I certify that this project report entitled “CHARGE-INDUCED ACTUATION OF TWO-DIMENSIONAL (2D) NIOBIUM-BASED TRANSITION-METAL DICHALCOGENIDES: A FIRST-PRINCIPLES STUDY” prepared by ELTON MAH SONG ZHE has met the required standard for submission in partial compliance of the requirements for the award of Bachelor of Science (Hons) Physics at Universiti Tunku Abdul Rahman. The copyright of this report belongs to the author under the provisions of the Copyright Act 1987 as qualified by the Intellectual Property Policy of Universiti Tunku Abdul Rahman. Proper acknowledgment will always be made of the use of any material contained in, or derived from, this report.
Yeoh Keat Hoe for his invaluable advice, guidance and great patience during the research development. Also, I would like to express my gratitude to my dear parents and friends who have helped and encouraged me throughout my university studies.
1 INTRODUCTION
- Introduction to Two-Dimensional (2D) Material
- Introduction to Transition Metal Dichalcogenides
- Problem Statement
- Aim and Objectives
- Scope and Limitation of the Study
- Many-Body System
- The Hohenberg-Kohn (HK) theorems
One of the most prominent types of materials from the 2D family are transition metal dichalcogenides (TMDCs). Since the realization of carbon nanotube (CNT) graphene in 1999 that could act as an electromechanical actuator, the charge-induced actuation of 2D nanomaterials has attracted the attention of the scientific community. The fourth objective is to calculate the band structures and density of states (DOS) of 2D TMDC materials.
However, to increase the accuracy of the results, I would need to increase the k-score values. This theorem describes that any ground state electron density can determine the potential and thus all possible properties of the system, even the wave function of the many-body system.
The overall functional that is corresponding to the solutions of the
- The Kohn-Sham equations
- Band Structure
- Spin-Orbit Coupling
- Density of States (DOS)
- Exchange-Correlation (XC) Functional
- Bloch’s Theorem
- Plane Wave
- Pseudopotential
- Norm-conserving pseudopotential
The Schrodinger equation gives the ground state energy of the system if and only if the input electron density that minimizes the energy (lowest energy) is the true ground state electron density. To paraphrase, the energy content of the Hamiltonian will be at its absolute minimum when the electron charge density is in the ground state. We should be able to tell the exact solution for the underlying energy and electron density if we know the exact functional for it.
Therefore, Walter Kohn and Lu Jeu Sham jointly designed a system of non-interacting particles from a system of interacting particles with the same electron density. Robert Oppenheimer in 1927, the Born-Oppenheimer (BO) approximation assumes that the position of nuclei in a system is fixed or "static", while solving the SE equation for dynamical electrons due to the relatively larger mass of the nucleus compared to the electron. . Thus, the motion of the two degrees of freedom can be decoupled and the nuclear kinetic energy can be neglected by having the nucleus locked in place.
The band structure of the crystal lattice is greatly affected by the spin-orbit (SO) coupling effect as it removes the degeneracy for the bands. 𝐸𝑋𝐶𝐺𝐺𝐴 =∫ 3𝒓𝑛(𝒓)𝜀𝑥𝑐(𝑛(𝒓),∇n(𝐫)) (2.17) where X the system is electrically neutral with a uniform positive background charge. Taking into account the electron density gradient, GGA is sometimes used to approximate the XC energy.
Thus, this wave vector k can be confined to the first Brillouin zone of the reciprocal lattice. Therefore, pseudopotentials are implemented in order to reduce the computational power burden on plane wave-based DFT calculations. The weaker pseudopotential allows nuclear electron pseudo-wavefunctions to be constructed smoothly (Sholl and Stecker, 2009).
3 LITERATURE REVIEW
Electronic Properties
Mechanical Properties
Niobium Diselenide (NbSe 2 )
- Mechanical Properties
The hexagonal 2H-NbSe2 phase is the most common polytype where the hexagonal layers of Se atoms stack on top of each other, known as hexagonal packing, with the sites between layers of Se atoms occupied by Nb in a trigonal-prismatic formation, thus forming a compressed layer structure. The interlayers are bound by van der Waals forces, which are weak forces, so bulk NbSe2 can be mechanically or liquid chemically exfoliated to obtain its 2D TMDCs nanosheets. Throughout this research project, an open source package of codes for electronic structure research calculations and modeling, Quantum Espresso (QE), is implemented for DFT calculations.
Quantum Espresso is actually an acronym for the Quantum Open Source Package for Electronic Structure Research, Simulation and Optimization (Giannozi, 2009). To run this package, it is mandatory to have a Linux-based operating system such as Ubuntu, although there are some software that are capable of running QE on Windows. On the other hand, to determine the electronic structure and crystalline materials at the quantum level, VASP is a better DFT computational package than QE.
