 

 

 

 

 

 

 

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ACKNOWLEDGEMENT 

 

In the beginning we would love to praise Allah the Al-Mighty without whose guidance this 

work would have not been possible. Secondly, our parents who have relentelessly work 

hard for us to be in this position today. Our sincere gratitude towards our honourable 

supervisor Dr.Rezwanul Karim. We are also deeply indebted to our former supervisor Mr. 

Sayedus Salehin for his guidance and encouragement throughout the project. We are glad 

to have Mohammed Raihan Uddin to guide us through the whole procedure with valuable 

directions.  

 

We are greateful to our Co-superviors Dr.Yeasir Arafat and Mr.Md Akibul Islam for their 

relentless support and motivation. Their experstise of materials had given the thesis group 

an enormous advantage. Their construrctive ciristism and reviews had given the work a 

world class flavor.  

 

We are thankful to Dr.Mohammad Tanvirul Ferdaous and Rafsan Subad for their logistical 

support. Their contribution made barriers easy to overcome.  

 

Lastly, we also appreciate the prompt response of Dr. Nuwan Dewapriya and Dr. Jiang 

Xiujuan for their expert opinion during the progression of the work.  

 

 

 

 

 

 

 

 

 



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ABSTRACT 

 

Ultra-thin materials like Graphene and Transition Metal dichalcogenides are a novel class of 

materials with robust applications in electronic devices. These 2D materials are one of the main 

driving forces behind the rise of nanotechnology. Therefore, researchers need to characterise 

such materials to find their suitable usage. These materials have multiple properties such as 

electronic, optical and mechanical. Mechanical properties such as elasticity, strength and 

plasticity define a material's usage. There are two common ways to investigate these materials. 

One such is Classical Mechanics, and the other is Density functional theory(DFT). Our work 

focuses on the application of Molecular dynamics (MD) simulation to derive stress-strain 

relationships of such materials. LAMMPS is the tool that aids in performing the simulation. 

Interatomic potentials such as AIREBO and Stillinger-Weber potential are used to derive the 

required outcomes. The visual simulation results aid us in understanding and describing their 

fracture behaviour. In our work, we primarily focus on the temperature-dependent fracture to 

determine the ultimate tensile stress(UTS) of a material. Initially, we worked to examine the 

stress-strain relationship of armchair graphene monolayer due to varying temperatures from 

300K to 2100K. Then, we thoroughly investigate molybdenum disulfide (MoS2) and 

molybdenum telluride (MoTe2) using the parameterised Stillinger-Weber potential. Finally, the 

fracture strength of MoTe2 is determined from 100K to 600K at an interval of 100K. The results 

for both armchair and zigzag are tabulated and plotted. We can observe that for each 

corresponding temperature, the armchair MoTe2 is stronger than zigzag MoTe2. Furthermore, 

we find that the young's modulus is unaffected due to the temperature change. The simulation 

results can be more accurate using a more accurate potential file if the exact bonding angle is 

incorporated into the code.  

 

  

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TABLE OF CONTENTS 

 

DECLARATION ............................................................................................................................................ 4 

ACKNOWLEDGEMENT .............................................................................................................................. 5 

ABSTRACT ................................................................................................................................................... 6 

TABLE OF CONTENTS ................................................................................................................................... 7 

LIST OF FIGURES ...................................................................................................................................... 10 

LIST OF TABLES ........................................................................................................................................ 14 

NOMENCLATURE ..................................................................................................................................... 15 

Chapter 1: INTRODUCTION ......................................................... Error! Bookmark not defined. 

1.1. Introduction to the research ............................................................................................................... 16 

1.2. Research problem statement .............................................................................................................. 16 

1.3. Objective of the study ........................................................................................................................ 17 

1.4. Scopes and limitations ....................................................................................................................... 17 

1.5. Methodology ...................................................................................................................................... 18 

1.6. Contribution ....................................................................................................................................... 18 

1.7. Arrangmnet of chapters ..................................................................................................................... 19 

Chapter 2: LITERATURE REVIEW .............................................................................................. 20 

2.1.Introduction ........................................................................................................................................ 20 

2.2. Two-Dimensional Materials. ............................................................................................................. 20 

2.3. Graphene ............................................................................................................................................ 24 

2.4. Transition Metal Dichalcogenide ...................................................................................................... 29 

2.5. Molybdenum sulfide .......................................................................................................................... 39 

2.6. Molybdenum ditelluride .................................................................................................................... 41 

Chapter 3: MOLECULAR DYNAMICS SIMULATION. ............. Error! Bookmark not defined. 

3.1. Introduction ....................................................................................................................................... 45 

3.2. Mechanical Deformations .................................................................................................................. 47 

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3.3. Research Objectives .......................................................................................................................... 48 

3.4. State-of-the-art ................................................................................................................................... 49 

3.5. Methodology ...................................................................................................................................... 51 

3.6. Building LAMMPS using CMake ..................................................................................................... 58 

3.7. Software & Applications ................................................................................................................... 61 

Chapter 4: DATA GENERATION OF UNIAXIAL STRESS ON 2D, RESULT & DISCUSSION

 ......................................................................................................... Error! Bookmark not defined. 

4.1.   Introduction ..................................................................................................................................... 62 

4.2. Structure of 2D materials .............................................................................................................. 62 

4.2.1. Graphene ..................................................................................................................................... 64 

4.2.2.  MoS2 .......................................................................................................................................... 66 

4.2.3. MoTe2 .................................................................................................................................. 68 

4.3.   Validation of 2D materials against literature ................................................................................... 71 

4.3.1. Validation of Graphene. ........................................................................................................ 71 

4.3.2. Validation of MoS2. .................................................................................................................... 75 

4.3.3. Validation of MoTe2 .................................................................................................................. 77 

4.4. The samples of fractures of 2D material simulation .......................................................................... 79 

4.4.1. Fracture Sample of Graphene. .................................................................................................... 79 

4.4.2. Fracture Sample of MoS2. ........................................................................................................... 81 

4.4.3. Fracture Sample of MoTe2 .......................................................................................................... 84 

4.5. Result of MoTe2 Exploration ............................................................................................................ 87 

4.5.1. Armchair Direction. .................................................................................................................... 88 

4.5.2. Zigzag Direction. ........................................................................................................................ 89 

4.5.3. Findings and Discussion ............................................................................................................. 90 

Chapter 5: CONCULSION .......................................................... Error! Bookmark not defined. 

5.1. Summary of the work ........................................................................................................................ 92 

5.2. Research outcome .............................................................................................................................. 92 

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5.3. Limitations and computational issues ................................................................................................ 92 

5.4. Future scopes ..................................................................................................................................... 92 

REFERENCES : ........................................................................................................................................... 93 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 



  

 

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LIST OF FIGURES 

 

 

 

Figure 1 : Schematic diagram of a hetero-structured 2D material. _________________________ 22 

Figure 2:  Schematic of Rippled graphene ,SEM images of wrinkled graphene and crumpled 

graphene. _____________________________________________________________________ 23 

Figure 3: AFM images of the 2H-MoTe2 1T’-MoTe2 flake that covers tens of holes. __________ 23 

Figure 4: Mother of all graphitic forms , Graphene , 0D buckyballs, 1D and 3D graphite. ______ 24 

Figure 5: The graphene family. ____________________________________________________ 25 

Figure 6: Large graphene crystal , suspension of microcrystals. ___________________________ 26 

Figure 7: Graphene and Hexagonal Boron Nitride. _____________________________________ 27 

Figure 8: Graphene nanoribbons ,graphene-based HEMTs ,graphene-based NEMS. ___________ 27 

Figure 9: Methods of mass-production of graphene. ____________________________________ 28 

Figure 10: Stacked TMD compounds in the periodic chart. ______________________________ 29 

Figure 11: Structure of TMDs. _____________________________________________________ 30 

Figure 12: Temperature–pressure phase diagram of 1T TaS2. ____________________________ 31 

Figure 13: Phase diagram of superconductivity in electrostatically and chemically doped 2H MoS2.

 _____________________________________________________________________________ 32 

Figure 14: Molybdenum disulphide (MoS2) ,Tungsten ditelluride (WTe2). __________________ 32 

Figure 15: Synthesis of 2D TMDC lateral hetero-structure, high-angle annular dark-field scanning 

transmission electron microscopy image of the lateral hetero-structure formed between MoSe2 and 

WSe2 , optical image of a p–n junction based on a MoS2 /WSe2. _________________________ 34 

Figure 16: Growth methods for the synthesis of ultrathin TMDCs. ________________________ 35 

Figure 17: Theoretical bandgap for various MX2 monolayers. ____________________________ 37 

Figure 18: (a) Optical microscopy image and AFM image of monolayer MoS2 ______________ 39 

Figure 19: Optical image of a MoTe2 single crystalline flake, after mechanical exfoliation . ____ 42 

Figure 20: Applications of MoTe2 hetero-phase homojunctions in electronic devices. _________ 43 

Figure 21: Time vs size relationship for simulation models. ______________________________ 46 

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Figure 22: AFM image of a hexagonal graphene flake with wrinkle formation , buckling formation 

on MoS2 , AFM topographic image of an internal tear in graphene and Failure modes observed in 

molecular dynamics simulations. ___________________________________________________ 47 

Figure 23: The fracture of graphene under tensile load for armchair and zigzag configuration. ___ 48 

Figure 24: Representative MD snapshots of the fracture dynamics for the 2H-MoTe2 & 1T-MoTe2 

armchair and zigzag monolayers at 300K. ____________________________________________ 49 

Figure 25:  Calculated stress–strain curves for all TMD membranes subjected to 10K and 300K,.

