Geometry and Self-stress of Single-Wall Carbon Nanotubes and Graphene via a Discrete Model Based on a 2nd-Generation REBO Potential

Formulae for the biaxial moduli along the directions of principal stress for \((\mathit{hkl})\) interfaces of cubic materials are given for situations in which there is equi-biaxial strain within the plane. These formulae are relevant in the consideration of the deposition of thin films on single crystal substrates such as silicon. Within a particular \((\mathit{hkl})\), the directions defining these principal biaxial moduli are shown to be those along which there are the extreme values of the shear modulus and Poisson’s ratio. Conditions for stationary values of the biaxial moduli are also derived, from which the conditions for the global extrema of the biaxial moduli are established.