M. I. Heggie & C. D. Latham / Stability of the hypothetical superhard carbon metal H-6
The energetics of carbon structures are extremely difficult to simulate, but a potential has been devised which can interpolate between the diamond structure and the graphite structure, correctly giving the energy barrier for conversion of rhombohedral graphite to diamond as calculated by ab initio methods [2]. The proximity cell potential has been described in full elsewhere [3], but here we note that it is a many body interatomic potential that gives the internal energy of an atom in terms of its local environment, as defined by the proximity or Wigner-Seitz cell around the atom. The potential is similar in spirit to the Tersoff potential [4], but does not suffer from some of the vagaries of that potential, because it takes account of the following facts: (a) physical interactions are unlikely to have a bond length dependence that drops sharply to zero between 1.8 and 2.1 Å and (b) the presence of an unhybridised p orbital adds extra anisotropy that can only be emulated by 3 extra degrees of freedom per atom (corresponding to the magnitude and direction of that orbital).
Experiences of modelling with the Tersoff potential indicate that the energy barrier to the concerted exchange of carbon atoms is strongly dependent on the chosen bonding cut-off distance. In addition the formation energies of the novel pi bonded carbon structures [1-5] to be studied here are unphysically low and degenerate with graphite. This is a consequence of ignoring the direction of the unhybridised p orbitals in deciding the strength of pi bonds.
In the proximity cell potential the criteria for the formation of a good sigma bond are that (1) there should be no more than 3 bonds to an atom with one totally unhybridised p orbital and no more then 4 to an atom without such a p orbital (this is essentially a "tight binding" condition and allowance is made for intermediate cases where a fourth bond is allowed, but weakened by withdrawal of p-orbital content in the direction of the bond) and (2) there be space sufficient for a bonding orbital to be substantially orthogonal to other bonding orbitals on the same atom. The criteria for a good pi bond are similarly dependent on geometry and the p orbital degrees of freedom. The bonding can be strong whenever there are unhybridised p orbitals on two neighbouring atoms and there is sufficient space for the pi bond so formed to be substantially orthogonal to other pi bonds in the vicinity.
[Abstract] [Introduction] [Computer Models] [Results] [Acknowledgement] [References] [Figure 1]
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