 ______________________________________________________ Error! Bookmark not defined. 

Figure 26: Stress-strain response of armchair MoTe2 structure at different temperatures. _______ 50 

Figure 27: Nominal strain vs stress of graphene under uniaxial tensile test along the armchair 

direction at various temperatures. __________________________________________________ 50 

Figure 28: : Example Command line for atom.sk ______________________________________ 51 

Figure 29: Workflow of the default operating mode of atoms. ____________________________ 51 

Figure 30:Some examples of lattices that can be generated with Atomsk, as visualized with VESTA.

 _____________________________________________________________________________ 52 

Figure 31: Example of interatomic potential curve. _____________________________________ 53 

Figure 32: Comparison of the computational cost on a per-atom, per-timestep basis of various 

manybody potentials and several machine learning interatomic potentials implemented in 

LAMMPS. ____________________________________________________________________ 53 

Figure 33: Flowchart of MD Simulation. _____________________________________________ 55 

Figure 34: Screenshot of the main window of OVITO. __________________________________ 56 

Figure 35: Monolayer Graphene sheet representing a 2D material before and during initial uniaxial 

tension applying ________________________________________________________________ 57 

Figure 36 : Step by step procedure of LAMMPS simulation ______________________________ 56 

Figure 37: Local environment around atom Mo in the MoS2 hexagonal lattice with the Mo layer 

sandwiched by two S layers. Atoms S1, S2,and S3 are in the top group of the MoS2 layer. Atoms 

S4, S5,and S6 are in the bottom group of the MoS2 layer. Atom S1 is substituted by atom Se. Note 

that the bending of angles like θMoS1S6 is not considered in the SW potential, and a modification is 

necessary for LAMMPS to exclude this term in the three-body SW potential. Acta Mechanica 

Solida Sinica 32, 1 (2019) ________________________________________________________ 57 

Figure 38: Zigzag direction of 2D material. ___________________________________________ 63 

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Figure 39 : Armchair Direction of 2D material. ________________________________________ 63 

Figure 40: Graphene unit cell[140]. _________________________________________________ 64 

Figure 41: Graphene Sheet[142]. ___________________________________________________ 65 

Figure 42: Graphene  5*5 nm Sheet made in VESTA ___________________________________ 65 

Figure 3.23: MoS2 unit Cell[143]. __________________________________________________ 66 

Figure 44 : The crystal structure of monolayer MoS2 showing a layer of molybdenum atoms (blue) 

sandwiched between two layers of sulfur atoms (yellow)[145]. ___________________________ 67 

Figure 45 : MoS2  1.2*1.1nm, and 5.4*5 nm Sheets made in VESTA. _____________________ 67 

Figure 46: MoTe2 Unit cell [143] __________________________________________________ 68 

Figure 47 : The crystal structure of monolayer MoTe2 showing a layer of molybdenum atoms 

(black) sandwiched between two layers of sulfur atoms (red) [147]. _______________________ 69 

Figure 48 : Shows sheets of different sizes in follow order left to right, small to big and more 

significant 3.5*3.0 nm,7*6 nm and 30*30nm Sheets, respectively, the snapshot taken from VESTA.

 _____________________________________________________________________________ 70 

Figure 49 : (a)Uniaxial Stress on Graphene (b) Stress-strain curve for armchair and zigzag [142]. 71 

Figure 50 : Nominal strain vs stress of graphene under uniaxial tensile test along the armchair 

direction at various temperatures[148]. ______________________________________________ 72 

Figure 51: Variation in Young’s modulus of graphene with temperature under uniaxial tensile test 

along the armchair direction[148]. __________________________________________________ 72 

Figure 52 : Graphene comparison of Stress-Strain curve at 300K for armchair simulation. ( lit- 

Literature & Sim- Our Simulation) _________________________________________________ 73 

Figure 53: Graphene comparison of Stress-Strain curve at 600K for armchair simulation.( lit- 

Literature & Sim- Our Simulation) _________________________________________________ 73 

Figure 54: Graphene comparison of Stress-Strain curve at 900K for armchair simulation.( lit- 

Literature & Sim- Our Simulation) _________________________________________________ 74 

Figure 55: Graphene comparison of Stress-Strain curve at 1200K for armchair simulation. ( lit- 

Literature & Sim- Our Simulation. _________________________________________________ 74 

Figure 56: Graphene comparison of Stress-Strain curve at 1800K for armchair simulation. ( lit- 

Literature & Sim- Our Simulation). _________________________________________________ 75 

Figure 57: Graphene comparison of Stress-Strain curve at 2100K for armchair simulation.( lit- 

Literature & Sim- Our Simulation). _________________________________________________ 75 

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Figure 58: Stress-strain for single-layer 1H-MoS2 of dimension 100 × 100 ˚ A along the armchair 

and zigzag direction s[16]. ________________________________________________________ 76 

Figure 59: Stress-strain for single-layer 1K and 300K along the armchair.( lit- Literature & Sim- Our 

Simulation). ___________________________________________________________________ 76 

Figure 60: Stress-strain for single-layer comparison of 1K and 300K along the zigzag. ( lit- 

Literature & Sim- Our Simulation). _________________________________________________ 77 

Figure 61: Stress-strain for single-layer 2H-MoTe2 of dimension 100 × 100 ˚ along the armchair and 

zigzag directions[16]. ____________________________________________________________ 77 

Figure 62: Stress-strain for single-layer 1K and 300K along the armchair.( lit- Literature & Sim- Our 

Simulation). ___________________________________________________________________ 78 

Figure 63: Stress-strain for single-layer comparison of 1K and 300K along the zigzag. (lit- 

Literature & Sim- Our Simulation). _________________________________________________ 78 

Figure 64:Single layer of graphene with stress direction applied on for visualization. __________ 79 

Figure 65: The atomic configuration evolution during crack in Armchair direction at 300K. ____ 79 

Figure 66: Plane Stress-strain for single-layer Graphene for Armchair at 300K. ______________ 80 

Figure 67: The atomic configuration evolution during crack in Zigzag direction at 300K. ______ 80 

Figure 68: Plane Stress-strain for single-layer Graphene for Zigzag direction at 300K. _________ 81 

Figure 69: Single layer of MoS2 with uniaxial stress.  __________________________________ 81 

Figure 70: The atomic configuration evolution during crack in Armchair direction at 1K. ______ 82 

Figure 71: Plane Stress-strain for single-layer MoS2 for Armchair at 1K. ___________________ 82 

Figure 72: The atomic configuration evolution during crack in Zigzag direction at 1K. ________ 83 

Figure 73: Plane Stress-strain for single-layer MoS2 for Zigzag at 1K. _____________________ 83 

Figure 74:Single layer of MoTe2 with uniaxial stress. __________________________________ 84 

Figure 75: The atomic configuration evolution during crack in Armchair direction at 10K. _____ 84 

Figure 76 : The atomic configuration evolution during crack in Armchair direction at 300K. ____ 85 

Figure 77: Plane Stress-strain for single-layer dimension 2H-MoTe2 for Armchair at 10K and 300K.

 _____________________________________________________________________________ 85 

Figure 78: The atomic configuration evolution during crack in Zigzag direction at 10K. _______ 86 

Figure 79: The atomic configuration evolution during crack in Zigzag direction at 300K. ______ 86 

Figure 80: Plane Stress-strain for single-layer dimension 2H-MoTe2 for zigzag at 10K and 300K. 87 

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Figure 81: Plane Stress-strain for single-layer dimension 2H-MoTe2 for Armchair from 100K to 

600K. ________________________________________________________________________ 88 

Figure 82: Plane Stress-strain for single-layer dimension 2H-MoTe2 for Zigzag  from 100K to 

600K. ________________________________________________________________________ 89 

Figure 83: Elastic modulus at different temperatures for armchair and zigzag. _______________ 90 

Figure 84: Plane stress-strain for single-layer dimension 2H-MoTe2 armchair and zigzag at 300K. 91 

 

 

 

 

LIST OF TABLES 

 

 

Table 1. Family of 2D materials. 21 

Table 2: Summary of TMDC materials and properties 33 

Table 3: Electronic character of different layered TMDCs 36 

Table 4 : Graphene 2D Sheet lattice parameters  64 

Table 5: MoS2 2D sheet parameters 66 

Table 6: MoTe2  2D Sheet lattice parameters 68 

Table 7 : Mechanical properties of Armchair simulation at different temperatures. 88 

Table 8: Mechanical properties of Zigzag simulation at different temperatures. 89 

 

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NOMENCLATURE 

 

 

 

LAMMPS Large scale atomic/molecular massively parallel simulator  
TMDCs Transition metal dichalcogenides 

MD  Molecular Dynamics  

CVD Chemical vapor deposition 

AR  Armchair 

ZG Zigzag 

CPU Central processing unit 

GPU Graphics processing unit 

MoS2 Molybdenum sulfide 

MoTe2 Molybdenum ditelluride 

SEM  Scanning electron microscope 

AFM  Atomic force microscopy 

HEMTs High-electron-mobility Transistor 
NEMS Nanoelectromechanical systems 
TEM Transmission Electron Microscopy 
CWD Charge Density Wave 
MBE Molecular Beam Epitaxy 
LIB Lithium ion batteries 
NIB Sodium ion batteries 
MPI Message-passing library 
UTS Ultimate tensile stress 
Atomsk Atom, Molecule, Material Software Kit 
VESTA Visualization for electronic and structural analysis 

 
  
  

  

  

  

  
  
  

  

  

  

  
  
  
  

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Chapter 1 

INTRODUCTION 

 

1.1. INTRODUCTION TO THE RESEARCH 

 

The 2D materials are a novel class actively under research due to their extensive properties such as 

high conductance, tensile strength and mobility. Researchers are exploring more into these materials 

to find their potential usage in the industries such as electronics, composites, sensors and etc. The 

most eminent progress was the discovery of graphene, which has caused a revolutionary change. 

