Structural properties and energetics of amorphous forms of carbon.

Abstract

We have made a comparative theoretical study of the most common forms of unhydrogenated amorphous carbon (\ensuremath{\alpha}-C), namely, of the dense, diamondlike phase and the low-density evaporated \ensuremath{\alpha}-C (e-C). Emphasis is given to the connection among the structure, energetics, and stability of these phases. To make the simulations of the amorphous structures (formed by quenching the liquid) tractable, we used the Monte Carlo method, combined with the empirical-potential approach. Our analysis employs a powerful total-energy-partitioning scheme, which is proved very useful in treating the energetics of disordered systems. It is found that threefold ${\mathit{sp}}^{2}$ sites are the energetically favorable geometries in e-C, and thus they are by far more numerous. The nonplanar character of ${\mathit{sp}}^{2}$ sites and the absence of sixfold rings indicate that medium-range order is rather not significant in e-C. The increasing graphitic character of e-C, as the temperature is raised, is explained by resorting to the effective temperatures ${\mathit{T}}^{\mathrm{*}}$, at which the atoms freeze in their lattice positions. For diamondlike \ensuremath{\alpha}-C, the simulations show that there exist two distinctly different dense structures. The ``as-quenched'' one (i-C) is mostly ${\mathit{sp}}^{3}$ bonded, but it is metastable. Upon annealing, it converts into a second phase (i-${\mathrm{C}}^{\mathrm{*}}$), mostly ${\mathit{sp}}^{2}$ bonded, with a significant energy gain. A specific mechanism is proposed for this transition. The insensitivity of density to annealing is explained if we use the concept of the ``glass transition temperature'' ${\mathit{T}}^{\mathrm{*}}$. Finally, by introducing an isotropic bulk modulus for the amorphous phase, it is found that e-C has a much lower compressibility than i-${\mathrm{C}}^{\mathrm{*}}$, enhancing the distinguishability among the two low-coordinated forms of \ensuremath{\alpha}-C.