A hyperboloid structure as a mechanical model of the carbon bond

Abstract

Please cite this article as: I.E. Berinskii, A.M. Krivtsov, A hyperboloid structure as a mechanical model of the carbon bond, AbstractWe present a new mechanical model of interatomic bonds, which can be used to describe the elastic properties of the carbon allotropes, such as graphite, diamond, fullerene, and carbon nanotubes. The interatomic bond is modeled by a hyperboloid-shape truss structure. The elastic characteristics of this bond are determined. Previous known structural models also used elastic elements (beams, trusses) to simulate a carbon bond. However unlike them our model satisfies to the correct ratio of the longitudinal and lateral stiffness, observed from the previous experimental and theoretical results. Parameters of the bond in application for graphene and diamond were determined.

Enhanced vector-based model for elastic bonds in solids

“…At nano scale level, covalent bonds (e.g. in graphene [4][5][6]22] and molybdenum disulfide [23]) can be simulated. At micro scale level, the EVM can be incorporated into coarse-grained models of macromolecules [13,14], nanotubes [15,16], aerogels, ceramics [11] etc.…”

“…For example, in materials composed of glued particles, bonds are usually short [8][9][10][11][12] and the stiffnesses are comparable. Similarly, for covalent bonds in graphene cA/cD ~2 [22]. Therefore in the present section an alternative model [21] is used for calibration of parameters Bk.…”

Thermal echo in a finite one-dimensional harmonic crystal

“…If the residual oscillations are taken into account the maximum temperature achieved by the first thermal echo is approximately 56.2 • C. The above characteristics depend only on the number of particles N , while the period τ 0 of the thermal echo realization depends on the physical properties of the crystal and the type of oscillations (longitudinal or tranversal). Let us consider longitudinal oscillations, the mass of the carbon atom m = 1.99 · 10 −26 kg and the stiffness of diamond bond C = 1824 N/m [47]. Then formula (21) gives τ 0 = 1.65 · 10 −12 s that is a N 4π ≈ 80 times greater than the atomic oscillation period.…”

Heat transfer in a one-dimensional harmonic crystal in a viscous environment subjected to an external heat supply

“…Simple lattice models can be used for the analytical investigation of the thermomechanical processes in solids at the microscale 38,[43][44][45][46] , and, in particular, in the carbon nanostructures 47,48 . One-dimensional systems due to their simplicity can be used to obtain analytical solu-tions in a closed form without loss of generality 5,39,44,49 , or to get the asymptotic description of non-stationary processes in media with complex structure [49][50][51][52][53][54] .…”