An Atomistic-Based Nonlinear Plate Theory for Hexagonal Boron Nitride

Abstract

Through the continuity of the DREIDING force field, we propose, for the first time, the finite-deformation plate theory for the single-layer hexagonal boron nitride (h-BN) to clarify the atomic source of the structure against deformations. Divergent from the classical Föppl-von Karman plate theory, our new theory shows that h-BN’s two in-plane mechanical parameters are independent of two out-of-plane mechanical parameters. The new theory reveals the relationships between the h-BN’s elastic rigidities and the atomic force field: (1) two in-plane elastic rigidities come from the bond stretching and the bond angle bending; (2) the bending rigidity comes from the inversion angle and the dihedral angle torsion; (3) the Gaussian rigidity only comes from the dihedral angle torsion. Mechanical parameters obtained by our theory align with atomic calculations. The new theory proves that two four-body terms in the DREIDING force field are necessary to model the h-BN’s mechanical properties. Overall, our theory establishes a foundation to apply the classical plate theory on the h-BN, and the approach in this paper is heuristic in modelling the mechanical properties of the other two-dimensional nanostructures.

Nonlocal Euler–Bernoulli beam theories with material nonlinearity and their application to single-walled carbon nanotubes

“…This section uses \left( {15,15} \right) SWCNTs to demonstrate the differences between the four theories. So the diameter is d=2.034\;\text{n}\text{m}, and the thickness is taken as h=0.34\;\text{n}\text{m}, the other physical and geometrical parameters are [15,22] [32,54]. The non-local parameter obtained by atomic calculations has also shown some confusion [17,31,55].…”

Water Electric Field Induced Modulation of the Wetting of Hexagonal Boron Nitride: Insights from Multiscale Modeling of Many-Body Polarization

“…The dimensions of the hBN sheet were 30.05 and 30.37 Å in the x - and y -directions, respectively, and a vacuum space of 60 Å in the z -direction was used to eliminate periodic image interactions. The induced dipoles on the boron and nitrogen atoms were modeled using the classical Drude oscillator model with Thole damping, while the vibration of these atoms was modeled using the DREIDING force field. , The expressions for the induced dipole moments on the boron and nitrogen atoms in the classical Drude oscillator model are given by μ i ,B ind = q D,B d i ,B and μ i ,N ind = q D,B d i ,N , respectively, where d is the DC–DP separation distance. The variations of the induced dipole moments, per unit cell of hBN, resulting from the external electric field applied along the y -axis and the z -axis, as a function of the MD simulation time, are shown in Figure a,b, respectively.…”

A Nonlinear Nonlocal Thermoelasticity Euler–Bernoulli Beam Theory and Its Application to Single-Walled Carbon Nanotubes

“…The parameters are shown in Table 1 . Determining the nonlocal parameter of SWCNTs is an open problem because there is an ambiguous understanding of the mechanical properties of a one-atom-thick nanostructure [ 22 , 23 ]. If the vibration frequency in CNTs is in the terahertz range, a conservative estimate is [ 8 ].…”

“…The stress gradient model has been widely used to describe the mechanical properties of CNTs and graphene [ 19 , 20 , 21 ]. As the mechanical properties of a single atomic layer require a more thorough understanding based on quantum mechanics [ 22 , 23 ], determining the scale parameter remains a controversial open question [ 24 ].…”