Graphene has attracted multiple researchers to investigate more about 2D Materials. The current 

technology also allows us to manipulate the properties as per requirement by adding new materials 

into such structures [1]. In addition, several other 2D materials are available in the literatures. These 

are silicene, Transition metal dichalcogenides (TMDs), Metal oxides, MXene and phosphorene [2].   

 

1.2. RESEARCH PROBLEM STATEMENT 

 

The procurement process of such materials is costly since they are not found naturally in nature. 

Additionally, handling such materials requires advanced lab facilities with sophisticated logistics and 

equipment requirements. Therefore, very few researchers have access to such materials to explore 

more about their properties. Theoretically, there is a need for alternative ways to extract more 

information about such products via simulation. Thus, it reduces the possibility of any waste or 

misusage of materials. Researchers can use intuition for such data before directly using such materials 

for any experimental purpose. Classical and Quantum physics use fundamental laws to describe the 

atomic motion resulting from a change in different parameters [3]. Large-scale Atomic/Molecular 

Massively Parallel Simulator (LAMMPS) is software that simulates atomic motion in terms of 

classical physics [4]. Lammps uses classical molecular dynamics simulations (MD), that aids in 

modeling fluids and solids' chemical and mechanical behavior. The accuracy of the work depends on 

the potential interatomic file, which contains the function of atomic positions and other properties 

[5]. Atom.sk [6] using or Vesta [7] is open source software used to create 2D atomic structures using 

the existing lattice parameters from the literature .

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1.3. OBJECTIVE OF THE STUDY  

 

This research focuses on the mechanical behavior of the range of 2D materials available in the 

industry. The fundamentals of 2D materials, their categories, and classification were covered, along 

with the naming convention of different configurations. Preparation of such materials can be as 

simple as using a scotch tape [8] to extract from bulk materials to complex processes like chemical 

vapor deposition (CVD) [9]. The prime ambition is to understand how the MD simulations work 

along with the supplements. The objective includes to learn how classical mechanics works and  

implements all three of newton’s laws [10]. Once the structures are made using the respective 

software as mentioned earlier, the primary assignment is to run the LAMMPS code. We successfully 

learn to run uniaxial tensile loading on the material. 2D materials, in general, are exposed to static 

and dynamic loading, which causes mechanical deformations like wrinkle [11], buckle [12], tear [13] 

and fracture behavior [14]. The fracture mechanism of each material is crucial for research to 

understand the fracture pattern of different materials to prevet this unprecedented accidents by 

predicting the ultimate tensile stress and elastic modulus. LAMMPS simulation allows researchers 

to study the fracture mechanics of 2D materials qualitatively and quantitatively. The results help 

model fracture behavior for different materials and compare the data with other materials regarding 

strength, flexibility and rigidity. Ovito [15] visualizer is helps to observe the fracture mechanism. 

Therfeore, we can identify the nature of the crack and the fracture strain at which the materials fail. 

Processing the quanitiative data produces stress-strain relationships we are invaluable information 

for designers. Researchers can use these reports to choose and compare between materials while 

designing a project or protoype.  

 

1.4. SCOPES AND LIMITATIONS 

 

MD simulation on materials allow characterizing the properties of materials in case of different 

conditions. The variation in conditions could be in temperature, defects, and doping. The material 

structure can be re-made into several options, and multiple simulations can be run upon it to 

understand how the materials behave in case of variations in parameters. The simulation results give 

results close to the accurate values. The results aid the researcher in understanding more about the 

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Chapter 1 Introduction  

 

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materials and implementing them in different applications—the main drawback being the need for 

high computation power to run the simulations. The simulation uses Central Processing Unit (CPU) 

cores to run the calculations. Additionally, the simulation can also be run in a Graphics processing 

unit (GPU), which requires extra configuration. The simulations can be run with parallel cores to 

speed up the process to get faster results. The initial investment of CPUs with such a configuration 

is quite expensive and consumes much electricity to give the output. Simulation time largely depends 

on the size of the sheet of material. A large sheet increases simulation time drastically; therefore, it 

takes several days to get a set of complete data sets. Furthermore, the CPU heats for continuous 

usage. Therefore, a code has to be prepared to stop the simulation when the ambient temperature 

surpasses the critical point of the material. Negligence in such a matter can end with a computer's 

motherboard melting, and fire can get ignited. 

 

1.5. METHODOLOGY  

 

The simulation process requires three files at once to initiate the process—the structural file, which 

contains the three coordinates for all the atoms in a sheet of material. Then the potential file contains 

the potential interatomic relationship. This file contains the function of relationships of how atoms 

behave when bought closer or taken away. Lastly, the instructions as a code written to command the 

LAMMPS simulator to carry out the task. The CPU process all the data using the governing equations 

to calculate stress-strain relationships.  

 

1.6. CONTRIBUTION 

 

The novelty of this work shall focus on the temperature-dependent fracture of TMDs, with a 

particular emphasis on molybdenum ditelluride (MoTe2). Each simulation was done with a varying 

temperature at 100K intervals from 100K to 600K. The simulation was conducted in both AR and 

ZG configurations for varying temperatures. The results were plotted together on a graph with the 

aid of Origin to compare the results. A general trend was discovered from the observation of 

quantitative data regarding the strength of the materials with varying temperatures and 

configurations. The code developed can be used for other thirty-four TMDCs available in the 



Chapter 1 Introduction  

 

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literature [16]. The Stress-Strain relationships can be calculated for this range of materials in a similar 

pattern in a similar pattern. 

 

1.7. ARRANGMNET OF CHAPTERS 

 

In this thesis, we shall further discuss the fundamentals and basic definitions in the 2D materials 

industry, where we will emphasize graphene and TMDs such as molybdenum sulfide (MoS2) and 

molybdenum ditelluride (MoTe2). In the following chapter, we will focus on how MD simulations 

work with the aid of LAMMPS and discuss in-depth the code and the supplement information 

required for the simulation to be complete. Here, we shall discuss how we resolved different 

computational and configuration-related issues to get more sensible data in line with the literature. 

Furthermore, we portray our results and discussion in a detailed manner where all the qualitative and 

quantitative results are compared. Lastly, we discuss our findings and how the results could be close 

to more experimental data. In the end, we talk about the potential of this industry and the possibilities 

for future work.
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Chapter 2 

LITERATURE REVIEW 

 

2.1.INTRODUCTION 

 

In the following chapters, different sub-sections will be discussed. In the sub-section, we introduce 

the rise of 2D materials. Materials have a fundamental parameter for all technological advancements 

through all ages. The sub-categories of 2D materials contain the key definitions of such materials and 

sample materials available in the literature. In the next section, we talk about graphene, which is made 

up of carbon atoms. The robustness of such materials and their dynamic capabilities is notable for their 

popularity. The contribution of these materials is widespread in industry for the decade. Besides 

graphene, the addition of Transition metal dichalcogenides (TMDCs) in the electronics industry due 

to their unique properties. Amongst the wide range of TMDCs, we focus solely on molybdenum 

disulfide (MoS2) and molybdenum telluride MoTe2. The objective of the section is to cover the state 

of the art of such materials to give an overview of all the possibilities. The current research also sheds 

light upon the progression in this field of science. The industry demands to learn more about the 

mechanical and electrical properties to find their best suitable application. 

 

2.2. TWO-DIMENSIONAL MATERIALS. 

 

Advancement of different civilizations depends on developing materials and some metals in particular 

are so influential that naming of several centuries begin with them. The discovery of copper, bronze 

and iron is revolutionary in history. We are undergoing another revolution of technology known as the 

age of nanotechnology. The potential of such materials is much beyond their visual capabilities. 

Researchers are continuously working on novel materials by playing with different chemical 

compositions and processes. The advent of potential technologies to visualize these materials on a 

nano-scale have broadened the possibility for more research. The dimensionality is a key parameter 

that defines its properties [17]. 

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In nanotechnology, carbon nanostructures pioneering since the beginning of the invention of graphene 

by Nobel Laureates Geim and Novoselov [18]. Theoretical investigation into graphene shows its 

robust characteristic from mechanical and electronic perspectives [19]. The discovery of graphene 

leads to the exploration of other 2D materials, which also have many possibilities. Apart from 

graphene, there are other 2D materials such as metal oxides and transition metal dichalcogenides. The 

unique properties adds more varieties to the comprehensive list of superconductors, semi-conductors, 

semi-metals and insulators for the electronics industry [20].  Table 1 lists all the possible 2D materials 

enlisted in the literature. 

 

                                                 Table 1. Family of 2D materials. 

Graphene 

Family 

Graphene h-BN BCN Fluoro-

graphene 

Graphene 

Oxide 

2D 

chalcogenides 

MoS2 , WSe2 Semi-conducting 

dichalogenides: 

MoTe2 , ZrSe2 

Metallic dichalogenides : 

NbSe2, NbS2 

Layered Semiconductors: 

GaSe, GaTe 

2D oxides Micas, 

BSCCO 

MoO2, WO3 Perovskite: 

LaNb2O2 

Hydroxides: Ni(OH)2 

Layered 

Cu-oxides 

TiO2, MnO2 Others. 

 

2D materials characterization is 1-atom thick sheets that detaches from the bulk mass as layers stand 

without substrate. Layers up to 10 atoms thick are often kept under consideration as 2D materials [17]. 

