[P1-67] Geometry of curved surface and energetics of in graphene with defects
Two-dimensional (2D) materials have attracted attentions as unique functional materials.
Among them, graphene is well-known as a fundamental structure of 2D materials of nano-carbon.
In 2D materials, lattice defects, such as dislocations and disclinations, cause out-of-plane deformation.
For example, carbon nano-cone or nano-horn is formed geometrically by the wedge disclination of graphene sheet (GS).
In this study, we focus on the fundamental mechanism which can explain how the shape of 2D materials with defects is determined.
Typical four structure models of GS with defects are studied, i.e. positive perfect wedge disclination, negative perfect wedge disclination, positive partial wedge disclination, and negative partial wedge disclination.
The partial wedge disclinations are implemented by the array of edge dislocations in which the local structure consists of pentagon-heptagon atomic bonds.
Then the equilibrium configuration is calculated by using large-scale atomic/molecular massively parallel simulator (LAMMPS).
The obtained surfaces are examined by fitting to analytical test functions.
All results of out-of-plane displacement z are organized by a universal form of z=rf(θ), in a cylindrical coordinate (r, θ, z), in which f(θ) is an appropriate function of θ.
This result means that the all models of GS are represented as conical surfaces in a broad sense.
From a local viewpoint, according to the distribution of atomic site potential energy, it is observed that the energy values at atoms in pentagon ring are relatively high, but the energy values at atoms in heptagon ring are relatively low.
From a global viewpoint, the energy values decrease with increasing distance r from the core of disclination.
After a detail examination, we found the site potential energy is proportional to the square of curvature.
The fundamental knowledge obtained would be applicable to desgin/control the shape of 2D materials.
Among them, graphene is well-known as a fundamental structure of 2D materials of nano-carbon.
In 2D materials, lattice defects, such as dislocations and disclinations, cause out-of-plane deformation.
For example, carbon nano-cone or nano-horn is formed geometrically by the wedge disclination of graphene sheet (GS).
In this study, we focus on the fundamental mechanism which can explain how the shape of 2D materials with defects is determined.
Typical four structure models of GS with defects are studied, i.e. positive perfect wedge disclination, negative perfect wedge disclination, positive partial wedge disclination, and negative partial wedge disclination.
The partial wedge disclinations are implemented by the array of edge dislocations in which the local structure consists of pentagon-heptagon atomic bonds.
Then the equilibrium configuration is calculated by using large-scale atomic/molecular massively parallel simulator (LAMMPS).
The obtained surfaces are examined by fitting to analytical test functions.
All results of out-of-plane displacement z are organized by a universal form of z=rf(θ), in a cylindrical coordinate (r, θ, z), in which f(θ) is an appropriate function of θ.
This result means that the all models of GS are represented as conical surfaces in a broad sense.
From a local viewpoint, according to the distribution of atomic site potential energy, it is observed that the energy values at atoms in pentagon ring are relatively high, but the energy values at atoms in heptagon ring are relatively low.
From a global viewpoint, the energy values decrease with increasing distance r from the core of disclination.
After a detail examination, we found the site potential energy is proportional to the square of curvature.
The fundamental knowledge obtained would be applicable to desgin/control the shape of 2D materials.