Computational investigation of a superhard all-sp³ hybridized cubic carbon

¹ School of Physics and Optoelectronic Engineering, Shandong University of Technology - Zibo 255000, China
² Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences Beijing 100190, China
³ School of Physical Sciences, University of Chinese Academy of Sciences - Beijing 100049, China

Received: 30 October 2025
Accepted: 19 January 2026

Abstract

Carbon is one of the most fundamental elements in nature hosting comprehensive allotropes, the understanding of carbon is one of the central topics in condensed-matter physics and materials sciences. In this work, we report by ab initio calculations a systematic investigation on an all-sp³ hybridized carbon allotrope. This carbon structure has a body-centered cubic unit cell in symmetry (, space group No. 206) with 64 carbon atoms, which can be discovered through a graph theoretic structural search method originally identified by Shi et al. (Phys. Rev. B, 97 (2018) 014104), and we term it as BC64 carbon in the present work. The dynamical stability of BC64 carbon has been confirmed with phonon band spectrum calculations and its thermal stability up to 1000 K has been confirmed with ab initio molecular-dynamics (AIMD) simulations. It is shown that BC64 is a superhard carbon allotrope with a large Vickers hardness of about 84.5 GPa. The electronic band structures calculations show that BC64 carbon is an insulator with an indirect band gap of about 4.52 eV. Remarkably, the simulated x-ray diffraction pattern of BC64 carbon matches well the experimental data derived from the chimney soot. Previously this experiment is mainly explained by a series of all-sp² hybridized carbon allotropes such as bco-C₁₆ and bct-C₁₆, and only one all-sp³ hybridized sc-C₄₆ is proposed to explain this experiment; however, BC64 shows a better match with this experiment comparing with sc-C₄₆ carbon. Our work has provided systematical understanding of a superhard all-sp³ hybridized carbon allotrope, and also provided a reasonable explanation for previous experimental data, which will also supply guidance for future theoretical and experimental studies in related fields.