2D materials have somewhat large lateral dimensions in contrast to their thickness [21]. The lateral to 

transverse ratio is quite large. In 2D material, adjacent atoms in the same plane connects via covalent 

bonding, while layers of 2D materials holds together by comparatively weak interlayer Van Der Waals 

coupling [22].  

2D materials have recently drawn much attention in the science community because of their promising 

electrical, mechanical, physical,  substance, and optical properties [23]. The 2D materials have high 

Young's modulus, ultra-low weight, high strength, high anisotropy, and outstanding carrier mobility 

between the in-plane and out-of-plane mechanical properties. Furthermore, a Weak Van Der Waals 

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connection between layers permits them to slide effectively with the application of shear stress, 

resulting in a change of lubrication properties. In order to ensure the best use of the novel mechanical 

and mechanoelectrical transduction properties. 2D materials utilization is a wide-going application, 

including adaptable hardware, strain sensors, nanogenerators, and imaginative nanoelectromechanical 

frameworks (NEMS) [22]. 

 

Figure 1 : Schematic diagram of a hetero-structured 2D material. Reproduced from Geim, A.K., et 

al., 2013. Van der Waals heterostructures. Nature 499, 419–425. 

 

 

 

 

 

 

 

 

 

 

 



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Figure 2: (a) Schematic of Rippled graphene (b) SEM images of wrinkled graphene and (c) SEM 

images of crumpled graphene. Nature 446 (2007) 60–63, Nat. Nano 4(2009) 

 

Figure 3: AFM images of the (a) 2H-MoTe2 flake that covers tens of holes. Inset shows its crystal 

structure defined by the SHG experiment (b) 1T’-MoTe2 flake that covers tens of holes. Inset shows 

its crystal structure defined by the SHG experiment. Nano Lett. 2019, 19, 2 

 

 

 

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2.3. GRAPHENE 

 

Research in 2D material is ramping ever since the identification of graphene in 2004. A simple 

adhesive tape peels off layer after layer of graphene from graphite [24]. Graphene is a carbon allotrope 

of a single layer of sp2 hybridized carbon in a 2D honeycomb lattice structure. In simpler terms, a 

single layer of isolated graphite is graphene. Every atom in graphene is bonds with the three nearest 

atoms by σ-bond and contributes one atom to the conduction band. The same type of bond is also 

available in carbon nanotubes and polycyclic aromatic hydrocarbon, partially in fullerenes and glassy 

carbons [25][26]. Conduction bands leads to graphene's one of the most valuable properties making it 

a zero-overlap semimetal [24]. Graphene conducts both electricity and heat along its plane very 

efficiently.  

Figure 4: Mother of all graphitic forms. Graphene is a 2D building material for carbon materials of 

all other dimensionalities. It can be wrapped up into 0D buckyballs, rolled into 1D nanotubes or 

stacked into 3D graphite [24]. Nat. Mater. 

 

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Graphene is an essential and valuable nanomaterial because of its outstandingly high  

rigidity, electrical conductivity, straightforwardness, and being the slenderest two-layered material 

[27]. Interest in innovative work of graphene encompasses from semiconductors, gadgets and  electric 

batteries to composites.  

 

In theoretical prediction, the 2D material family expands out to more than 1,000 individuals [28]. 

Many of these materials undergo synthesis experimentally [29]. 2D materials are sorted into four 

types:  

(i) Graphene family  

(ii) Chalcogenides  

(iii) 2D oxides  

(iv) Xenes  

as displayed by their nuclear designs, shown in Figure 5 .  

 

Figure 5: The graphene family: (a) graphene (gray atom represents C), (b) CX (X = H, F, Cl; gray 

and blue atoms represent C and X, respectively), (c) graphene (α-graphene, β-graphene, γ-graphene 

and 6,6,12-graphyne from left to right, top to bottom; gray atom represents C), (d) h-BN (red and blue 

atoms represent B and N, respectively), (e) BCN (reproduced from Ref. [30]; red, gray and blue atoms 

represent B, C and N, respectively), (f) SixC1−x(x = 2/10, 5/6, 2/6, 14/18 from left to right, top to 

bottom; gray and yellow atoms represent C and Si, respectively) (reproduced from Ref. [31]), (g) TiC 

(reproduced from Ref. [32]; red and blue atoms represent C and Ti, respectively) [33]. 

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Figure 6:  (a) Large graphene crystal prepared on an oxidized Si wafer by the scotch tape technique. 

[Courtesy of Graphene Industries Ltd.] (b) Left panel: Suspension of microcrystals obtained by 

ultrasound cleavage of graphite in chloroform. Right panel: Such suspensions can be printed on 

various substrates. The resulting films are robust and remain highly conductive even if folded. 

[Courtesy of R. Nair, University of Manchester] Nat. Mater. 8, 203 (2009) 

Figure 5 (a–g), the family of graphene includes its variants made up of various hybridized carbon atoms 

or heterogeneous components. The saturated carbon atoms (sp3 hybridization) bind with non-carbon 

elements in fluoro-graphene, chloro-graphene, and graphene oxide, generating an alternating pattern. 

The network of sp- and sp2-hybridized carbon atoms that make up carbon allotropes (such as graphene) 

is made up of sp- and sp2-hybridized carbon atoms. The graphene structure can be thought of as 

acetylene chains replacing incomplete aromatic C–C connections in graphene. α-, β-, γ- and 6,6,12-

graphyne are produced by complete, 2/3, 1/3, and 5/12 substitutions, respectively (Figure 5 c)[34][35]. 

Graphene structures have fascinating semiconducting properties that make them feasible for electronic 

devices. Their inherent nanopores and structures make them potential candidates for gas separation, 

filtration, and water desalination [36][37]. 

 Two or more elements can replace the initial carbon atoms to generate more complex layered 

structures, such as h-BN (Figure 5 d), boron–carbon–nitrogen (BCN) (Figure 5 e) [30], and SixC1x 

(Figure 5 f) [31], in a similar way to graphene. A 2D material having a tetragonal configuration, like 

the similar hexagonal structure above, is found to be extremely stable. In the side view, TiC with p(pi)–

d(pi) bound (Figure 5 g) is buckled into a zigzag configuration. It has anisotropic features because of 

its unique structure. 

 

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Figure 7: Although Graphene (left) and Hexagonal Boron Nitride (right) both are 2D and both have 

hexagonal lattice structure, they possess very different physical properties. Hexagonal boron nitride 

is a wide-bandgap insulator while graphene is an excellent electrical conductor. 

 

Graphene is optically transparent, absorbing just 2% of transmitted light and has the greatest tensile 

strength. Even the weight of a football might be supported by a single monolayer of graphene that is 

only 0.3 nm thick [38]. Hexagonal boron nitride (h-BN) is an isomorph (similar crystallographic 

appearance), but instead of carbon, it comprises boron and nitrogen atoms. It is a wide-bandgap 

insulator, unlike graphene, which is an excellent conductor [39]. 

 

 

 

Figure 8: (a) Graphene nanoribbons of sub-10-nm scale exhibit the transistors action with large on-

off ratios. (b) graphene-based HEMTs. (c) Graphene-based NEMS. (d) Ready to use: Graphene 

membranes provide an ideal support for TEM. Science 324, 1530 (2009). 

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The application of graphene in different markets is depended on the production rate of such materials. 

Previously, the conventional techniques were used to extract small amount of graphene at time. 

Currently, more advanced techniques are in practice to prepare graphene in multiple shapes and sizes. 

There is a big challenge in the optimization of the quality of graphene and the method of production. 

Such processes are as follows:  

 

(i) Liquid phase and thermal exfoliation 

(ii) Chemical vapour deposition 

(iii) Synthesis on SiC 

 

 

 

 

Figure 9: There are several methods of mass-production of graphene, which allow a wide choice in 

terms of size, quality and price for any particular application. Nature 490, 7419 (2012). 

  

 

 

 

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2.4. TRANSITION METAL DICHALCOGENIDE 

 

The transitional metal dichalcogenide (TMDC) MX2 represents a class of developing 2D material 

known as chalcogenides. MX2 has two layers of chalcogen atoms X sandwiched between two layers 

of transitional metal atoms M (Mo, W, Nb, Ta) and chalcogen atoms X (S, Se, Te). Figure 10 shows the 

all the elements that can react together to form a TMCS compound.  

 

 

 

Figure 10: There are around 40 distinct stacked TMD compounds. In the periodic chart, the transition 

metals and three chalcogen elements that primarily crystallize in such layered structures are 

indicated. Nature Chemistry 5, (2013). 

 

MX2 is commonly divided into two phases: 2H and 1T [40][41][42]. Till now, there is much research 

into the 2H phases. In Figure 10 the MX2 (M = Mo, Nb, W, Ta; X = S, Se, Te) tends to be in the 2H 

phase in equilibrium, whereas MX2 (M = Zr, Hf; X = S, Se) tends to be in the 1T phase [78][79]. 

Under certain conditions, the transition from 2H to 1T phases can occur [40][41][42].  

 

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Figure 11: Structure of TMDs. Atomic structure of single layers of transition metal dichalcogenides 

(TMDCs) in their trigonal prismatic (2H), distorted octahedral (1T) and dimerized (1Tʹ) phases. 

Lattice vectors and the stacking of atomic planes are indicated.  

