Monatomic structures of B, C, N, and O: first-principle study of relative stabilities and bulk moduli

Abstract

Abstract Relative stabilities and bulk moduli of monatomic structures with coordination numbers 4 (cubic diamond or cd), 6 (simple cubic or sc), 8 (body-centered cubic or bcc), and 12 (face-centered cubic or fcc) for elements B, C, N, and O were calculated based on the first-principles. The structure for each element may be stabilized by the geometrical matching between the coordinated positions and the orbital shape. Thus, all elements favor loosely packed cd structure at low pressures, and they prefer moderately packed sc structure at high pressures. However, denser phases with bcc and fcc structures may become more stable at much higher pressures. B has only three valence electrons that are insufficient to fill up all sp 3 orbitals in a cd structure. Moreover, these three p-electrons can only fill half of the three mutually perpendicular bonds in sc structure. As a result of reduced stabilities of cd and sc structures, relative stabilities of the four structures for B are less distinctive. C has four valence electrons that match perfectly with four tetrahedral coordinated atoms. Hence, its cd structure is greatly stabilized by the extensive overlap of bonded electrons. As a result of this expanded region of stability, the equilibrium pressure between cd and sc structures is pushed up substantially. Both N and O have sufficient p-electrons to align with octahedrally coordinated atoms. Hence, their sc structures are greatly stabilized and the equilibrium pressures between cd and sc structures for N and O are much reduced relative to that for B and C. The electron density maps of cd coordination for N and O suggest that these monatomic structures may be isotropic superconductors. Bulk modulus of a symmetric structure may be determined by the average concentration of electrons in overlapped orbitals. C has the smallest atomic volume of the four elements studied, so it is uniquely capable to form the cd structure with the highest bulk modulus (447 GPa) of all structures. Although C’s p-orbitals are not fully occupied for effective bonding in octahedral coordination, its small atoms still make the bulk modulus of the sc structure the second highest (337 GPa) among various phases of the four elements studied. Except for diamond, the structures discussed above are all hypothetical. However, they may be synthesized by the bombardment of collimated beams of atoms focussed to a common center. Moreover, the structures so formed, even though they may be metastable, can be studied by the laser spectroscope fired in femtosecond (10 −15 s) bursts. Such femtochemistry has been developed by Dr. Ahmed Zewail, the latest Nobel laureate.