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

Overview

Nanoscale entities

2D materials

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.

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)).

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

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

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.

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

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

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

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.

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

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.

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

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.