TMDCs are two-dimensional semiconductor materials with distinct mechanical, electrical and optical 

characteristics. For the applications of advanced semiconductor devices, the materials can substitute 

for graphene (metallic substance) and hexagonal boron nitride (hBN, insulator). TMDC growth 

techniques is a focus in this section. TMDCs require a different approach because of  the various 

chemicals and growth processes. TMDCs have a unique property of charge density wave phases 

supported by the fermi momentum theory [43]. A slight distortion causes the modulation of the 

electronic charge density. The phenomena of CWD depend on the crystalline phase and the chemical 

composition of the material. A functional relationship is derived between the temperature and pressure, 

which is shown in the Figure 12. 

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In addition, TMDC doping for customizing characteristics by adding alien materials into the structure. 

This affects the mobility, bandgap and contact resistance of the impure material. Furthermore, doping 

can alter the magnetic characteristics too [44]. Figure 13 shows how doping affects the conductivity 

of TMDCs. 

Figure 12: Temperature–pressure phase diagram of 1T TaS2 showing various charge density wave 

(CDW) phases. The deformation patterns corresponding to the different phases are shown. 

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Figure 13: Phase diagram of superconductivity in electrostatically and chemically doped 2H MoS2. 

 

 

 

Figure 14: Molybdenum disulphide (MoS2) in the left. Tungsten ditelluride (WTe2) in the right. Both 

are transition metal dichalcogenides with a two-dimensional structure. WTe2 tends to adopt the 

metallic 1T phase , whereas MoS2 favours the semiconducting 2H. 

The best thing about these materials is that they are not just remarkable for LIBs; they are in usage as 

an electrode for Na-ion batteries (NIBs), an excellent cost-effective alternative to LIBs [45]. TMDCs 

based on metal sulfides, such as MoS2,  react with Li atoms to create lithium sulfide, which causes 

phase changes in electrode systems [46]. Yang et al. [45] used first-principle simulations to study the 

potential of different TMDCs when used as NIB electrode material. The findings indicate low energy 

barriers for Na surface diffusion in TMDCs and notable phase transitions in several transition metal 

sulfides. MoS2 and WSe2 are the most commonly investigated TMDCs for LIB electrodes. Su et al. 

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[47] were among the first to reveal MoS2's excellent performance capabilities as a NIB anode with 

ultrathin designs. Similar to graphene, utilization of defective  MoS2 form with antisites, 

vacancies and grain boundaries increases its specific capacity [48].  

 

The Li adsorption increase is principally responsible for the performance enhancement of defective 

MoS2. Chen et al. [49] created a tubular MoS2 structure that connects with carbon nanotubes in 

2016(CNTs). CNT is used extensively in this structure to address the issue of structural deterioration 

in MoS2 as a result of conversion processes, resulting in an anode with long cycle life. TMDCs have 

a fundamental structural and chemical stability limitation, making them rely on other composite 

materials to use their electrode capabilities entirely [50]. 

 

                                Table 2: Summary of TMDC materials and properties 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 
-S2 -Se2 -Te2 

 
Electronic Properties 

Nb Metal; superconducting; CDW Metal; superconducting; 

CDW 

Metal 

Ta Metal; superconducting; CD Metal; superconducting; 

CDW 

Metal 

Mo Semiconducting 1L: 1.8 eV Bulk: 

1.2 eV 

Semiconducting 1L: 

1.5 eV Bulk: 1.1 eV 

Semiconducting 

1L: 1.1 eV 

Bulk: 1.0 eV 

W Semiconducting 1L: 2.1 eV 1L: 

1.9 eV Bulk: 1.4 eV 

Semiconducting 1L: 

1.7 eV Bulk: 1.2 eV 

Semiconducting 

1L: 1.1 eV 

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TMDCs crystals are generally from the extraction and filtration of natural minerals. These minerals 

contain bulk amounts of TMDCs as large crystal structures. These natural crystals or synthetic crystals 

are source of thin flakes of TMDCs. Sheets of TMDCs is a output of mechanical peel-off using sticky 

tapes [51]. This process help researchers to understand more about the materials; however, this method 

is not scalable for mass production. Alternatively, liquid-phase exfoliation using an organic solvent is 

a well-known technique that makes the thickness of the flakes controlable [52]. These are conventional 

method in usage for early-stage investigation. Figure 16 portrays scalable methods to produce 

adequate amounts for mass usage. Figure 16 (a) shows molecular beam epitaxy (MBE) which uses 

ultra-thin vacuum chambers to collect the deposition on a hot substrate [53]. The highest quality 

TMDCs are is due to chemical vapor deposition (CVD), illustrated in 16 (b). The set-up is much 

simpler than MBE and the overall cost is much less in this process. The final method is similar to CVD 

but uses MOCVD's metal-organic gas phases [54]. Figure 16 (c) shows how this method works. 

 

Figure 15: Examples of synthesis of 2D TMDC lateral hetero-structures. (a) High-angle annular 

dark-field scanning transmission electron microscopy image of the lateral hetero-structure formed 

between MoSe2 and WSe2. (b) Optical image of a p–n junction based on a MoS2 /WSe2. 

 

 

 

 

 

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Figure 16: Growth methods for the synthesis of ultrathin TMDCs. (a) In molecular beam epitaxy. (b) 

Chemical vapor deposition (c) Metal–organic chemical vapour deposition. Nature Reviews Materials 

2, 8 (2017) 

 

 

 

 

 

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The electronic properties of these materials are essential for applications. In general, the dissimilarity 

of the electronic properties of TMDCs is result of variation in band structure with bulk to monolayer 

transitions [55]. DFT [56] calculations can be applicable  to calculate the energy gap of  TMDCs on 

the basis of well-known Hohenberg and Kohn theorems. DFT [56] furnished a legitimate foundation 

for the improvement of computational techniques for obtaining records approximately the energetics 

and structure properties of (atoms and) molecules at a much lower cost than traditional wave function 

techniques[56]. It is a method of theoretical investigation of solids [57]. Using ab initio DFT 

simulations, this bandgap alteration is possible just by applying mechanical stresses [58]. While the 

electronic properties of graphene is unchanagble due to tensile stress, TMDCs are sensitive to both 

tensile and shear stress. In addition, much less strain is essential to vary the bandgap of TMDCs 

compared to graphene. Mechanical stress decreases the bandgap of semiconductor TMDCs, leading 

to a direct to the indirect bandgap thus causing a semiconductor to metal transition. 

 

                             Table 3: Electronic character of different layered TMDCs 

Group M X Properties 

4 Ti, Hf, Zr S, Se, Te Diamagnetic. Semiconducting (Eg = 0.2~2 eV).  

5 V, Nb, Ta S, Se, Te Superconducting. Narrow band metals (ρ ~10–4 

Ω.cm) or semimetals. Charge density wave 

(CDW). Paramagnetic, antiferromagnetic, or 

diamagnetic 

6 Mo, W S, Se, Te Sulfides and selenides are semiconducting 

(Eg ~1 eV). Tellurides are semimetallic (ρ ~10–

3Ω cm). Diamagnetic. 

7 Tc, Re S, Se, Te Diamagnetic. Small-gap semiconductors.. 

10 Pd, Pt S, Se, Te Sulfides and selenides are semiconducting 

(Eg = 0.4eV) and diamagnetic. Tellurides are 

metallic and paramagnetic. PdTe2 is 

superconducting. 

 

 

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TMDCs monolayer can absorb rays in the near-infrared and visible spectra region. Its primary 

determination by a direct transition between the valance and the conduction band that states around k 

and k’ points[59]–[62]. When there is no excitonic effect in the case of 2D, it is often indicates a step 

function. A spectrum originating from the energy-independent joint density of states and transition 

matrix elements near parabolic band edges. Prediction of very large exciton binding energies is 

common by theoretical studies [38][42], and recent observations verify them based on optical 

spectroscopy [68]–[71] and scanning tunneling spectroscopy[54][55].   

Apart from these, 2D TMDCs also possess higher-order excitonic quasiparticles. In the case of doping 

monolayer of TMDCs trions (bound state of two electrons and one hole or two holes and one electron) 

is possible [69], [73]. Thus promising possibilities of trions application for room-temperature electrical 

transport of absorbed light energy [74] and creating high-temperature and high-density quantum 

coherent states of excitons [75]. TMDC monolayers exhibit electronic characteristics ranging between 

superconducting and semiconducting depending on their chemical composition. A direct bandgap in 

the 1–2 eV region, group-4 TMDC monolayers (e.g., WS2, MoS2, MoSe2, and WSe2) display 

semiconductor behavior. An indirect bandgap exists in TMDC bilayers and multilayers.  

 

 

 Figure 17: Theoretical bandgap for various MX2 monolayers as a function of lattice constant 

changed by uniform isotropic strain ranging from 5% to 5%. Each monolayer's equilibrium lattice 

constant is indicated by a red arrow. 

 

 

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TMDC monolayers are presently being studied in photonics, spintronics and valleytronics 

[76][77][60]. In addition, circularly polarized  light with orthogonal polarizations can treat different 

valleys individually [76][78].  Furthermore, because TMDC monolayers lack surface dangling bonds, 

they make vertical heterostructures without lattice matching. The edges of TMDC nanoribbons can 

have intriguing qualities like increased catalytic activity [79]. Therefore, various applications like dye-

sensitized solar cells [80] or robust electrocatalysis, which might be helpful for hydrogen 

production[81]. Edgy topology, Quantum confinement and electrical interaction between edges for 

very narrow nanoribbons [40] are three main principles that explain the dynamic behaviors owing to 

edges. 

 

Photonics applications: The observations of the Purcell effect, coupled exciton–polaritons, lasing in 

2D TMDC optical cavities, and single-photon emitters have opened new opportunities for their 

photonic applications and development.  Characteristics like tough light-matter interactions that 

initiate from the strong excitonic effects in 2D TMDCs are a crucial feature of these exciting 

phenomena [82]. 

