We report on the finding of a hard carbon structure in body centered cubic $\left(I{2}_{1}3\right)$ symmetry that possesses an extremely high bulk modulus (386 GPa) and Vickers hardness (60 GPa) comparable to that of $c$-BN and diamond. This carbon phase has a 14-atom primitive cell in an all-${sp}^3$ bonding network comprising five-membered rings, making it a truly full-fledged pentadiamond. Total energy calculations show that it is more stable than the previously reported diamondlike six-membered-ring bonded BC8 and BC12 carbon phases. Electronic band structure calculations show that it is an insulator with an indirect band gap of 5.64 eV. Simulated x-ray diffraction patterns and lattice parameters provide an excellent match to the previously unexplained distinct diffraction peaks found in carbon soot. The present results establish a distinct type of carbon phase and offer insights into its outstanding structural, mechanical, and electronic properties.

• Received 23 July 2020
• Revised 13 September 2020
• Accepted 27 October 2020

DOI:https://doi.org/10.1103/PhysRevB.102.184106