# Theoretical studies on mechanical and electronic properties of $s$-triazine sheet

## TL;DR

This study uses first-principles calculations to explore the mechanical and electronic properties of $s$-triazine sheets, revealing their stability, strain responses, and electronic behavior under strain and electric fields.

## Contribution

It provides the first detailed theoretical analysis of $s$-triazine's mechanical and electronic properties, including strain effects and stability, using density functional theory.

## Key findings

- $s$-triazine has lower in-plane stiffness and bulk modulus than heptazine.
- The bandgap of $s$-triazine increases linearly with biaxial tensile strain.
- $s$-triazine's electronic properties are unaffected by electric fields up to 10 V/nm.

## Abstract

Mechanical and electronic properties of $s$-triazine are studied using first-principles calculations based on density functional theory. The in-plane stiffness and bulk modulus for $s$-triazine sheet 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. The Poisson's ratio of $s$-triazine is half the value to that of graphene. Additionally, the calculated values of the two critical strains (elastic and yielding points) of $s$-triazine sheet are in the same order of magnitude to that for heptazine which was calculated using MD simulations in the literature. It is also demonstrated that $s$-triazine sheet can withstand larger tension in the plastic region. These results established a stable mechanical property for $s$-triazine sheet. We found a linear relationship of bandgap as a function of bi-axial tensile strain within the harmonic elastic region. The reduced steric repulse of the lone pairs ($\mathrm{p}_x$-, $\mathrm {p}_y$-) causes the $\mathrm {p}_z$-like orbital to shift to high energy, and consequently an increase in the bandgap. We find no electronic properties modulation of the $s$-triazine sheet under electric field up to a peak value of 10 V/nm. Such noble properties may be useful in future nanomaterial applications.