 

Superconductivity: In their phase diagram, all bulk TMDCs with a charge density wave (CDW) [83] 

also display superconductivity. There are indeed two phenomena. Two-phase can either coexist or 

compete. In TMDCs, the superconducting phase can be either inherent or prompt by chemical doping, 

electrostatic doping or applied pressure[84].    

 

Mobility engineering: The mean free path of charge carriers, spin or valley determines the 

applicability of 2D materials for applications established on quantum transport. In this the charge 

carrier mobility determines the suitability of application of the charge carriers as they are directly 

related to the mobility of the carriers. Although theoretically predicted principles for the charge-carrier 

mobility for 2D TMDCs [85]–[87] are very promising, in practice, the mobility is hindered by disorder 

and scattering sources. 

 

 

 

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2.5. MOLYBDENUM SULFIDE 

 

Molybdenum disulfide (MoS2) is a TMDC with honeycomb-shaped lattice[62]. Molybdenum 

disulfide (MoS2) has a layered hexagonal arrangement composed of covalently bonded S and Mo 

atoms. A plane of Mo atoms is covalently inserted between two planes of S atoms in an intercalating 

trigonal-prismatic pattern. In Bulk MoS2, S-Mo-S layers attach through Van der Waals forces resulting 

in a bandgap of 1.8eV [88].  

Comparing with graphene, MoS2 is more resilient to buckling due to a greater bending modulus by a 

factor of seven [89]. Mechanical property verification of MoS2 via investgation using density 

functional theory (DFT) [90], experiments [91] and reactive potentials such as reactive empirical 

bond-order (REBO) [90], [92], [93]  and ReaxFF [94], [95]. Literature shows that it a has high Young's 

modulus of about 0.2 TPa and the fracture stress beyond 10 GPa.  

Molecular dynamic (Lammps) simulation reported that for a single layer MoS2 the young’s modulus 

equals 152.8 GPa in the armchair directions. In addition, the fracture strain and fractures tress are 

observed to be 0.131 and 13.89 GPa, respectively [96].  

Temperature, layer number and stacking order of multiple layers have effect on the stress-strain curve 

and elastic properties. For example, it has been observed that Elastic constants, fracture strain and 

fracture stress of single layer structures decrease with the temperature rise. However, the increased 

layer number has minimal effect on the stiffness of the multilayer [96].  

 

 

Figure 18: (a) Optical microscopy image of monolayer MoS2. (b) AFM image of monolayer MoS2(c) 

SEM image of MoS2 powder. Small Methods 11, 2 (2018). 

 

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From classical molecular dynamics simulations (Lammps) on the tensile response of the 2H- MoS2 

monolayer in an armchair (X-direction) and zigzag (Y-direction) directions. At a temperature of 300 

K using the ReaxFF force field. In case of  the armchair configuration, the fracture starts at a tensile 

stress of 25.5% and the specimens fail at 27%. For a zigzag configuration, the corresponding values 

are 24.6% and 28.9%, respectively [129]. 

Classical molecular dynamics simulations (Lammps) were used to observe the single-layer fracture 

mechanics of MoS2. It turns out that for a flawless single-layer MoS2 (crack-free and non-porous), the 

fracture classification is a brittle fracture[97]. Bonds in the armchair direction have greater resistance 

to crack transmission than in the zigzag direction.[97].  

Temperature affects the mechanical properties of samples with cracks and pores. As an effect of 

increasing temperature, both failure stress and strain are weakened. 

MD (Lammps) simulations of the failure mechanism of armchair and zigzag cracks in MoS2 monolayer 

sheets under mixed fracture modes. Modes I and II anticipate that both chair and zigzag cracks 

preferentially and disseminate along a zigzag surface, similar to graphene [14]. 

Strain rate, size, and chirality also affect the young's modulus and thermal conductivity of a single 

layer of MoS2. From classical molecular dynamics simulations (Lammps), the elastic modulus is 

affected by both the chirality and the width of a single  MoS2 layer [98].  

The modulus of elasticity decrease with decreasing width for both the zigzag and armchair single layer 

MoS2. Although this differs from the size-dependent trend observation[99], it is similar to the results 

found in graphene nanoribbons[100]. In addition, the relative thermal conductivity of the single-layer 

armchair MoS2 at 300K decreases with increasing strain rate[98]. 

 

The defect and grain boundary influence the mechanical properties of mono- or polycrystalline MoS2. 

Classical molecular dynamics (MD) simulation (LAMMPS) shows a lower tensile strength of 

polycrystalline MoS2, suggesting that GBs, vacancy as well as oxygen doping significantly degrade 

the mechanical properties of MoS2 [101].  

 

 

 

 

 

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2.6. MOLYBDENUM DITELLURIDE 

 

Molybdenum (IV) telluride, also known as molybdenum ditelluride or simply molybdenum telluride. 

Molybdenum and tellurium compound with the formula MoTe2, equals 27.32 percent molybdenum 

and 72.68 percent tellurium by mass. It can form two-dimensional sheets that can be broken down into 

transparent and flexible monolayers. It is a semiconductor with the ability to glow. It belongs to the 

transition metal dichalcogenides family of materials [102]. 

 

MoTe2 is black when in its powdered form [103]. Sticky tape peels off very thin MoTe2 crystals. Red 

light may pass through them when they are thin, roughly 500 nm thick. Even the thinnest layers have 

the potential to be orange or translucent. Wavelengths longer than 6720 transmits and shorter 

wavelengths severely experience resistance. An absorption edge appears in the spectrum. At 77 K, this 

edge becomes 6465. This is a deep red color [104].  

 

MoTe2 is found in three crystalline forms with layered structures that are quite similar: hexagonal (2H-

MoTe2), monoclinic (1T-MoTe2), and orthorhombic' (1T'-MoTe2). It crystallizes in the hexagonal 

system at ambient temperature, analogous to molybdenum disulfide [105]. Flat crystals are platy 

crystals [106]. MoTe2 has a specific gravity of 7.78 gcm3 with unit cell sizes of a=3.519 c=13.964 

[105]. In a trigonal prism, each molybdenum atom is surrounded by six tellurium atoms, with a spacing 

of 2.73 between the Mo and Te atoms. [105] Molybdenum sublayers are sandwiched between two 

sublayers of tellurium atoms, and the three-layer structure is then stacked [107]. Each layer has a 

thickness of 6.97 mm [104]. Two tellurium atoms in the same sublayer subtend an angle of 80.7° 

within this layer. At the molybdenum atom, the tellurium atoms on one sublayer lie exactly above 

those on the lower sublayer, forming an angle of 83.1°. 136.0° is the other Te-Mo-Te angle across 

sublayers. Within a sublayer, the spacing between molybdenum atoms is 3.518. The spacing between 

tellurium atoms in a sublayer is the same as this. 3.60 is the distance between a tellurium atom in one 

sublayer and the atom in the other [108]. Only the van der Waals force holds the layers together [109]. 

The tellurium atoms are 3.95 atoms apart throughout the strata [108]. The centre of a triangle of 

tellurium atoms on the top of the layer below is align with the tellurium atom at the bottom of one 

layer. As a result, the layers are in two distinct places [108]. The crystal is readily split on the plane 

between the three-layer sheets [107].The sizes alter with temperature, with a=3.492 at 100 K and 3.53 

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at 400 K. Thermal expansion causes “c” to vary from 13.67 to 14.32 in the same range [107]. 2H-

MoTe2 is another name for the hexagonal form, where "H" refers to hexagonal and "2" indicates that 

the layers are in two separate places. MoTe2 crystallizes in the monoclinic 1T form (β–MoTe2) at 

temperatures over 900 °C, with space group P21/m and unit cell sizes of “a=6.33”, “b=3.469”, and 

“c=13.86:”, with an angle of 93°55′. Rod-shaped crystals are in the high-temperature form. This 

polymorph's density is 7.5 gcm3, whereas it normally 7.67 gcm3. Around the molybdenum atoms, 

tellurium atoms create a distorted octahedron [106]. Rapid cooling can bring this high-temperature 

form, known as β–MoTe2, down to room temperature [110]. MoTe2 may live below 500 °C in this 

metastable form [111]. The crystal shape of metastable β– MoTe2 transforms to orthorhombic when it 

is cooled below 20 °C. The monoclinic angle c moves to 90°. This shape is known β' or, more 

misleadingly, Td [112].  

 

The temperature necessary to transition from α- to β-MoTe2 is 820 °C, however, if Te is lowered by 

5%, the required transition temperature rises to 880 °C [111]. According to K. Ueno and K. 

Fukushima, when the form heats in a low or high vacuum, it oxidizes to create MoO2 and no reversible 

phase changes occur [113]. 

Figure 19: Optical image of a MoTe2 single crystalline flake, after mechanical exfoliation, used for 

Raman spectroscopy in conjunction with atomic force microscopy. ACS Nano 40 (2020). 

 

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In nanoindentation, biaxial deformation of suspended membranes is commonly utilize to study the 

elastic characteristics of structurally isotropic two-dimensional (2D) materials. However, in the case 

of biaxial deformation, the elastic characteristics and the fracture mechanics of anisotropic 2D 

materials remain entirely unknown. MoTe2 exhibits polymorphic behavior having isotropic (2H) and 

anisotropic (1T′ and Td) phases, making it an ideal single-stoichiometric material system for studying 

these essential concerns. Using a combination of temperature-variant nanoindentation and first-

principles computations, we present the elastic properties and fracture behaviors of biaxially 

deformed, polymorphic MoTe2 [114]. 