However, QE is chosen over VASP here due to the fact that it is free to use and more accessible to students. What Quantum Espresso does on its own is to apply the plane wave (PW) density functional theory (DFT) along with pseudopotentials and periodic boundary conditions. To visualize the atomic structure and geometries generated by QE, we need to use another software package known as XCrySDen (Kokalj, 1999).
XCrySDen is used to display the modeled atomic structure from PWscf input or output files. Moreover, we can also measure the distance between atoms and also change the bond angles. Once the crystal structure has been geometrically relaxed via VC-relax QE, XCrySDen is useful to help us.
Performing Calculations
- Structural Optimization and Electronic Properties Calculation We first perform DFT calculations using Quantum Espresso with the flowchart
- Calculation of Actuator Performance
- Calculation of Mechanical Properties
- Band Structure and Density of States
- Band Structure and Density of States
To calculate the band structure and density of states, the k-point with high symmetry must be determined and reported in the input file. With the addition of the total charge injected into the input file, a total of 9 sets of data is expected from each material. 0.6% to +0.6% strain in the biaxial direction, along the xx direction, and along the yy direction is applied at 0.2% intervals to determine three sets of strain data, where each set consists of seven subsets of cell parameters.
𝐸0 denotes the energy of the material in the neutral state while 𝐶11 is the linear elastic constant along the xx direction, 𝐶22 is the linear elastic constant along the yy direction and 𝜀 refers to the strain. Based on the standard operating unit of Quantum ESPRESSO, the total energy must be in Rydberg unit, so the elastic constant value must be converted to SI unit:. The required values for the stress-strain curve can be obtained from the diagonal element of the Cauchy stress tensor of NbS2 and NbSe2.
Before performing band structure calculations, the optimal cutoff kinetic energy and k-point grid must be determined. The total energy is then plotted against the limiting kinetic energy, showing a curve that converges to a constant value. As you can see, the total energy converges after the 40 Ry point and remains relatively constant from 60Ry to 100Ry.
The total energy is then plotted in relation to the k-point number, showing a curve that converges to a constant value. As you can see, the total energy converges after 4 k-point and remains relative from 6 to 8. Although there is a dip at 5 k-point, the difference is relatively small and insignificant. This was probably due to the discrepancy in computer processes.
For the calculation, the kinetic cut-off energy is set to 80 Ry and the k-point mask is set to 5×5×1. As observed, our data are in excellent agreement with the reviewed values in the literature from the theoretical studies.
Mechanical Performance
Looking at the stress-strain curves, anisotropic behavior of this 2D hexagonal material can be observed under tensile stress. The linear elastic limit of NbS2 is at about 𝜀=0.20 while the elastic limit of NbSe2 is at about 𝜀=0.25. Assuming effective layer thickness of NbS2 and NbSe2, the voltage generated can determine the power of electromechanical actuators,𝜎 = 𝑌𝜀.
This work density per cycle is at least 300 times greater than that of mammalian muscle, which is only about 0.08 MJ/m3. These results suggest that electron doping should be excellent for achieving high-performance electromechanical actuator for NbS2 and NbSe2 in artificial muscle application. The properties of hexagonal H-phase NbS2 and NbSe2 are investigated using this framework via Quantum ESPRESSO.
We evaluated the charge-induced actuation performance of NbS2 and NbSe2 by studying their structural properties and electromechanical properties. The lattice structure constants of NbS2 and NbSe2 agree with the results obtained from literature review. With charge doping per atom ranging from +0.12 e/atom to -0.12 e/atom, linear and isotropic characteristics of the strain of NbS2 and NbSe2 were observed.
The electromechanical actuator performance of NbS2 and NbSe2 is highly dependent on the charge doping level. NbS2 and NbSe2 have the best electromechanical performance when electron doped with work densities per cycle up to 41.4 MJ/m3 and 25 MJ/m3, respectively. These results of this first-principle study show promising information for the design and fabrication of artificial muscles with NbS2 and NbSe2.
Recommendation for Future Works
In summary, we have studied the electromechanical actuator performance of 2D TMDC materials with 1H structures using first-principles DFT calculations. Young's modulus and Poisson's ratio obtained from this work are in excellent agreement with published values. With the same lines of code and files used, the calculated output of scf, bands and DOS can be slightly pushed based on the model of the central processing unit (CPU) of that particular computer.
For example, when the calculation is done with my personal computer with the CPU model Ryzen 5 3600, the fermi energy of NbS2 is -0.9077 eV, while if the calculations are performed on my HP Z230 workstation, the fermi energy - is 0.9076 eV. We may not know whether this minor discrepancy will cause larger errors from the results obtained in future calculations.
Recommended Solutions
