Designing sp3 networks of two novel carbon allotropes in the P4/mmm phase

Abstract

Two novel carbon allotropes in the P4/mmm phase with sp3 hybridization, denoted as P4/mmm C40 and P4/mmm C60, are predicted using the density functional theory. Both the carbon allotropes are dynamically, mechanically, and thermodynamically stable. The shear modulus G, Young's modulus E, and bulk modulus B of both P4/mmm C40 and P4/mmm C60 are larger than those of any other carbon allotropes in the P4/mmm phase in the present, with the G, E, and B of P4/mmm C40 being all larger than those of P4/mmm C60. Three empirical hardness models (the Lyakhov–Oganov model, Chen's model, and the Mazhnik–Oganov model) show that only P4/mmm C40 is a superhard material. Both P4/mmm C40 and P4/mmm C60 are indirect, wide band gap semiconductor materials. By studying the mechanical anisotropies of the elastic moduli (such as E and Poisson's ratio v, G, and B) along with some mechanical anisotropy factors (such as the universal elastic anisotropy index AU, the linear bulk modulus, the percentage of mechanical anisotropy for G and B, and shear anisotropic factors) and sound wave velocity, it is proved that P4/mmm C40 and P4/mmm C60 are mechanically anisotropic materials.