A tensile strain of 0.2 percent brings the 2H-1T′ phase transition temperature of MoTe2 down to 

ambient temperature. A substantial temperature-stress coefficient, which derives from a huge volume 

change and negligible latent heat, enables first-order SM transition, enhancing conductance by 10,000 

times [115]. 

 

 

 

 

 

 

 

 

 

 

 

 

 

Figure 20: Applications of MoTe2 hetero-phase homojunctions in electronic devices. (a) Optical 

microscope image and (b) transfer characteristics of a coplanar contacted 1T0–2H-MoTe2 transistor  

(c) schematic diagram and (d) signal gains of a hetero-phase MoTe2 inverter, Reprinted with 

permission from 2019 Springer Nature; (e) SEM images and (f) I–V characteristics of a vertical 

MoTe2 RRAM device, Reprinted with permission from 2018 Springer Nature; (g) schematic diagram, 

(h) measured strain curves, and (i) strain-induced operation of a ferroelectric strain MoTe2 FET, 

Reprinted with permission from  2019 Springer.  

 

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The effective moduli of the three phases differ by less than 15% due to comparable atomic bonding. 

As a result of their unequal distribution of bonding strengths, the breaking strengths of distorted 1T′ 

and Td phases are only half that of the 2H phase. Both isotropic 2H and anisotropic 1T′ phase fractures 

satisfy the theorem of minimum energy, creating triangular and linear fracture patterns along the 

orientations parallel to Mo–Mo zigzag chains, respectively. Our findings give a reference database for 

the elastic behaviors of many MoTe2 phases, but they also provide a universal technique for 

mechanical exploration of any isotropic and anisotropic 2D material [115]. 

 

Various applications based on polymorphic MoTe2 transistors are almost reaching exhaustion, such as 

MoTe2 radiofrequency (RF) transistors with excellent air stability and a remarkable cutoff frequency 

(320 MHz with a 5 m gate length), an ultrashort-gate-length 1T0–2H-MoTe2 FET based on a CNT 

gate with a trivial subthreshold swing (73 mV dec1) and a high on/off current ratio (~105) [116]. 

 

Arrays of hetero-phase MoTe2 logic inverter creation by tellurizing patterned distinct precursors, 

which displays outstanding logic-level conservation, good air stability, and eligibility for IC consisting 

of numerous cascaded inverters (Figure 20 c,d) [116]. Hou et al. found a reversible phase transition 

between few-layer 1T0 and 2H-MoTe2 in a FET configuration under the electric-field-induced strain 

created by a ferroelectric substrate [117]. This innovative transistor switching approach avoid the 

concerns of static and dynamic power intake in conventional FETs. Moreover, they obtain substantial 

nonvolatile alterations in channel conductivity between two states at ambient temperature. (Figure 20 

g–i) showing that the sub-nanosecond low-power nonvolatile strain switching technique has a lot of 

promise in applications like logic and memory. 

 

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Chapter 3 

MOLECULAR DYNAMICS SIMULATION. 

 

3.1. INTRODUCTION  

 

Previously, all types of research using theoretical or experimental framework to perform investigation 

upon different materials. Theoretical solutions involve multiple mathematical equations that leads to 

solutions. These results help to justify and understand their behavior. Alternatively, experimental 

research extract results from a system using the measurement of specific parameters by varying 

independent parameters.  

The results produce a functional relationship. However, it is very laborious to solve problems using 

the following methods. In some cases, the experimentation is highly costly and nearly impossible due 

to the lack of adequate resources. In order to come up with faster results, the introduction of high-

speed computers enable researchers to mimic different systems. Simulation systems are models in a 

computer using theoretical and experimental knowledge to perform computer simulations. The results 

from the computer may have a lower accuracy but give an idea of the pattern of data or results.   

 

At the nano-scale, molecular dynamics simulations are applicable [118] —this is a computer 

simulation tool that can investigate atomic movements and physical properties. The calculation is done 

using classical mechanics. Therefore, takes into consideration newton’s laws of motion. 

The three basic requirement for the simulation to run [118]:  

i) Interatomic Potential: information on atomic interaction . 

ii) Integration of equations of motion.    

iii) Initial Conditions: velocities and positions. 

The accuracy of results depends on the potential file. This file contains the potential energy as a 

function of the position of the atoms away from other atoms. Concept development from 

experimentation updates the relationship curves for more accurate simulation results.  

 

 

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LAMMPS (Large-scale Atomic/Molecular Massively Parallel Simulator) is a simulator that runs using 

Molecular dynamics simulation code. It can model nano-scale to macroscopic systems using various 

atomic potentials and boundary conditions. Recently, a considerable amount of research is under 

pogress on the field of 2D materials. In collaboration with Lawrence Livermore National Laborator 

and three other companies, Sadia National laboratories develop the LAMMPS open-source. The first 

version development started using Fortran and later shifted C++.  LAMMPS can be built on a CPU or 

Desktop and run on  parallel computing facilities. In addition, it is applicable to run LAMMPS on 

facilities with a message-passing library (MPI) feature. In LAMMPS, parallelism is applicable to  

scale up computing capabilities using parallelism. Therefore, along with appointing CPUs, Graphical 

processing units (GPUs) can be coupled to speed up the simulation. Furthermore, the open-source 

feature allows further modification and extension of capabilities as per the user’s requirement[4], [10], 

[119].  

 

This chapter will further discuss about different simulations on 2D materials using LAMMPS. 

Initially, different mechanical deformation due to loading. Then, the research objectives of using 

LAMMPS to investigate the fracture mechanics of materials. An overview of the current status quo of 

nanotechnology's experimental and computational progress. Then, a brief description of the 

methodology of how the LAMMPS simulation works. Lastly, a summary of the application of the 

developer package. 

 

                               Figure 21: Time vs size relationship for simulation models.

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3.2. MECHANICAL DEFORMATIONS 

 

Materials inside any electronic device are always undergoing adverse conditions. Certain parameters 

affect the extrinsic properties of the materials. Therefore, engineers need to understand their behavior 

when such material interact with different environments. The behavior helps optimize the usage by 

developing functional relationships that govern their properties. Development of predictive models 

can identify materials' yield points or failure criteria. Generally, 2D materials are exposed to two 

different types of loading conditions that are as follows: 

i) Static Loading [120] : Load on the material is fixed or stationary. 

ii) Dynamic loading [121] : Load on the material varies with time.  

 

The main difference between them is the time of application of the load. Faster loading is considered 

dynamic and vice-versa; slow loading is known as static loading. In the first case, the loading remains 

constant and is applied in a specific orientation without any movement. In the case of dynamic loading, 

there are further sub-categories such as harmonic, periodic, and non-periodic. The behavior of mater 

varies also varies depending on conditions. Researchers observe different phenomena to characterize 

them using phenomena to explain them better.  

The deformation which are notable in literature are wrinkle/crumple [11], buckle [12], tear [13] and 

fracture [122]. Figure 22 shows samples of deformations.  

Figure 22: (a) An AFM image of a hexagonal graphene flake with wrinkle formation.(b) Buckling 

formation on MoS2 (c) AFM topographic image of an internal tear in graphene (d) Failure modes 

observed in molecular dynamics simulations. 

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3.3. RESEARCH OBJECTIVES 

 

Literature talks about the intense investigation done on how such loading conditions affect the 

structure of 2D materials. Graphene, along with other two-dimensional materials, has a variety of 

applications in micro-electromechanical systems (MEMS) and nanoelectromechanical systems 

[62][61]. Investigation of mechanical and fracture properties of 2D materials is essential to predict 

their behavior when incorporated into nano-scale devices. Superlatively, it is a recommendation to 

characterize the material properties via uniaxial tensile stress. However, on a nano-scale, such 

experiments are pretty complex. Alternatively, the most widely common process for 2D materials is 

atomic force microscopy [123] and nano-indentation [124].   

 

The research objective is to learn the usage of MD simulation on different 2D materials. Learning how to gain 

an in-depth understanding of the simulator works and its functionality. Understanding the fundamental 

knowledge in deriving a stress-strain relationship of materials. Our work also covers the different parameters 

that affect the fracture mechanics of the material—finally, the application of LAMMPS in 2D materials to 

observe the fracture behavior in uniaxial stress. Visual results can also explain the mechanics of fracture due to 

tensile stress. Alteration of several parameters like temperature and strain rate produces a behavior change 

[125] Similarly, the material alters by applying vacancy [126] or doping the materials with foreign 

atoms [127]. 

 

Figure 23: The fracture of graphene under tensile load. a) armchair b) zigzag Computational 

Materials Science 188 (2021) 

 

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3.4. STATE-OF-THE-ART 

 

The current simulation research focus on the stress-strain analysis of materials using MD and DFT 

simulations. The objective is to predict fracture mechanics of graphene and other novel 2D materials. 

Figure 24 shows snapshots of the fracture pattern of materials in both armchair and zigzag 

configurations. The images provides insight on mechaics of fracture within the material. There are 

relatively similar works similar to this. For example, M. A. N. Dewapriya et al. [128] investigate the 

effect of temperature on the fracture of graphene. M.C. Wang et al. [129] shows the effect of defects 

on graphene’s fracture mechanics. X Wang et al. [14] use MD simulation to fracture and crack 

propagation in a single monolayer of MoS2. 

Similarly, M.S.R. Elapolu et al. [130] perform a similar investigation on multi-layers of MoS2. 

Furthermore, Luiz et al. [131] investigate the fracture pattern and elastic properties for TMDC with 

MoX2 (X = S, Se, Te) configuration. Finally, Shoaib et al.  [132] simulate the results for the mechanical 

properties of MoTe2 films. 

