# Elastic Properties of BCN Alloys, Graphene, and h‑BN Monolayers Containing Point Defects

## TL;DR

This study explores how point defects affect the mechanical properties of 2D materials like graphene and h-BN, showing that defects can either weaken or tune material stiffness.

## Contribution

The paper systematically assesses the impact of substitutional impurities and vacancies on the mechanical properties of 2D materials using first-principles calculations.

## Key findings

- Substitutional carbon atoms in h-BN significantly reduce Young’s modulus, especially when replacing nitrogen atoms.
- Pair substitution of B and N atoms with carbon in h-BN results in stiffness values between those of graphene and pristine h-BN.
- B vacancies in h-BN cause a greater decrease in stiffness than N vacancies due to stronger local strain fields.

## Abstract

Point defects can
strongly affect the mechanical properties of
two-dimensional (2D) materials, causing an overall detrimental effect
on the strength, stiffness, and elasticity. However, the opposite
has also been reported in the literature, which indicates that our
understanding of the role of defects at the atomic level remains incomplete.
This computational study provides a systematic assessment, based on
first-principles calculations, of the mechanical properties of the
archetypal 2D materials (h-BN and graphene monolayers)
containing substitutional impurities and vacancies, which is further
extended to 2D BCN alloys representing the case of high concentration
of substitutional impurities in h-BN and graphene.
In general, the stiffness of these materials, as described by Young’s
modulus, decreases in the presence of point defects. The Young’s
modulus of h-BN decreases rapidly with increasing
concentration of C atoms in the N positions, while the drop is smaller
for C impurities in the B positions. Notably, a defect configuration,
in which carbon atoms replace the neighboring N and B atoms as a pair,
results in the values of the Young’s modulus in the range between
that of pristine graphene and h-BN. In h-BN, B vacancies give rise to a greater decrease in stiffness than
N vacancies, as explained by the analysis of the local defect-mediated
strain fields formed near the point defects. The effects of graphene
weakening through the introduction of substitutional defects and vacancies
are similar to those observed in h-BN. This mechanical
behavior persists in materials with few atomic percent of point defect
concentration and agrees with most experimental results found in the
literature. As the mechanical properties of 2D BCN alloys can be manipulated
by a preferential substitution of B and N atoms with C atoms, our
predictions may guide future efforts in defect-mediated engineering
of the mechanical properties of 2D materials.