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Theoretical studies of the mechanical and electronic properties of graphitic heptazine and s-triazine sheets
Yusuf Zuntu Abdullahi
Venue: Theory Lab, USMDate: 26th Sept, 2017
Time: 11:00 am
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Overview
Nanoscale entities
2D materials
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Cont..
o Atoms bind weakly between the compacted hexagonal 2D sheets e.g graphene and BN sheets.
o Moreover, having a regular defects on BN or graphene might lead to ambiguous results experimentally at low coverage.
➢ To overcome these difficulties, the need for 2D sheets with inherently periodically arranged cavity is essential.
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Cont..
o Road yet to be explored is the mechanical properties and strain-induced responses on the electronic properties of heptazine and s-triazinesheets.
o When examining the literature for an effective method of tuning material properties, external environment (strain/electric field) is the leading approach in the band gap manipulation of various 2D monolayer nanosheets (e.g., boron nitride, graphene, silicene and molybdenum disulfide (MoS2)).
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Computational methodDensity Functional Theory (DFT) based on quantum mechanical approach, Most popular and widely adopted technique to investigate the ground state properties of many-body systems
Walter Kohn received the Nobel prize in 1998 for the development of DFT
Quantum ESPRESSO package
iiixcc rrV
)()(
2
1 2
periodic
non-spin polarized
Basis Set
Plane wave basis set
General gradient approximation (GGA)(PBE)
Ultrasoft pseudopotential method
non relativistic
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Computational procedureCandidates
configurations
Convergence test
Set up the parameters GGA
Plane wave basis set
Spin restricted
Ground state is obtained with minimized energy and approximately
zero forces on each atom
Perform perturbation calculations and
optimization
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Charge density plot
Preliminary calculations
➢ To ensure that calculations are done within the bench of accuracy, computational parameters and preliminaries calculations are verified.
Heptazine sheet
s-triazine sheet
Phys. Chem. Chem.
Phys., 15 (2013)
7142
Surf. Sci., 606
(2012) 892.
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Heptazine sheetE-strain curves
s-triazine sheetE-strain curvesPHYSICAL REVIEW B 82, 235414 2010
uni-axial uni-axial
bi-axial bi-axial
bulk modulus bulk modulus
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Uni-axial Bi-axial
Harmonic constant, 𝑘 (Ry) 43.42 95.68
Proportionality limit, 𝑠c1 0.0194 0.0194
Yielding strain, 𝑠c2 0.0581 0.0790
𝜈, Poisson’s ratio 0.1017
𝐸, in-plane stiffness 2124.6 GPa ⋅ Å
𝐺, Bulk modulus 1141.1 GPa ⋅ Å
Uni-axial Bi-axial
Harmonic constant, 𝑘 (N/m) 134.41 290.10
Proportionality limit, 𝑠m1 0.086 0.065
Yielding strain, 𝑠m2 0.107 0.112
𝜈, Poisson’s ratio 0.08
𝐸, in-plane stiffness 1335.5 GPa ⋅ Å
𝐺, Bulk modulus 828 GPa ⋅ Å
The calculated in-plane stiffness and bulk modulus are 212.46 N/m, 133.55 N/m and 114 N/m, 82.8 N/m for heptazine and s-triazinerespectively.
The poison ratios 0.1, 0.08 are comparable to each other and are of the same order with related 2D material like graphene.
Both heptazine and s-triazine sheets are mechanically stable. s-triazine sheetHeptazine sheet
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Numerically computed mechanical strain on the structural stabilities. We applied both uni-and bi-axial tensile strains on the sheets by gradually increasing the lattice constant up to 40% of their equilibrium values. Linear elastic, elastic and plastic regions marked by points.
Heptazine sheet
s-triazine sheet
DFT data
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C1
C2
C1
C2
Heptazine sheet
s-triazine sheet
While we find some differences in values of the calculated critical strains and the mechanical
properties of s-triazine and heptazine sheet, de Sousa et al. recent work reported some numerical
results which are not much different from this present work RSC Adv., 6 (2016) pp. 76915-76921.
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Formation energy
The formation energy is defined as, 𝐸 = 𝐸𝑎 − 𝐸𝑏 where 𝐸𝑎 and 𝐸𝑏 denote relaxed and unrelaxed energy of CN sheet.
The formation energies as functions of external strain are computed and depicted in Figures above.
The structure with biaxial strain has a smaller formation energy than that of uniaxial strain, showing that the structures under biaxial strain are more stable
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Heptazine sheet, band structure TDOS, and PDOS
s-triazine sheet, band structure, TDOS and PDOS
• Symmetric deformation modulates the electronic properties of heptazine and striazine sheets.
• PDOS shows delocalized of pz orbital. pz at high energy due to repulsive effect with the extra N-(px, py) electrons.
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Heptazine and striazine under perpendicular electric field
striazine @ 10 V/nm heptazine @ 10 V/nm
The geometric and electronic properties of heptazine and striazine sheets remain unchanged under perpendicular electric field with no obvious wrinkles in the final structure
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Summary
• The in-plane stiffness and bulk modulus for s-triazinesheet are found to be less than that of heptazine.
• The reduction can be related to the nature of the covalent bonds connecting the adjacent sheets and the number of atoms per unit cell.
• It is also demonstrated that both heptazine s-triazinesheets can withstand larger tension in the plastic region. These results established a stable mechanical property for both heptazine and s-triazine sheets.
• We found a linear relationship of bandgap as a function of bi-axial tensile strain within the harmonic elastic region.