Figure 24: Representative MD snapshots of the fracture dynamics for the (a) 2H-MoTe2 & 1T-MoTe2 

armchair (b) 2H-MoTe2 & 1T-MoTe2 zigzag monolayers at 300K. Condens. Matter 2020, 5, 73. 

Figure 25:  Calculated stress–strain curves for all TMD membranes studied here when subjected to 

10K and 300K, considering a uniaxial strain applied in both h and v directions. (a,b) 2H/1T-MoTe2 

membranes, respectively. Condens. Matter 2020, 5, 73 

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Figure 26: Stress-strain response of armchair MoTe2 structure at different temperatures. Journal of 

Engineering Materials and Technology 144, 1 (2022) 

 

Figure 27: Nominal strain vs stress of graphene under uniaxial tensile test along the armchair 

direction at various temperatures. Journal of Applied Physics 108, 6 (2010). 

 

 

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3.5. METHODOLOGY 

 

The simulator requires three different elements to initiate the simulation process which are as follows: 

i) Atomic structure file: File that contains the all the information regarding the material. 

These includes atom type, coordinates, shape and size.  

ii) Interatomic potential: Describes the interaction between the pairs of atoms or groups of 

atoms.  

iii) Input Script: File that contains the input script that contains all the constraints, ensembles 

and boundary conditions for the simulation to run.  

 

Atomic structure file: There are three ways to produce the atomic structure file. Create this file 

directly by adding an extra line in the instructions. This process requires the size and mass of the 

material as the input. Create using an atom.sk [6]. Atom.sk is an open-source tool that generates the 

data file for materials ab into calculations. A simple command line, e.g., shown in Figure 28 , 

generates the material. The third method of producing volumetric data files uses VESTA [7]. VESTA 

is unique compared to the other two methods since it aids in visualizing and creating the structure 

simultaneously. VESTA uses ball-stick, wireframe, space-filling, and dot surfaces to represent the 

material model. Additionally, it uses different color codes to distinguish the different types of atoms. 

Figure 29 shows some examples of a lattice made using Atomsk visualized with VESTA.  

 
                                      Figure 28: : Example Command line for atomsk 

                          Figure 29: Workflow of the default operating mode of atoms. 
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Figure 30:Some examples of lattices that can be generated with Atomsk, as visualized with VESTA. . 

The unit cells appear as thick black lines. (a) Simple cubic. (b) Body-centered cubic. (c) Face-centered 

cubic lattice. (d) The L12 structure of Ni3Al. (e) The carbon diamond lattice. (f) The rocksalt lattice 

of NaCl, MgO, or LiF. (g) The cubic perovskite lattice of SrTiO3. TiO6 octahedra are shown in 

transparent blue. (h) The hexagonal close-packed lattice. (i) The carbon graphite lattice. (j) A (10,0) 

carbon nanotube. 

Interatomic Potential: The potential file contains the force field that contains the potential energy as 

function positions or distances. Figure 31 shows an example of the relationship between interatomic 

energy and distance. These potential files are obtained using phenomenological methods to select 

parameterized mathematical formulas. The outcome depends on the interaction of neighboring atoms. 

A simulation may use a combination of two or more interatomic potentials in the case of simulation 

for TMDC (MX2) simulation. For example, one potential models the covalent bonds of X-M-X, and 

the other potential model is for the van der Waals bond between X-M-X layers. In our work, we use 

Stillinger–Weber (SW) potential, which describes the interaction of atoms inside a TMDC and the 

coupling between them. The computationally intensive and complex development of potential files 

enables the simulator to give more accurate results. 

Moreover, generic physics equations are undergone modification using experimental data. Notable 

potential files which are currently in usage are  AIREBO[133], REBO [134] and Tersoff , which 

include bond orders. These are known as pairwise potentials. The potential files applicable in the case 

of charge variables are ReaxFF [135] and COMB [136].  Figure 32 illustrates the computational cost 

of developing potential files over time. The upward trend depicts that researchers have opted for faster 

computing instead of older, cheaper models. 

 

 

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                               Figure 31: Example of interatomic potential curve. 

 

 

Figure 32: Comparison of the computational cost on a per-atom, per-timestep basis of various 

manybody potentials (red) and several machine learning interatomic potentials (blue), as implemented 

in LAMMPS. Computer Physics Communications 271 (2022) 

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Input Script: The LAMMPS input scripts are designed to provide a dynamic amount of flexibility to 

users to implement different forms of material modeling. The feature allows a user to customize a 

model by changing a few lines in the input script or adding novel interatomic potential files, 

diagnostics, and constraints. The three key features of flexibility: 

i) Flexibility via input script options: Customization without programming  

ii) Flexibility via source-code styles: Writing codes to extend capabilities. 

iii) Flexibility via use of LAMMPS as a library 

 

The performance accelerates using advanced hardware such as multi-thread CPUs and GPUs. 

Application of Algorithms such as the rendezvous algorithm [137] to create an intermediate 

decomposition of data, allowing entry and exit processors to identify all the intermediate data. This 

aid in distributing the workload in an extensive computing system. LAMMPS enables the MPI 

parallelism protocol. Therefore, the simulation can run across parallel CPUs connected by a network. 

In molecular dynamics (MD) simulations, different conditions can be under itertative simulation 

process. First, a different set of governing equations is put into use by choosing the right ensemble 

format. These parameters are the number of atoms, volume, temperature, and enthalpy/energy. For 

instance, in the case of the NPT ensemble, all the other parameters remain constant except for volume. 

Other ensembles are NVE, NVT, and NPH. Then comes the boundary conditions, which are typically 

periodic and non-periodic. The periodic boundary condition, for instance, encloses the material in a 

single box that can replicate to an infinite number of translations in all directions. Additional 

information includes thermosetting settings, pressure control, harmonic constraints, bond angle 

constraints, etc.  

MD program runs using time integration algorithms; this integrates the equations related to the motion 

of intermingling atoms and produces their trajectory. Some familiar integrators available are a 

velocity-verlet integrator, rigid body integration, etc.  

The simulation starts after introducing randomization to distort the symmetry in the material. Since 

atoms are symmetrically equivalent the equations cannot perform any calculation. There is no net force 

on the atom until they are in asymmetric condition. Thus, atoms shall remain idle.  Figure 33 shows 

the flowchart of the MD simulation.  

 



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                                                   Figure 33: Flowchart of MD Simulation. 

 

Once the simulation is over, the simulator provides two different output files. It is first the user-defined 

system (log file) that contains the per atom calculations. This data file needs processing to plot graphs 

and other empirical relationships. Another file contains the simulation video of the whole process. The 

video segments depend on the time step chosen for the simulation. The video is played using OVITO 

[15], a 3D visualization software that post-process the atomistic data. Figure 34 shows the interface of 

the OVITO software. The whole simulation can be played back and forth to understand the material's 

behavior as the code runs. In Figure 35 , a graph was plotted using the data files extracted after the 

simulation was complete. Finally, Figure 36 summarizes the whole LAMMPS simulation and gives a 

clear fundamental understanding of the steps in the process. 

 

 

 

 

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                                 Figure 34: Screenshot of the main window of OVITO. 



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Figure 35: (a) Monolayer Graphene sheet representing a 2D material before and during initial 

uniaxial tension applying (b) Initialization of fracture in the sheet (c) The 2D sheet after complete 

fracture. 

 

                                 Figure 36 : Step by step procedure of LAMMPS simulation 

 

 

 

 

 

 

 

  

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3.6. BUILDING LAMMPS USING CMAKE 

 

CMake allows users to compile LAMMPS alternative to the traditional manual customization of files.  

This allows beginners to easily compile software if they want to modify or extend the capabilities of 

LAMMPS. CMake uses a twostep process to produce a functional simulator with new capabilities. 

Initially, generate a new building environment inside a new directory. Then the compilation of all the 

executables and libraries.  

The parametrized SW potential [138] for TMDCs is the most common interatomic potential file for 

conducting simulations on two-dimensional materials. Figure 37 shows that bond angles are not 

considered in the general SW potential; therefore, there is a need for modification for LAMMPS. 

Incorporating two inequivalent angels into the code increases the accuracy of the result. After the 

modification, Jiang et al [139] testes the strain-induced buckling on a composite TMDC 

heterostructure. The modified code uses a bending angle of θ=80.581 for all TMDCs. 

Figure 37: Local environment around atom Mo in the MoS2 hexagonal lattice with the Mo layer 

sandwiched by two S layers. Atoms S1, S2,and S3 are in the top group of the MoS2 layer. Atoms S4, 

S5,and S6 are in the bottom group of the MoS2 layer. Atom S1 is substituted by atom Se. Note that the 

bending of angles like θMoS1S6 is not considered in the SW potential, and a modification is necessary 

for LAMMPS to exclude this term in the three-body SW potential. Acta Mechanica Solida Sinica 32, 

1 (2019). 

 

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The following five steps modifies the LAMMPS using CMAKE [119].  

i) Downloading the CMake Developer Packages for Lammps.  

 

 

 

 

 

 

 

 

 

 

 

 

 

 

ii) Editing the SW file using CodeBlocks. 

 

 
 

 

 

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iii) Adding the additional code into SW file 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

iv) Generating modified SW file using compiler. 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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3.7. SOFTWARE & APPLICATIONS 

 

 

 

 

Download links: 

 

1. https://atomsk.univ-lille.fr/dl.php    

2. https://jp-minerals.org/vesta/en/download.html 

3. https://lammps.sandia.gov/download.html 

4. https://www.ovito.org/windows-downloads/ 

5. https://www.python.org